CWB Xii Physics 2021-22 2

Cycle Topic:: Current Electricity
Physics Electric current, flow of electric charges in a

metallic conductor, drift velocity, mobility and
Class-XII their relation with electric current; Qhm’s law,
electrical resistance, V-1 characteristics, (lin-
Code 12P (01) ear and non-linear), electrical energy and
power, electrical resistivity and conductivity.
Topic:: Electrostatics
Carbon resistors, colour code for carbon re-
Contents sistors; series and parallel combinations of re-
Electric Charges; Conservation of charge, sistors; temperature dependence of resistance.
Coulomb’s law-force between two point Suggested Reading
charges, forces between multiple charges;
1. Concept of Physics: H C Verma
superposition principle and continuous charge
distribution. 2. Physics - Resnick & Halliday.
Electric field, electric field due to a point Code 12P (04)
charge, electric field lines; electric dipole, Topic::Current Electricity
electric field due to a dipole; torque on a di- Internal resistance of a cell, potential difference
pole in uniform electric field. and EMF of a cell, combination, of cells in se-
Electric flux, statement of Gauss’s theorem ries and in parallel.
and its applications to find field due to infi- Kirchhoff’s laws and simple applications.
nitely long straight wire, uniformly charged Wheatstone bridge, metre bridge. Potentiom-
infinite plane sheet and uniformly charged thin eter- principle and its applications to measure
spherical shell (field inside and outside). potential difference and for comparing emf of
Suggested Reading two cells; measurement of internal resistance
1. Concept of Physics: H C Verma of a cell.
2. Physics - Resnick & Halliday. Suggested Reading
Code 12P (02) 1. Concept of Physics: H C Verma
Topic :: Electrostatics (Cont.) 2. Physics - Resnick & Halliday.
Electric potential, potential difference, Code 12P (05)
electric potential due to a point charge, a Topic:: Magnetic Effects of Current and
dipole and system of charges; equipotential Magnetism
surfaces, electrical potential energy of a sys- Contents
tem of two point charges and of electric di-
Concept of magnetic field, Oersted’s experi-
pole in an electrostatic field.
ment.
Conductors and insulators, free charges and
Biot-Savart law and its application to current
bound charges inside a conductor. Dielec-
carrying circular loop.
trics and electric polarisation, capacitors and
capacitance, combination of capacitors in Ampere’s law and its applications to infinitely
series, and in parallel, capacitance of a par- long straight wire, straight and toroidal sole-
allel plate capacitor with and without dielec- noids. Force on a moving charge in uniform
tric medium between the plates, energy stored magnetic and electric fields. Cyclotron.
in a capacitor. Suggested Reading
Suggested Reading 1. Concept of Physics: H C Verma
1. Concept of Physics: H C Verma 2. Physics - Resnick & Halliday.
2. Physics - Resnick & Halliday. Codel2P(06)
Code 12P (03) Topic:: Magnetic Effects of Current and Magne
Assignment-physics-XII-2021 3
Contents 1. Concept of Physics - H.C. Verma
Force on a current-carrying conductor in a 2. Physics - Resnick & Halliday
uniform magnetic field. Force between two Code 12P (09)
parallel current carrying conductors-defini-
Topic:: Wave Optics
tion of ampere. Torque experienced by a
current loop in uniform magnetic field; mov- Contents:
ing coil galvanometer-its current sensitivity Wave optics: wave front and Huygens’ prin-
and conversion to ammeter and voltmeter. ciple, reflection and refraction of plane wave
Current loop as a magnetic dipole and its at a plane surface using wave fronts. Proof of
magnetic dipole moment. Magnetic dipole laws of reflection and refraction using Huygens’
moment of a revolving electron. Magnetic principle, Interference, Young’s double slit ex-
field intensity due to a magnetic dipole (bar periment and expression for fringe width, co-
magnet) along its axis and perpendicular to herent sources and sustained
its axis. Torque on a magnetic dipole (bar interference of light. Diffraction due to a single
magnet) in uniform magnetic field; bar mag- slit, width of central maximum. Resolving
net as an equivalent solenoid, magnetic field power of microscopes and astronomical tele
lines; Earth’s magnetic field and magnetic Scopes. Polarisation, plane polarised light;
elements. Para-, dia- and ferro -magnetic Brewster’s law, uses of plane polarised light
substances, with examples. Electromagnets and Polaroids.
and factors affecting their strengths. Per- Suggested Reading
manent magnets . 1. Concepts of Physics - H.C. Verma
Suggested Reading 2. Physics - Resnick & Halliday.
1. Concept of Physics: H C Verma Code 12P (10)
2. Physics - Resnick & Halliday. Topic :: Optics
Code 12P (07) Contents
Topic:: Electromagnetic Induction and Alter- Reflection of light, spherical mirrors, mirror for-
nating Currents mula. Refraction of light, total internal reflec-
Contents tion and its applications, optical fibres.
Electromagnetic induction; Faraday’s law, Code 12P (11)
induced emf and current; Lenz’s Law, Eddy Topic:: Optics
currents. Self and mutual inductance.
Contents
Refraction at spherical surfaces, lenses, thin lens
Suggested Reading formula, lens-maker’s formula. Magnification,
1. Concept of Physics: H C Verma power of a lens, combination of thin, lenses in
2. Physics - Resnick & Halliday. contact. Refraction and dispersion of light
through a prism.
Code 12P (08)
Scattering of light - blue colour of the sky and
Topic:: Electromagnetic Induction and Alter-
reddish appearance of the sun at sunrise and
nating
sunset.
Alternating currents, peak and rms value of
Optical instruments: Simple and compound
alternating current / voltage; reactance and
Microscopes and astronomical telescopes (re-
impedance; LC oscillations (qualitative
flecting and refracting) and their magnifying
treatment only), LCR series circuit, reso-
powers and resolving powers
nance; power in AC circuits, wattless cur-
rent. Suggested Reading
AC generator and transformer. 1. Optics - Ghatak
Suggested Reading 2. Concepts of Physics
Code 12P (12)
Topic:: Electronic Devices LAB MANUAL
Contents
Semiconductors; semiconductor diode - I-
V characteristics in forward and reverse bias,
diode as rectifier; I-V characteristics of LED.
photodiode, solar cell, and Zener diode;
Zenei diode as a voltage regulator.
Suggested Reading
1. NCERT (XII) - Part II
Code 12P (13)
Electromagnetic waves
Electromagnetic waves and their character-
istics (qualitative ideas only). Transverse na-
ture of electromagnetic waves. Electromag-
netic spectrum (radio waves, microwaves,
infrared, visible, ultraviolet, Xrays, gamma
rays) including elementary facts about their
uses.
Dual Nature of Matter and Radiation

Dual nature of radiation. Photoelectric effect,
Hertz and Lenard’s observations; Einstein’s
photoelectric equation-particle nature of light.
Matter waves-wave nature of particles, de
Broglie relation. Davisson-Germer experi-
ment.
Suggested Reading
Code 12P (14)
Topic:: Atoms and Nuclei
Contents
Alpha-particle scattering experiment;
Rutherford’s model of atom; Bohr model,
energy levels, hydrogen spectrum.
Composition and size of nucleus, atomic
masses, isotopes, isobars; isotones. Radio-
activity-alpha, beta and gamma particles/rays
and their properties; radioactive decay law.
Mass-energy relation, mass defect; binding
energy per nucleon and its variation with mass
number; nuclear-fission and fusion.
Suggested Reading
Practicals
A. Every student will perform 15 experiments 5 activities and a project during the academic year.
B. Evaluation Scheme for Practical Examination:

* Two experiment one from each section 8 Marks
* Practical record (experiments & activities) 6 Marks
* Project 3 Marks
* Viva on experiments & activities and projects. 5 Marks
Total 30 Marks
Unit - Electrostatics
Code : 12P (01 & 02)
1. Four charges +q, +q, -q and -q are placed respectively at the four corners A,B,C and D of a
square of side a. Calculate the force on a charge Q placed at the centre of the square.
1 4 2Qq
(Ans. , parallel to AD or BC )
4πε a2
2. Two opposite corners of a square carry charge Q each and the other two opposite corners of the
square carry q charge each.If the resultant force on Q is zero, how are Q and q related?
(Ans. Q = −2 2 q )
3. The electric field in a region can be expressed as
∧
v 3∧ 4
E = i+ j × 2 ×103 NC-1
5 5
Determine the flux of this field through a rectangular surface of area 0.2 m2 situated parallel to the
Y-Z plane.
(Ans. 240 Nm2 C-1)
Ex
E= 1̂.
4. The electric field in a region is given by b Find the charge contained in the cubical volume
bounded by the surfaces x = 0, × = a,y = 0, y = a, z = 0 and z = a. Take E0 = 5 × 103 NC-1,
a = 1 cm and b = 2 cm.
(Ans. 2.2 × 10-12 C)
5. Fig. shows some equipotential surfaces. What can you say about the magnitude and the direction
of the electric field?
6
(Ans . E = Vm, radially outward)
r2
6. An infinite plane sheet of charge density 10-8 Cm-2 is held in air. In this situation how far apart are
two equipotential surfaces, whose p.d. is 5 V?
(Ans. 8.85 mm)
7. A point charge q moves from a point P to a point S along the path PQRS in a uniform electric field
E acting along the positive direction of X-axis. The coordinates of the points P, Q, R and S are
(a,- b,0), (2a, 0, 0) (a,- b,0),(0, 0, 0)respectively, Find the work done by the field in the process.
(Ans. – q Ea)
8. In Fig. , C1 = 1 µ F, C2 = 2 µ F and C3 = 3 µ F. Find the equivalent capacitance between points
A and B.
(Ans. 6 µ F)
9. A small metal sphere carrying charge +Q is located at the centre of a spherical cavity in a large
uncharged metal sphere. Use Gauss’s theorem to find electric fields at points P1 and P2.
kQ
(Ans. 2
, zero )
r1
10. Three charges − 2 µC ,2 2 µC and − 2 µC are arranged along a straight line as shown in the
figure. Calculate the total electric field intensity due to all these three charges at the point P.
(Ans.11.7 2 × 103 N/C)
11. An electric dipole with moment p is placed un a uniform electric field of intensity E . Write the
expression for the torque τ experienced by the dipole. Identify two pairs of perpendicular vectors
in the expression.
Show diagrammatically, the orientation of the dipole in the field for which the torque is: (i) maxi-
mum, (ii) half the maximum value, (iii) zero.
(Ans. τ and E, τ and p)
12. Obtain an expression for the energy stored in a parallel plate capacitor. In the given figure, the
energy stored in C4 is 27J. Calculate the total energy stored in the system.
(Ans. 594 J)
13. Find the total energy stored in the capacitors in the given network:
(Ans. 54 µ J)
14. Calculatethe equivalent capacitance between the points A and B in the following combination.
(Ans. 15 µ F)
15. A point charge of +2 µ C is kept fixed at the origin. Another point charge of +4 µ C is brought
from a far off point to a point distant 50 cm frim the origin. Calculate the electrostatic potential
energy of this two charge system.
Another charge of +1 µ C is brought to a point distant 100 cm from each of these two charges
( assumed to be kept fixed). What is work done?
(0.054J)
16. The following figure shows the network of very large number of capacitors each of capacity 2
µ F. Calculate the equivalent capacity between the points A and B.
(0.732 µ F)
17. What is the function of dielectric in a capacitor? Calculate the equivalent capacitance of the
combination between the points P and Q as shown in figure.
4
( Ans. µF )
3
18. Two point electric charges of values q and 2q are kept in a distance d apart each other in air. A
third charge Q is to be kept along the same line in such a way that the net force acting on q and 2q
is zero. Calculate the position of charge Q in terms of q and d.
 d 2d 
Ans. , 
 1+ 2 1+ 2 
19 In the figure shown calculate the total flux of the elector static field through the spheres S1 and S2
The wire AB,shown here,has a linear charge density,given by given by =kx where x is the
distance measured along the wire from the end A
L
A B
Q
S1 S2
(Q/ε0 , Q + KL /2 )
2
ε0
20. A proton placed in a uniform electric field of magnitude 2000 N/C moves between two points in
the direction of electric field. If the distance between the points is 0.2 m, find the value of (i) p.d.
between the points, (ii) work done.
(Ans. (i)-400 V, (ii) 6.4 × 10-17 J)
21. Two point charges 5 × 10-8 C and -2 × 10-8 C are separated by a distance of 20 cm in air as
shown in the figure.
(i) Find at what distance from point A would the electric potential be zero.
(ii) Also calculate the electrostatic potential energy of the system.
(Ans.14cm, 45 µ J)
22. Calculate the effective capacitance between the points X and Y of the arrangement shown in the
figure. The value of capacity of each capacitor is 4 µ F.
(Ans. 4 µ F)
23. The given graph shows the variation of charges q versus potential difference V for two capaci-
tors C1 and C2. The two capacitors have some plate separation but the plate area of C2 is
double than that of C1. Which of the lines in the graph correspond to C1 and C2 and why?
b)
24. For the network shown in Fig. b). compute
(i) the equivalent capacitance between points a and b.
(ii) the charge on each of the capacitors nearest to a and b when Vab = 900 V.
(iii) Vcd , when Vab = 900 V.
(Ans. (i) 1 µ F (ii) 900 uC (iii) 100 V)
25. Find the total energy stored in the capacitors in the following network shown on the next page.
(Ans. 3.6 × 10-5 J)
26. A 10 µ F capacitor is charged by a 30 V d.c. supply and then connected across an uncharged 50
µ F capacitor. Calculate (i) the final potential difference across the combinaton, and (ii) the initial
and final energies. How will you account for the difference in energy?
(Ans. (i) 5V, (ii) Ui = 4.5 × 10-3 J, Uf = 0.75 × 10-3J)
27. X and Y are two parallel plate capacitors having the same area of the plates and same separation
between the plates. X has air between the plates and Y contains a dielectric medium of K = 5 They
are connected in series.
(i) calculate the ratio of potential difference between the plates of X and Y.
(ii) What is the ratio electrostatic energy stored in X and Y?
(Ans. 5:1, 5:1)
28. An electric field E = 3 × 104 Vm-1 is established between the plates, 0.05m apart, of a parallel
plate capacitor. After removing the charging battery, an uncharged metal plate of thickness
t = 0.01m is inserted between the capacitor plates. Find the p.d. across the capacitor (i) before,
(ii) after the introduction of the plate. (iii) What would be the p.d. if a dielectric slab (k=2) were
introduced in place of metal plate?
(Ans. 1500xV, 1200V, 1350V)
29. (i) Two circular metal plates, each of radius 10cm, are kept parallel to each other at a distance
of 1 mm. what kind of capacitor do they make? Mention one application of this capacitor.
(ii) If the radius of each of the plates is increased by a factor of 2 and their distance of
separation decreased to half of its initial value, calculate the ratio of the capacitance in the
two cases.
(iii) Suggest any one possible method by which the capacitance in the second case be increased
by n times.
30. The charges q1 = 3 µ F, q2 = 4 µ F and q3 = -7 µ F are placed on the circumference of a
circle of radius 1.0 m, as shown in Fig. What is the value of charge q4 placed on the same circle
if the potential at centre, VC = 0? (Ans. q4 = 0)
31. Two point charges q1 = + 0.2 C and q2 = +0.4 C are placed 0.1 m apart. Calculate the electric
field at.
(i) the mid-point between the charges.
(ii) a point on the line joining q1 and q2 such that it is 0.05 m away from q2 and 0.15 m away from
q1.
(Ans. 7.2 × 1011 N/c, 1.52 × 1012 N/c)
32. S1 and S2 are two hollow concentric spheres enclosing charges Q and 2 Q respectively as shown
in the Fig.
(i) What is the ratio of the electric flux throgh S1 and S2 ?
(ii) How will the electric flux through the sphere S1 change, if a medium of dielectric constant 5
is introduced in the space inside S1 in place of air?
Q
(Ans.1 : 3 )
5 ∈o
33. In the arrangement of capacitors shown here, the energy stored in the 6 µF capacitor is E. Find the
following:
(a) Energy stored in the 12 µF capacitor.
(b) Energy stored in the 3 µF capacitor.
(c) Total energy drawn from the battery.
(Ans. 2E, 18E, 21E)
34. An electric dipole of length 2 cm is placed with its axis making an angle of 60o to a uniform electric
field of 105 N/C. If it experiences a torque of 8 3 Nm, calculate the :
(i) magnitude of the charge on the dipole, and

(ii) potential energy of the dipole.
(Ans. (i) 8 × 10-3 C (ii) -8 J)
35. A uniform electric field E exists between two charged plates as shown in the figure. What would be
the work done in moving a change ‘q’ along the closed rectangular path ABCDA?
(Ans 0)
36. ABC is a right-angled triangle, where AB and BC are 25 cm and 60 cm respectively ; a metal
sphere of 2 cm radius charged to a potential of 9 × 105 V is placed at B. Find the amount of work
done in carrying a positive charge of 1 C from C to A.
(Ans. 0.045 J)
37. In Fig. , the potentials at points A and B are VA and VB respectively. Calculate VA-VB for the given
arrangement.
 1 2qy 
Ans.VA − VB = , 
 4π ε o x( x + y ) 
38. Two plane sheets of charge densities + and - are kept in air as shown in Fig. What are the electric
field intensities at points A and B?
.A
+σ
.B
-σ
39. Fig. shows a parallel plate capacitor of plate area A and plate separation d. Its entire space is filled
with three different dielectric slabs of same thickness. Find the equivalent capacitance of the ar-
rangement.
 3ε o A K1 K 2 K 3 
Ans. C = 
 d ( K1 K 2 + K 2 K 3 + K 3 K1 ) 
40. The space between the plates of a parallel plate capacitor of capacitance c is filled with three
dielectric slabs of equal thickness, as shown in Fig. If the dielectric constants of the three slabs are
K1 K 2 and K 3 , find the new capacitance.
 C 
Ans. C′ = 3 ( K1 + K 2 + K 3) 
 
41. Two identical plane metallic surfaces A and B are kept parallel to each other in air, separated by a
distance of 1cm, as shown in Fig.
A is given a positive potential of 10 V, and the other surface of B is earthed.

(i) What is the magnitude and direction of the uniform electric field between Y and Z?
(ii) What is the work done in moving a charge of 20 µ C from X to Y.
V
(Ans.10 3 , zero)
m
42. The electric potential as a function of distance x is shown in Fig.. Construct a graph of the electric
field strength E.
43. Two small balls, having equal positive charge q coulomb are suspended by two insulating strings of
equal length from a hook fixed to a stand. The whole set up is taken in a satellite into space where
there is no gravity. What is the angle between the two strings and the tension in each string?
(Ans 1800)
44. An electric dipole of dipole moment 20 × 10-6 Cm is enclosed by a closed surface. What is the
net flux coming out of the surface?
45. How does the coulomb force between two point charges depend upon the dielectric constant of
the medium?
46. Two fixed point charges +4e and +e units are separated by a distance a. Where should a third
charge be placed for it to be in equilibrium?
(Ans 2a/3 from 4e)
47. Three charges, each equal to q are placed at the three corners of a square of side a. Find the
electric field at the fourth corner.
 q 
Ans. (2 2 + 1) 
 8πε o a 2 
48. Fig shows four point charges at the corners of a square of side 2 cm. Find the magnitude and
direction of the electric field at the centre O of the square, if Q = 0.02 µ C.
(Ans.9 2 × 105 NC -1 , parallel to BA)
49 Eight identical point charges of q coulomb each are placed at the corners of a cube of each side
0.1 m. Calculate the electric field at the centre o of the cube. Calculate the field at the centre when
one of the corner charges is removed.
(Ans. zero, 1.2 × 1012 q NC-1, towards the corner having no charge)
50. Find the equivalent capacitance between the points P and Q as shown in Fig. . Given C = 18 µ F
and C1 = 12 µ F.
(Ans. 11 µ F)
51. The insulated plates of a parallel plate capacitor has a charge density σ. Show that the work done
in changing the distance from d1 to d2 is.
σ 2A
U= ( d 2 − d1 )
2 ε ok
52.
The given figure shows a network of five capacitors connected to a 100 V supply. Calculate the
total charge and energy stored in the network.
(Ans. 4 × 10-4 C)
53. Use Gauss’s law to obtain an expression for the electric field due to an infiniety long straight
uniformly charged wire.
Electric field in the following figure is directed along +X direction and given by Ex = 5Ax + 2B,
where Ex is in NC-1 and x is in metre, A and B are constants with dimensions. Taking A = 10 NC-
1
m-1 and B = 5NC-1 calculate.
(i) the electric flux throught the cube. (5 × 10-4 Vm)

(ii) net charge enclosed with the cube. (4.43 × 10-11C)
54. Four point charges are placed at the four corners of a square in the two ways (i) and (ii) as shown
below. Will the (i) electric field and (ii) electric potential, at the centre of the square, be the same or
different in the two configurations and why?
55. Keeping the voltage of the charging source constant, what would be the percentage change in the
energy stored in a parallel plate capacitor if the separation between its plates were to be de-
creased by 10%?
100
( % increase)
9
56 A charge ‘Q’ is placed at the centre of a cube of side L.What is the electric flux passing through
Q  ε
each face of the cube. ?  
 6ε 0  ε
57 A test charge’Q’ is moved without acceleration from A to C along the path from A to B and then
from B to C in electric field E as shown in the figure
i) calculate the potential difference between A and C (ii)At which points(of the two) is the electric
potential more and why ? B(2,3)
(4E, VC >VA)
E
A(6,0)
C(2,0)
58 An electric dipole is held in a uniform electric field. (i)Show that net force acting on it zero.
(ii) The dipole is aligned parallel to the field find the work done in rotating it through the angle of 1800
(2 PE)
59. How will (i) energy stored and (ii) the electric field inside the capacitor be affected when it is
completely filled with a dielectric material of dielectric constant ‘K’ ?
60 Draw a plot showing the variation of (i)electric field (E) and (ii) electric potential (V) with distance
r due to a point charge Q.
61 Why is the potential inside a hollow spherical charged conductor constant and has the same value as
on its surface. ?
62 Two point charges placed at a distance r in air exert a force F on each other. At what distance
will these charges experience the same force F in a medium of dielectric constant K?
63. A metallic sphere is placed in a uniform electric field. Which path is followed by lines of
force shown in Fig..
64. Two similarly equally charged identical metal spheres A and B repel each-other with a force of
2.0 ×10–5 N. A third identical uncharged sphere C is touched to A, then placed at the mid-point
between A and B. Calculate the net electrostatic force on C.
65 Five point charges, each of value +q coulomb are placed on five vertices of a regular hexagon
of side L metres. Find the magnitude of force on a charge-q coulomb placed at the centre of the
hexagon.
66. Two identical metal plates are given charges and (q2<) respectively. If they are now brought
close together to form a parallel plate capacitor with capacitance C, what will be the potential
difference between the plates?
q −q
V = 1 2.
2C
67 An electric field X is set up between the two parallet plates of a capacitor, as shown in Fig. An
electron enters the field symmetrically between the plates with a speed .The length of each plate is
l. Find the angle of deviation of the path of the electron as it comes out of the field.
68 A charge Q is distributed uniformly on a ring of radius r. A sphere of equal radius r is constructed

with its centre at the periphery of the ring, as shown in Fig. Find the electric flux through the sphere.
69. A charge Q is distributed over two concentric hollow spheres of radii r and R, where R>r, such
that the surface charge densities are equal. Find the potential at the common centre.
70. Three concentric metallic shells A, B and C of radii, a, b and c (a<b<c) have surface charge
densities respectively, as shown in Fig.
(i) Find potential of three shells A, B, C.
(ii) If shells A and C are at the same potential, obtain the relation between radii a,b, c.
σ a2 
VB =  − b + c
ε0  b  , c = a+b
71. Two equally charged hydrogen gas filled balloons A and B are shown in the figure. The volume
of gas in each baloon is 1 litre. Calculate the charge on each balloon. Given density of hydrogen gas =
0.9 kg/m3, density of air = 1.2 kg/m3,
72. The plate A of a parallel plate capacitor is connected to a spring of force constant k and can move,
while the plate B is fixed. The arrangement is held between two rigid supports as shown in Fig.2.173.
If a charge +q is placed on plate A and -q on plate B, by now much does the spring elongate?
73. The following data was obtained for the dependence of the magnitude of electric field, with distance,
from a reference point O. within the charge distribution in the shabed region.
Field Point A B C A’ B’ C’
Magnitude of E E/8 E/27 E/2 E/16 E/54
electric field
(i) Identify the charge distribution and justify your answer.
(ii) If the potential due to this charge distribution has a value V at the point A, what is its value at
point C?
σ
74. Show that the fields at the surface of a changed conductor is given by E = n Where σ
E0
is the surface charge density and n is a unit vector normal to the surface in the outward
direction.
75 A cube which each side “a” is kept is an electric field given by E = Cxi (as is shown in the
figure) where, C is a positive dimensional constant. Find out the .
(i) the electric flux through the cube, and
(ii) the net charge inside the cube.
76. Figure shows two identical capacitors, C1 and C2, each of 1 uF capacitance connected to a battery
of 6 V.Initially switch ‘S’ is closed.After sometimes ‘S’ is left open and dielectric slabs of dielectric con-
stant K =3 are inserted to fill completely the space between the plates of the two capacitors.How will the
(i) charge and (ii) potential difference between the plates of the two capacitors be affected after the slabs
are inserted.
(i) Q1 = 18 x 10-6 C , Q2 = 6 X 10-6 C
(ii) V1 = 6V V2 =2V
77. Four particles,each having a charge q are placed on the four vertices of regular pentagon.The distance
of each corner from the centre is a .Find the electric field at the centre of the pentagon
MULTIPLE CHOICE QUESTIONS

1. A, B and C are three points in a uniform electric field. The electric potential is
(A) Maximum at A
(B) Maximum at B
(C) Maximum at C
(D) Same at all the three points A, B and C
2. An electric dipole is placed at an angle of 30° with an electric field intensity 2 × 105 N/C. It
experiences a torque equal to 4 N m. The charge on the dipole, if the dipole length is 2 cm, is
( A) 8 mC
(B) 2 mC
(C) 5 mC
(D) 7 ìC
Completion type questions
3. A capacitor plates are charged by a battery. After charging battery is disconnected and a dielectric
slab is inserted between the plates, the charge on the plates of capacitor ______________.(decreases)
4. Equipotential surfaces due to long linear charge distribution will be ………. in shape.
(Ans-Cylindrical)
5. Work done to bring a unit positive charge un-accelerated from infinity to a point in electric field is
called ……….(Ans-Electrostatic Potential)
6. It is safer to be inside the car rather than standing outside under a tree during lightening is based on
_______________ concept.
True/false type questions
7. If an electron has an initial velocity in a direction different from that of an uniform electric field, the
path of the electron is parabolic.
8. A conducting hollow sphere of radius 10 cm has an electric potential on the surface 10V. Then the
electric potential at the centre of the hollow sphere will be zero. ans - false
9. The minimum field required to produce breakdown of air is 3.0x106V/m. Therefore, a conducting
sphere 10 cm in radius can easily hold a charge of 4x10-6C in air without breakdown. Ans - false
10. Electrostatic force at a point due to multiple charges is equal to algebraic sum of forces due to all
charges at that point.
11. Three equal charges (‘Q’ each) are placed at the corners of an equilateral triangle of side ‘a’.
The force on any one of the charge is . ans - true
Matching Type questions
12. (i) Direction of dipole moment (a) positive charge to negative charge
b) negative charge to positive charge
(ii) Direction of electric field lines (c) positive charge to positive charge
Ans (i)- b (ii) a
13. (a) Equivalent capacitance of 3 equal capacitors in series combination (P) 3C
(Q) 2C/3
(b) Equivalent capacitance of 3 equal capacitors two in parallel & one in series with it (R) C/3
14. (a) The value of electric field just outside the charged conductor is (P)
Q)
(b) The value of electric field inside a charged capacitor is (R)

15. (a) In series combination of capacitors (P) potential difference across each capacitor is
same
(Q) energy stored by each capacitor is same
(b) In parallel combination of capacitors (R) charge on each capacitor is same
(a) -R - (b) -P
16. (i) Net force on a dipole is zero (a) Dipole in non uniform electric field
(b) Dipole in uniform electric field
(ii) A scale rubbed with hair attracts small pieces of paper. (c) Charging by conduction.
17. A tin nucleus has charge +50e. If the proton is at distance 10 - 12 fm from the nucleus, then the
potential V at this position
(a) 14.4 × 104 volts (b) 7.2 × 104 volts
(c) 7.2 × 108 volts (d) 14.4 x 108 volts.
18. Figure shows lines of constant potential in a region in which an electric field is present. The values
of the potential, are written in brackets of the points A, B and C. The magnitude of electric field is
greatest at the point.
(a) A (b) B
(c) C (d) equal at all three points.
19. Two insulated charged spheres of radii R1 and R2 having charges Q1 and Q2 respectively are
connected to each other. There is
(a) no change in the energy of the system
(b) an increase in the energy of the system
(c) always a decrease in the energy of the system
(d) a decrease in the energy of the system unless Q2 R1 = Q1 R2.
20. Four metallic plates, each with surface area of one side A, are placed at a distance d from each
other. The alternate plates are connected to points A and B The equivalent capacitance of the
system will be
(a) 6 ε0 A/d (b) 2 ε 0A/d
(c) 3 εo A/d (d) 4εo A/d.
For question numbers 21 to 25, two statements are given-one labelled Assertion (A) and the other
labelled Reason (R). Select the correct answer to these questions from the codes (a), (b), (c) and (d) as
given below.
(a) Both A and R are true and R is the correct explanation of A
(b) Both A and R are true but R is NOT the correct explanation of A
(c) A is true but R is false
(d) A is false and R is also false
21 Assertion(A): The Coulomb force between two points charges depend upon the dielectric
constant of the intervening medium.
Reason(R): Coulomb’s force varies inversely with the dielectric constant of medium.
Ans: A
22. Assertion(A): A proton is placed in a uniform electric field, it tend to move along the direction of
electric field.
Reason(R): A proton is placed in a uniform electric field it experiences a force.
Ans: B
23. Assertion(A): The interior of a conductor can have no excess charge in the static situation
Reason(R): Electrostatic potential is constant throughout the volume of the conductor and
has the same value (as inside) on its surface.
Ans: B
24. Assertion(A): A metal plate is introduced between the plates of a charged parallel plate capacitor,
its capacitance increased.
Reason(R): A metal plate is introduced between the plates of a charged parallel plate capacitor,
the effective separation between the plates is decreased.
Ans: A
25. Assertion(A) The field intensity in between such sheets having equal and opposite uniform
surface densities of charge become constant.
Reason(R): The field intensity does not depend upon the distance between the thin sheet.
Answer: A
CASE STUDY BASED QUESTION

Dielectric with polar molecules also develops a net dipole moment in an external field, but for a different
reason. In the absence of any external field, the different permanent dipoles are oriented randomly due to
thermal agitation; so the total dipole moment is zero. When an external field is applied, the individual dipole
moments tend to align with the field. When summed overall the molecules, there is then a net dipole
moment in the direction of the external field, i.e., the dielectric is polarised. The extent of polarisation
depends on the relative strength of two factors: the dipole potential energy in the external field tending to
align the dipoles mutually opposite with the field and thermal energy tending to disrupt the alignment. There
may be, in addition, the ‘induced dipole moment’ effect as for non-polar molecules, but generally the
alignment effect is more important for polar molecules. Thus, in either case, whether polar or non-polar, a
dielectric develops a net dipole moment in the presence of an external field. The dipole moment per unit
volume is called polarization.
1. The best definition of polarisation is
(a) Orientation of dipoles in random direction (b) Electric dipole moment per unit volume
(c) Orientation of dipole moments (d)Change in polarity of every dipole
2. Identify which type of polarisation depends on temperature.
(a) Electronic (b) Ionic (c) Orientational (d) Interfacial
3. Dielectric materials do not have
(a) Free electrons (b) Bound charge (c)Proton (d) neutron
4. Dipoles are created when dielectric is placed in __________
(a) Magnetic Field (b) Electric field (c) Vacuum (d) Inert Environment
5. Calculate the polarisation vector of the material which has 100 dipoles per unit volume
in a volume of 2 units.
(a) 200 (b) 50 (c) 0.02 (d) 100
Answer: 1. b 2. c 3. a 4. b 5. a
Unit - (CURRENT ELECTRICITY)
Code 12P (03 & 04)
1. A current of 2 mA is passed through a colour coded carbon resistor with first, second and third
rings of yellow, green and orange colours. What is the voltage drop across the resistor ?
(Ans. 90v)
2. A wire of 10 ohm resistance is stretched to thrice its original length. What will be its (i) new
resistivity, and (ii) new resistance?
( same ,90 Ω )
3. A uniform copper wire of mass 2.23 × 10-3 kg. carriers a current of 1 A when 1.7 V is applied
across it. Calculate its length and area of cross-section. If the wire is uniformily stretched to
double its length, calculate the new resistance. Density of copper is 8.92 x 103 kg m-3 and resis-
tivity is 1.7 × 10-8 Ω m.
(Ans. 5m, 5 x 10-8 m2, 6.8 Ω )
4. One metre long metallic wire is broken into two unequal parts P and Q. The part P is unformily
extended into another wire R. The length of R is twice the length of P and the resistance of R is
equal to that of Q. Fine the ratio of the resistances of P and R and also the ratio of the lengths P
and Q.
(Ans.1 :4)
5. Two wires A and B of he same material have their lengths in the ratio 1 : 5 and diameters in the
ratio 3 : 2. If the resistance of the wire B is 180 Ω , find the resistance of the wire A.
(Ans. 16 Ω )
6. A uniform wire is cut into four segments. Each segment is twice as long as the earlier segment. If
the shortest segment has a resistance of 4 Ω , find the resistance of the original wire.
(Ans. 60 Ω )
7. A voltage of 30 V is applied accross a colour coded carbon resistor with first, second and third
rings of blue, black and yellow colours. What is the curent flowing through the resistor?
(Ans. 0.5 × 10-4 A)
8. The resistance of a coil used in a platinum-resistance thermometer at 0 C is 3.00 Ω and at

100 C is 3.75 Ω . Its resistance at an unknown temperature is measured as 3.15 Ω . Calculate
the unknown temperature.
(Ans. 20 C)
9. The temperature coefficient of a resistance wire is 0.0012.5 C-1. At 300 K, its resistance is 1 Ω .
At what temperature the resistance of the wire will be 2 Ω ?
(Ans. 1100 K)
10. The temperature coefficient of resistivity of copper is 0.004 C-1. Find the resistance of a 5m long
copper wire of diameter 0.2 mm at 100 C, if the resistivity of copper at 0 C is 1.7 × 10-8 Ω m.
(Ans. 3.8 Ω )
11. The current through a conductor is 1 ampere when the temperature is 0 C and 0.7 ampere when
the temperature is 100 C. What would be current when the temperature of the conductor is
1200 C?
12. A set of n identical resistors, each of resistance R Ω , when connected in series have an effective
resistance X Ω and when the resistors are connected in parallel, their efective resistance is Y Ω .
Find the relation between R, X and Y.
(Ans. XY = R2)
13. The lengths and radii of three wires of some metal are in the ratios 2 : 3 : 4 amd 3 : 4 : 5
respectively. They are joined in parallel and included in a circuit having 5 A current. Find current
through each wire.
(Ans. 1.40 A, 1.66 A, 1.94 A)
14. A battery of emf 10 V is connected to resistances as shown in the folowing fig. Find the potential
difference between the points A and B.
15. Find the equivalent resistance of the circuit shown in the following Fig. between the points P and
Q. Each resistor has a resistance r.
16. Calculate the resistance between points A and B for the following networks :
 2 4 R 
Ans. (a) 3 Ω(b) 3 Ω(c) 3 Ω(d )6Ω 
 
17. Find the current drawn from a cell of emf 1 V and internal resistance 2/3 Ω connected to the
network given below.
(Ans. 1 A)
18. A battery of emf 12.0 V and internal resistance 0.5 Ω is to be charged by a battery charger which
supplies 110 V d.c. How much resistance must be connected in series with the battery to limit the
charging current to 5.0 A? What will be the p.d. across the terminals of the battery during charg-
ing?
(Ans. 19.1 Ω , 14.5v)

19. In the circuit shown in the following Fig. , a potential difference the points A and B is 3V. Find the
value of resistance R1.
(Ans. 3 Ω )
20. Two identical cells of emf 1.5 V each joined in parlellel provide supply to an external circuit
consisting of two resistances of 17 Ω each joined in parallel. A very high resistance voltmeter
reads the terminal voltage of cells to be 1.4 V. Calculate the internal resistance of each cell.
(Ans. 1.2 Ω )
21. Four identical cells, each of emf 2 V, are joined in parallel providing supply of current to external
circuit consisting of two 15 Ω resistors joined in parallel. The terminal voltage of the cells, as read
by an ideal voltmeter is 1.6 volt. Calculate the internal resistance of each cell.
(Ans. 7.5 Ω )
22. Two cells E1 and E2 of emfs 4 V and 8 V having internal resistances 0.5 Ω and 1.0 Ω respec-
tively are connected in opposition to each other. This combination is connected in series with
resistances of 4.5 Ω and 3.0 Ω . Another rsistance of 6.0 Ω is connected in parallel across the
3 Ω resistor.
(a) Draw the circuit diagram
(b) Calculate the total current flowing through the circuit.
(Ans. 0.5A)
23. A series combination of a 2 k Ω resistor and 1 k Ω resistor, is connected across a battery of emf
6V and negligible internal resistance. The potential drop, across the 2 k Ω resistor, is measured
by (i) a 30 k Ω voltmeter (ii) a 1 k Ω voltmeter and (iii) both these voltmeters connected across
it. If the voltmeter readings in the three cases are V1, V2 and V3respectively, arrange these read-
ings in descending order.
How will the three readings compare the one another if the potential drop were measured across
the series combination of the 2 k Ω and the 1 k Ω resistor i.e., across the points A and B?
(Ans. V1 > V2 > V3 )
24. For the potentiometer circuit shown in the given figure, points X and Y represent the two termi-
nals of an unknown emf E. A student observed that when the jockey is moved from the end A to
the end B of the potentiometer wire, the deflection in the galvanometer remains in the same
direction. What are the two possible faults in the circuit that could result in this observation?
If the galvanometer deflection at the end B is

(i) more
(ii) less than at the end A, which of the two faults, listed above, would be there in the circuit?
Give reasons in support of your answer in each case.
25. A 24 V battery of internal resistance 1.5 Ω is connected to three coils of resistences 18 Ω , 9 Ω
and 6 Ω in parallel, a resistor of 3.5 Ω and a reversed battery (e.m.f. = 12 V and internal
resistance = 3 Ω ) as shown. Calculate (i) the current in the circuit, (ii) current in resistor of 18 Ω
coil, and (iii) p.d. across each battery.
 12 2 246 168 
Ans.( a ) I = 11 (b) I1 = 11 (c)V2 = 11 volt , V1 = 11 volt 
 
26. AB is one metre long uniform wire of 10 Ω resistance. The other data are shown in the following
circuit diagram given below:
Calculate (i) Potential gradient along AB, and (ii) length AO of the wire, when the galvanometer
shows no deflection.
(Ans. 0.8 V/m (ii) 0.3 V, length AO = 37.5 cm)
27. The length of a potentiometer wire is 600 cm and it carrires a current of 40 mA. For a cell of
e.m.f. 2V and internal resistance 10 Ω the null point is found to be at 500 cm. If a voltmeter is
connected across the cell, the balancing length is decreased by 10 cm. Find (i) the resistance of
whole wire, (ii) reading of voltmeter, and (iii) resistance of voltmeter.
(Ans. (i) 60 Ω (ii) 1.96 V (iii) 490 Ω )
28. Two cells of e.m.f.’s 1.5 V and 2 V having internal resistances 2 Ω and 1 Ω respectively, have
their negative terminals joined by a wire of 6 Ω and + ve terminals by a wire of 4 Ω resistance. A
third resistance wire of 8 Ω connects middle points of these wires. Draw the circuit diagram.
Using Kirchhoff’s laws, find the potential difference at the end of this third wire.
(Ans. 92/73 V)
29. Find the value of unknown resistance X and the curent drawn by the circuit from the battery, if no
current flows through the galvanometer. Assume the resistance per unit length of the wire AB to
be 0.01 Ω /cm.
(Ans. I=2.8 A)
30. Calculate the current drawn from the battery in the given network sketched here.
(Ans. 2A)
31. A voltmeter V of resistance 400 Ω is used to measure the potential difference across a 100 Ω
resistor in the circuit shown here.
(a) What will be the reading on the voltmeter?
(Ans. 24 V)
(b) Calculate the potential difference across 100 Ω resistor before the voltmeter is connected.
(Ans. 28 V)
32. A potential difference of 2 volt is applied between the points A and B as shown in the network
drawn in the figure. Calculate
(i) equivalent resistance of the network across a point A and B, and
(ii) the magnitudes of currents flowing in the arms AFCEB and AFDEB.
(Ans. R = 2 Ω , 0.5 A, 0.5A)
33. Using Kirchhoff’s laws in the given electrical network, calculate the values of I1, I2 and I3.
 48 18 66 
Ans.I1 = 31 ; I 2 = 31 ; I 3 = 31 
 
34. Two cells of e.m.f. 6 V and 12 V and internal resistances 1 Ω and 2 Ω respectively are connected
in parallel so as to send current in the same direction through an external resistance of 15 Ω .
(i) Draw the circuit diagram.
(ii) Using Kirchhoff’s laws calculate
(a) current through each branch of the circuit
(b) p.d. across the 15 Ω resistance.
 78 102 
 Ans.(a)I1 = A, I 2 = A, I 3 (ii)(b)7.66V 
 47 47 
35. A potential difference V is applied across a conductor of length L and diameter D. How are the
electric field E and the resistance R of conductor affected when in turn (i) V is halved, (ii) L is
halved, and (iii) D is doubled?
Ans (i) E half R same (ii) E double , R half (iii) E same R one fourth
36. The variation of potential difference V with length I in case of two potentiometers X and Y is as
shown in the given diagram. Which one of these two will you prefer for comparing e.m.f.’s of two
cells and why?
37. Name any one material having a small value of temperature coefficient of resistance. Write one
use of this material.
38. V-I graph for a metallic wire at two different temperature T1 and T2 is as shown in the following
figure. Which of the two temperatures is higher and why?
39.
A.d.c. supply of 120 V is connected to a large resistance X.
A voltmeter of resistance 10 k Ω placed in series in the
circuit reads 4 V. What is the value of X? What do you think
is the purpose in using a voltmeter instead of an ammeter, to
determine the large resistance X?
(Ans. x =290 k Ω )
40. Find the value of the unknown resistance X, in the following circuit, if no current flows throught
the seciton AO. Also calculate the current drawn by the circuit from the battery of e.m.f. 6 V and
negligible internal resistance.
(Ans. X=6 Ω ; I=1A)
41. Six resistors, each of value 4 Ω , are joined together in a circuit as shown in the figure. Calculate
equivalent resistance across the points A and B. If a cell of emf 2 V is connected across AB,
compute the current through the arms AB and DF of the circuit.
(Ans. 2 Ω , 0.5A)
42. The voltage-current variation of two metallic wires ‘X’ and ‘Y’ at constant temperature are as
shown. Assuming that the wires have the same length and the same diameter, explain which of the
two wires will have larger resistvity.
43. The circuit diagram shows the use of a potentiometer to measure a small emf produced by a
thermocouple connected between X and Y. The cell C, of emf 2V, has negligible internal resis-
tance. The potentiometer wire PQ is 1.00m long and the resistance 5 Ω . The balance point S is
found to be 400 mm from P. Calculate the value of emf V, generated by the thermocouple.
(Ans. 4mV)
44. In the potentiometer circuit shown, the balance (null) point is at X. State with reason, where
the balance point will be shifted when.
(i) Resistance R is increased, keeping all parameters unchanged.
(ii) Resistance S is increased, keeping R constant.
(iii) Cell P is replaced by another cell whose e.m.f. is lower than that the cell Q.
45. In the given network, find the values of the currents, I1, I2 and I3 .
 5 1 6 
 I1 = A, I 2 = − A, I 3 = A 
 13 13 13 
46. In a potentiometer, a standard cell of emf 5V and of negligible resistance maintains a steady
current through the potentiometer wire of length of 1 m. Two primary cells of emfs E1 and E2 are
joined in series with (i) same polarity, and (ii) opposite polarity. The combinattion is connected
through a galvanometer and a jockey to the potentiometer. The balancing lengths in the two cases
are found to be 350 cm and 50 cm respectively.
(i) Draw the necessary circuit diagram.
(ii) Find the value of the emfs of the two cells.
47. When two known resistances, R and S, are connected in the left and right gaps of a meter bridge,
the balance point is found at a distance L1 from the ‘zero end’ of the meter bridge wire. An un-
known resistance X is now connected in parallel to the resistance S and the balance point is now
found at a distance L2 from the zero end of the meter bridge wire. Obtain a formula for X in terms
of L1 ,L2 and S.
 
 
 S 
 Ans. x = 
 ℓ2  100 − ℓ 1   
   − 1 
 
  ℓ1  100 − ℓ 2   
48. A potentiometer wire has a length L and a resistance R0 . It is connected to a battery and a
resistance combination as shown. Obtain an expression for the potential drop per unit length of
this potentiometer wire.
What is the maximum emf of a ‘test cell’ for which one can get a ‘balance point’ on this potenti-
ometer wire? What precaution should one take, while connecting this ‘test cell’, in the circuit?
 
 
 ER0

   R + RS   
  L 
  R + S 
49. Two primary cells of e.m.f. E1 and E2 ( E1 > E2 ) are connected to the potentiometer wire AB as
shown in the figure.
If the balancing lengths for the two combinations of the cells are 250 cm and 400 cm, find the
ratio of E1 and E2 .
 Ans. E1 = 13 
 E2 3 

50. 4 cells of identical emf ∈, internal resistance r, are connected in series to a variable resistor. The
following graph shows the variation of terminal voltage of the combination with the current output:
(i) What is the emf of each cell used?

(ii) For what current from the cells, does maximum power dissipation occur in the circuit?
(iii) Calculate the internal resistance of each cell.
(Ans. 1.4 V, 1A, 0.7 Ω )
51. In the circuit shown in Fig., find the current through the 4 Ω resistor.
(Ans. 0.25 A)
52. In a metre-bridge experiment, with a resistance R1 in the left gap and a resistance X in the right
gap, null point is obtained at 40 cm from the left end. With resistance R2 in the left gap and the
same resistance X in the right gap, null point is obtained at 50 cm from the left end. Where will be
the null point if R1 and R2 are put in series in the left gap, right gap containing X?
(Ans. 62.5 cm)
53. Fig. shows a cell of emf ∈ and internal resistance r, connected to a voltmeter V and a variable
resistance R. Deduce the relationship among V, ∈ , R and r. How will V very when R is reduced.
 E 
V = 
 1 + r/R 
54. The diagram shows a piece of pure semiconductor, S in series with a variable resistor R, and a
source of constant voltage V. Would you increase or decrease of value of R to keep the reading
of ammeter (A) constant, when semiconductor S is heated ? Give reason.
55. The V-I graphs of two resistors, and their series combination, are shown in the following Fig.
Which one of these graphs represents the series combination of the other two? Give reasons for
your answer.
56 A cell gives a balance point with 85 cm of a potentiometer wire. When the terminals of the cell
are shorted through a resistance of 7.5 Ω , the balance is obtained at 75 cm. Find the internal
resistance of the cell.
(Ans. 2 Ω )
57. A cell of emf (E) and internal resistance (r) is connected across a variable external resistor (R).
Plot graphs to show variation of (i) E with R, (ii) Terminal p.d. of the cell (V) with R.
58. Calculate the temperature at which the resistance of a conductor becomes 20% more than its
resistance at 27° C. The value of the temperature ecoefficient of resistance of the conductor is
2.0 × 10 −4 /K.
(Ans. 300 K)
59. 12 cells, each of emf 1.5 V and internal resistance 0.5 Ω , are arranged in m rows each containing
n cells connected in series, as shown in thefigure. Calculate the values of n and m for which this
combination would send maximum current through an external resistance of 1.5 Ω .
(Ans. n = 6, m = 2)
60. A cell of unknown emf E and internal resistance r, two unknown resistances R1 and R2 ( R2 > R1 )
and a perfect ammeter are given. The current in the circuit is measured in five different situations:
(i) without any external resistance in the circuit, (ii) with resistance R1 only. (iii) with
resistance R2 only. (iv) with both R1 and R2 used in series combination and (v) with R1 and R2
used in parallel combination. The current obtained in the five cases are 0.42A, 0.6A, 1.05A,
1.4A and 4.2A, but not necessarily in that order. Identify the currents in the five cases listed
above and calculate E, r, R1 and R2 . (E = 4.2 V, R1 = 3ohm, r = 1 ohm, R2 = 6 ohm)
61. Describe the formula for the equivalent EMF and internal resistance for the parallel combina-
tion of two cells with EMF’s E1 and E2 and internal resistances r1 and r2 respectively. What is
the corresponding formula for the series combination? Two cells of EMF 1V, 2V and internal
resistances 2 Ω and 1 Ω respectively are connected in (i) series, (ii) parallel. What should be
the external resistance in the circuit so that the current through the resistance be the same in the
two cases? In which case more heat is generated in the cells.
(Ans.9/4 r, series)
62 Two wires of equal length,one of copper and the of maganin have the same resistance Which
wire is thicker. ?
63 Calculate the value of the resistance R in the circuit shown in the figure so that the current
in the circuit is 0.2A.What would be the potential difference between points A and D ?
64 When electrons drift in a metal from lower to higher potential ,does it mean that all the free
electrons of the metal are moving in the same direction ?
65 Two students X and Y perform an experiments on potentio meter separately using the circuit
given below.
Keeping other parameter changed how will the position of the null point be affected if (i) ‘X’
increases the value of resistance R in the set up by keeping the key K1 closed and the K2 open ?
(ii) ‘Y’ decreases the value of resistance S in the set up,while the key K2 remains open and the
key K1 closed ?
66 Find the current flowing through the resistance R1of the circuit shown in Fig. Given R1=10, R2=20
and R3 =30and the potentials of points 1,2 and 3 are =10V, 6V and 5V. ( 1.2 A)
67. The length of a potentiometer wire is 600 cm and it carries 40m A current. For a cell of emf 2
volt and internal resistance 10 ohm, the null-point is found at 500 cm. If a voltmeter is connected across
the cell, the balancing length of the wire is decreased by 10 cm. Find (i) the resistance of the whole
wire,(ii) reading of voltmeter,(iii) resistance of voltmeter. (60 ohm,1.96V,490 ohm)
68. The variation o fthe resistance of a metallic conductor with temperature is shown in Fig.
(i)Calculate the temperature coefficient of resistance from the graph.
(ii)State why the resistance of the conductor increases with the rise in temperature.
R − R0
α=
R 0 ×θ
MULTIPLE CHOICE QUESTIONS
1. The resistance of a conductor increases for a given material at ‘constant temperature when?
a. its thickness increases
b. its length increases
c. its length decreases and thickness increases.
d. Its length increases and thickness decreases. Ans- d
2. The equivalent resistance of a circuit between A and B is
(A) 3 Ù (B) zero (C) 6 Ù (D) 3/2 Ù
3.The V-I graph for a conductor at temperatures T1 and T2 are as shown in the figure, (T2 – T1) is
proportional to
(A) cos 2è
(B) sin 2è
(C) cot2è
(D) tan 2è
4. The figure shows in apart of an electric circuit, then the current I is
(A) 1 A
(B) 3A
(C) 2 A
(D) 4 A
5. A cell of e.m.f E and internal resistance r is connected across a resistance r. The potential difference
between the terminals of the cell must be
(A) E
(B) E/2
(C) E/4
(D) 3E/2
6. In the given circuit below the equivalent resistance between points A and D
(A) 40 Ù (B) 20 Ù (C) 30 Ù (D) 10 Ù

7. A potentiometer wire has length 4 m and resistance 8 Ù. The resistance that must be connected in
series with the wire and an accumulator of e.m.f. 2 V, so as to get a potential gradient 1 mV per cm on
the wire is
(A) 32 Ù
(B) 40 Ù
(C) 44 Ù
(D) 48
8. In balanced metre bridge, the resistance of bridge wire is 0.1 Ù / cm. Unknown resistance 45 X
is connected in left gap and 6 Ù in right gap, null point divides the wire in the ratio 2 : 3. Find the
current drawn from the battery of 5 V having negligible resistance.
( A) 1 A
(B) 1.5 A
(C) 2 A
(D) 5 A
9. When 5 V potential difference is applied across a wire of length 0.1 m, the drift speed of electrons is
2.5 × 10–4 ms–1. If the electron density in the wire is 8 × 1028 m–3, the resistivity of the material is close
to
(A) 1.6 × 10–8 Ùm
(B) 1.6 × 10–7 Ùm
(C) 1.6 × 10–6 Ùm
(D) 1.6 × 10–5 Ùm
Completion Type Questions

10. The alloys which are used for making resistances have very low Temperature coefficient of
resistance and high _______________.
11. Wheat Stone Bridge experiment is most sensitive when all the resistances are of
_______________.
12. A battery of e.m.f. 2 volt and internal resistance 0.1 Ù is being charged with a current of 5 ampere.
The p.d. between the two terminals of the battery is ________________ volt.
13. There is a metal block of dimensions 20x10x15 cm .The ratio of the maximum and minimum
resistance of the block is _______________ .
14. Kirchhoff’s I law for electric network is based on _______________ .
True/False Type Questions
15. In a meter bridge experiment, copper plates are used due to their low conductivity.
16. The emf of a cell depends upon the internal resistance of a cell.
17. Temperature coefficient of resistance of a good conductor is negative.
Matching type Questions
18. (i) Ohm’s law is applicable for (a) Alloys
(ii) Ohm’s law is not applicable for (b) Carbon resistors
(c) Diodes
19. (i) Conductance is reciprocal of (a) Conductivity

(ii) Resistivity is reciprocal of (b) E. F. Intensity
(c) Resistance
20 . In the given circuit if reading of A1 is 2.4 A then
(i) Reading of A3 (a) 1.6A

(ii) Reading of A2 (b) 4.0A
(c) 3.0A
given below.
21. Assertion (A): The 200 W bulbs glow with more brightness than 100 W bulbs.
Reason(R) : A 100 W bulb has more resistance than a 200 W bulb.
Answer: A2.
22 Assertion (A): A current flows in a conductor only when there is an electric field within the conduc-
tor.
Reason(R): The drift velocity of electron in presence of electric field decreases. Two wires of same
length and material have different areas of the cross-section.
Answer: C
23. Assertion (A): In a simple battery circuit, the point of the lowest potential is positive terminal of the
battery.
Reason (R): The current flows towards the point of the higher potential, as it does in such a circuit from
the negative to the positive terminal.
Answer: d
24. Assertion (A): Potentiometer is used only to compare potential differences.
Reason (R): The potentiometer draws current from the voltage source being measured .
Answer: c
25. Assertion (A): A potentiometer of longer length is used for accurate measurement.
Reason (R): The potential gradient for a potentiometer of longer length with a given source of e.m.f.
becomes small.
Answer: A
CASE BASED QUESTIONS
Unit : Magnetic Effect of current and Magnetism
Code:12P (05) & (06)
Section - A
Multiple choice questions:
I. Select the best option from the choices given in the following questions :
1. The path of a charged particle in a magnetic field when its direction of motion is not at right angles to
the magnetic field will be a
(a) circle (b) straight line
(c) parabola (d) helix
2. A rectangular loop carrying a current I is situated near a long straight wire such that the wire is
parallel to one of the sides of the loop and is in the plane of the loop. If a steady current I, is
established in the wire the loop will
(a) remain stationary (b) move towards the wire
(c) move away from the wire (d) rotate about an axis parallel
to the wire
3. A vertical wire carries a current in upward direction. An electron beam horizontally towards the wire
will be deflected
(a) towards right (b) towards left
(c) upwards (d) downwards
4. A current carrying straight wire is kept along the axis of a circular loop carrying a current. The
straight wire
(a) will exert an inward force on the circular loop
(b) will exert an outward force on the circular loop
(c) will not exert any force on the loop
(d) will exert a force on the loop parallel to itself
5. A charged particle is moved along a magnetic field line. The magnetic force on the particle is
(a) along its velocity (b) opposite to its velocity
(c) perpendicular to its velocity (d) zero
6. A moving charge produces
(a) electric field only (b) magnetic field only
(c) both electric and (d) none of them
magnetic field
7. Two particles X and Y having equal charge after being accelerated through the same potential differ-
ence enter a region of uniform magnetic field and discribe circular paths of Radii R1 and R2 respec-
tively. The ratio of the mass of X to that of Y is
(a) (R1/R2)l/2 (b) R2 /R1
(c) R /R2 (d) R1, R2
1
8. Two parallel wires carry currents of 20A and 40A in opposite directions Another wire carrying a
current antiparallel to 20A is placed midway between the two wires. The magnetic force on it will be
(a) towards 20A (b) towards 40A
(c) zero (d) perpendicular to the plane of the currents
9. Consider a long straight wire of cross-rectional area A carrying a current i. Let there be n free
electrons per unit volume. An observer places himself on a trolley moving in a direction opposite to
the current with a speed v = 2/nAe and separated from the wire by a distance r. The magnetic field
seen by the observer is very nearly
(a) µ 0 I (b) Zero
2 πr
(c) µ 0 i (d) 2 µ 0i
πr r
10. Magnetic meridian is
(a) a point (b) a line along north-south
(c) a horizontal plane (d) a vertical plane
11. A tangent galvanometer is connected directly to an ideal battery. If the number of turns in the coil is
doubled deflection will
(a) increase (b) decrease
(c) remain unchanged (d) can be increased or decreased
12. Pick-the correct options
(a) Magnetic field is produced by electric charges only
(b) Magnetic poles are only mathematical assumptions having no real existence
(c) A north pole is equivalent to a clockwise current and a south pole is equivalent to an anticlockwise
current.
(d) A bar magnet is equivalent to a long straight current.
13. A charged particle is whirled in a horizontal circle on a frictionless table by attaching it to a string fixed
at one point. If a magnetic field is switched on in the vertical direction the tension in the string
(a) will increase (b) will decrease
(c) will remain the same (d) may increase or decrease
14. Which of the following particles will experience maximum magnetic force (magnitude) when pro-
jected with the same velocity perpendicular to a magnetic field
(a) electron (b) proton
2+ 3+
(c) He (d) Li
15. A current carrying wire is along the normal axis of a current carrying circular loop. The loop will
experience
(a) F = 0, τ = 0 (b) F ≠ 0, τ ≠ 0
(c) F = 0, τ ≠ 0 (d) F ≠ 0, τ = 0
Ans. 1. (d), 2(B), 3(c), 4(a), 5(d), 6(c), 7(a), 8(a), 9(b), 10(d), 11(a), 12(b), 13(d), 14(d), 15(a)
Assertion -Reason Questions ( 16 to 18)
a) Assertion and Reason both are acorrect and Reason is correct explanation for assertion.
b) A & R both are correct and R is not correct explanation for A.
c) A is correct but R iswrong
d) A is wrong but R is correct.
16. A-Motion of electron arond a positively charged nucleus is different from motion of a planet
around sun.
R- The force acting in both the cases is of different kind.
Ans-D
17. A- A cyclotron does not accelerate electrons. R-Mass of electron is very small,so it gains relativistic
speed very soon.
18. A-Galvanometer cannot as such be used as an ammeter to measure the value of the current in the
given circuit Ans-A
R-It gives full scale deflector for a current of the order of micro-ampere
19. If a conducting wire carries a direct current through it, the magnetic field associated with the
current will be______.
a) Both inside and outside the conductor
b) Neither inside nor outside the conductor
c) only inside the conductor
d) only outside the conductor Ans-A
20. Statement:The magnetic field emerging out of the plane of the paper is denoted by a dot. (0)
Statement Q: The magnetic field going into the plane of the paper is denoted by a cross ( x)
a) Both P and Q are true.
b) P is true, but Q is false
c) P is false, but Q is true. Ans-A
Section - B
+
1. A He travels in a uniform magnetic field of 0.5T with a velocity of 104 m/s in a direction making an
angle of 30° with the magnetic field. Calculate the magnitude of force on the ion. (Ans : 8.0 x 104N)
2. A singly charged carbon ion is accelerated through a potential difference of 4000V. It then enters
into a region permeated by a uniform magnetic field in a direction perpendicular to the field and
moves in a circle of radius 20.0 cm. Calculate the strength of the magnetic field. Relative atomic
mass of carbon is 12 and the unified atomic mass unit u = 1.66 x 10 27 Kg. (25.35 x 104 T)
3. Calculate the magnetic field due to an overhead horizontal cable carrying a current of 10A at a point
-5
10 cm vertically below the cable. ( 2 × 10 T )
4. In the previous problem if the cable is held in the east and west direction perpendicular to the
horizontal component BH of the earth’s magnetic field. where and how far from the cable will the
neutral point be obtained when (i) current flows from east to west
(ii) current flows from west to east (BH = 0.32G) (Ans : 6.25 cm)
5. Caluclate the velocity v of a certain ion that passes undetected through a crossed electric field .
E = 10.0 k V/m and magnetic field B = 0.1OT.
Ans. (v = 105 m/s)
6. On a smooth plane inclined at 30° with the horizontal a thin current carrying rod is placed horizon-
tally. The plane is located in a magnetic field of 0.15T in the vertical direction. For what value of the
current can the rod remain stationary? The mass per unit length of the wire is 0.30 gm-1.
(Ans : I = 11.26 mA)
7. A short magnet is placed in the magnetic meridian. With north pole pointing towards north. Null
points are obtained 12.0 cm from the centre of the magnet on its normal bisector. Calculate the
dipole moment of the magnet. (BH = 0.3 8G)
Ans. (m = 0.66 JT-1)
8. What is the magnetic moment associated with a coil of 1 turn and area of cross section 10– 4m2
carrying a current of 2A? Ans. (2 ×10– 4 A m2)
9. A chamber is maintained at a uniform magnetic field of 5× 103T. An electron with a speed of 107 m/
s enters the chamber in a direction normal to the field. Calculate
(a) the radius of the path
(b) frequency of revolution of the electron Ans. (r= 1.14 x 10-2m, w= 1.4 x 108Hz)
10. Calculate the force per unit length on a straight wire carrying 4A due to a parallel wire carrying 6A
-5
current. Distance between the wires = 3 cm. Ans. (16 × 10 N/m)
11. A circular coil is placed in a uniform magnetic field of strength 0.1 T normal to the plane of the coil.
If the current in the coil is 5A find (i) total torque on the coil (ii) total force on the coil (iii) average
force on each electron in the coil due to the magnetic field. The coil is made of copper wire of cross
-5
sectional area l0 m2 and the free electron density in copper is 1029 m–3.
25
{(a) zero r (b) zero (c) F = 5.0 × l0 N}
12. What is the magnitude of the force on a wire of length 0.04m inside a solenoid near its centre making
an angle of 30° with the axis. The wire carries a current of 12A and the mangetic field due to solenoid
has a magnitude of 0.25T. (F = 0.06N)
13. A short bar magnet of magnetic moment 0.9J T placed with its axis at 45° with a uniform external
magnetic field experiences a torque of magnitude 0.063J. Find the strength of the magnetic field.
(0.099T).
14. A point charge q is moving with a speed v perpendicular to a magnetic field B What should be
the magnitude applied electric field so that net force acting on the charge is zero.
(E=vB )
15. A proton, a deutron and an alpha particle having the same kinetic energy are allowed to pass through
a uniform magnetic field perpendicular to their direction of motion. Compare the radii of their circular
paths.
(rp:rd:r α = 1 : 2 : 1)
16. The figure shows a right-angled isosceles triangle PQR having its base equal to a. A current I ampere
is passing inwards along a thin wire cutting the plane of the paper normally, as shown at Q. Likewise
a similar wire carries an equal current passing normally inwards at R. Find the magnitude and direc-
µ0 I
tion of the magnetic induction at P. Assume the wires to be infinitely long. Ans.( )
πa
17. Two concentric and coplanar circular loops along with a semi circle loop carry currents as shown in
the figure. What should be the magnitude and direction of the current in the semi-circular loop so that
the net magnetic field at the center O becomes Zero?
(5A, clockwise direction)
18. An electron has an initial velocity of (14.5 ĵ + 18.5 k̂ ) km/s and a constant acceleration of (1.20x
1012 m/s2) iˆ in a region in which uniform electric and magnetic fields are present. If B =(400 T) ,
find the electric field. ( E = − 6.83 iˆ V/m)
19. A beam of protons passes undeflected with a horizontal veocity v through a region of electric and
Magnetic fields, mutually perpendicular to each other and normal to the direction of the bean.If the
magnitude of electric and magnetic fields are 50K v/m and 100mt respectively
Calculate
(i) velocity of the beam
(ii) force with which it strikes a target , if I = 0.80 MA
Ans v = 5 ×105 m/s F = Mvi/ne N
20. A monoenergetic electron beam of initial energy 18 KeV moving horizontally is subjected to a
horizontal magnetic field of 0.4 G normal to its initial direction. Calculate the vertical deflection of the
beam over a distance of 30 cm.
(4mm)
21 A solenoid 60 cm long and radius 4.0 has three layers of windings of 300 turns each. A 20 cm long
wire of 2.5 gm lies inside the solenoid (near its center) normal to its axis; both the wire and the axis
of the solenoid are in horizontal plane. The wire is connected through two leads parallel to the axis of
the solenoid to an external battery, which supplies a current of 6.0, A in the wire. What value of
current (with appropriate sense of circulation) in the windings of the solenoid can support the weight
of the wire?
Ans.(108.3A)
22 A proton after being accelerated through a potential difference of 450 volt enters a uniform magnetic
field of 30 Gauss pointing along y-axis It moves in xy plane such that its initial velocity makes an
angle of 600 with x-axis as shown in the figure.
a) Trace the helical path followed by the proton
b) Find Radius of the helical path
c) Period of the revolution.
d) Time taken it takes to cover a distance of 50 cm along y-axis.
[(a. 3x105 m/s) (b. helical) (c.0.5m) (d. 2.1x10-5s)]
23. A particle of charge –1.6x10-16 C moving with velocity 10 ms-1 along the x-axis enters a region
where magnetic field of induction B is along the y-axis and an electric field of magnitude 104 Vm-1
is along the negative z-axis. If the charged particle continues moving along x-axis, find the magnitude
of B.
(103Wbm-2)
24. A wire is carrying a steady current of 12 A and is lying on the table .Another wire CD(carrying 5A
is held directly above AB at a height of 1 mm.Find the mass per unit length of the wire CD so that it
remains suspended at its position when left free.Give the direction of the current flowing in CD with
respect to that in AB(g =10 m/s2)
Ans 1.2×10-3 kg /m
25. In the given diagram, four identical long wires carry current of 23A each. Wires 1 and 2 carry current
out of the page and wire 3 and 4 carry current into the page. What is the force per unit length on the
wire 2?
(F =1.27x10-4 N/m at 161.50 with +ve x axis)
26. A long solenoid has 140turns/cm and carries current ‘I’. An electron moves within the solenoid in a
circle of radius 2.20 cm perpendicular to the solenoid axis. The speed of electron is 0.048c (c=speed
of light). Find ‘I’. (0.212A)
27 Two long wires carrying current I1, and I2 are arranged as shown in the figure. The one
carrying current I, is along x-axis. The other carrying current l2 is along a line parallel to the y-axis given
by x = 0 and z = d. Find the force exerted at O2 because of the wire along
the x-axis.
28 Two identical circular loops, P and Q, each of radius r and carrying currents I
and 21 respectively arc lying in parallel planes such that they have a common axis. The direction of
current in both the loops is clockwise as seen from O which is equidistant from both loops. Find the
magnitude of the net magnetic field at point O.
29 A wire of uniform cross-section is bent into a circular loop of radius R- Consider two points
A and B on the loop, such that <AOB = θ as shown. If now a battery is connected between A and
, show thai the magnetic field at the centre of the loop will be zero
irrespective of angle θ
30.Write the expression for the force acting on a charged particle of charge q moving with
velocity v in the presence of magnetic field B - Show that in the presence of this force : i) the kinetic
energy of the particle does not change. (ii) its instantaneous power is zero.
31 'A long straight wire carrying current of 25A rests on a table as shown in the figure. Another wire
PQ of length lm, mass 2.5 g carries the same current but m the opposite direction. The wire PQ is free
to slide up and down. To what height will PQ rise?
32. Shows a right –angled isosceles ∆PQR having its base equal to a.A current of I ampere is
passing downwards along a thin straight wire cutting the plane of paper normally as shown atLikewise a
similar wire carries an equal current passing normally upwards at R. Find the magnitude and direction of
the magnitude induction B at P. Assume the wires to be infinitely long.
µ0I
B=
πa
33. An infinitely long conductor is bent into the shape as shown in .The semicircular part lies in the
YZ–plane ;While of the two straight parts ,one is along X–axis and the other parallel to Y–axis at a
distance r from it.If the conductor carries a current I, as shown in the figure ,find the magnetic field at the
centre C of the semicircular loop.
→ µ 0 2I ∧
B1 = . j
4π r
34. If the current density in a linear conductor of radius a varies with r according to the relation
:j=kr2where k is a constant and r is the distance of a point from the axis of the conductor .Find the
magnetic field at a point distance r from the axis when (i)r < a (ii) r > a
µ 0 kr 3
B=
4
35. A coil in the shape of an equilateral triangle of side 0.02 m is suspended from a vertex such that it
is hanging in a vertical plane between the pole pieces of permanent magnet producing a horizontal
magnetic field tesla.Find the couple acting on the coil when a current of 0.1A is passed through it and
the magnetic field is parallel to its plane. = 5 3 ×10 −7 Nm
36. A galvanometer having 30 divisions has a current sensitivity of 20 microampere . It has a

resistance of 20 ohm. How will you convert it into an ammeter measuring upto 1 ampere?How will you
convert this ammeter into voltmeter reading into 1volt?
0.985Ω.
37. A proton and an alpha particle enter at right angles into a uniform magnetic field of intensity
B.Calculate the radii of their paths ,when they enter the field with (i)same momentum ,(ii)same kinetic
energy.
0.15Ω 1:1
38 A particle of mass m=1.6 10-27kg and charge q=1.610-19coulomb enters a region of uniform
magnetic field of strength 1tesla along the directon shown in the figure.The speed of particle is 107ms-
1(i).The magnetic field is directed along the inwards normal to the plane of paper.The particle leaves the
region of the field at the point F. Find the distance EF and angle .(ii).If the direction of the magnetic field
is along the outward normal to the plane of paper ,find the time spent by the particle in the region of the
magnetic field after entering it at E?
(0.11414 m, 8.56 × 10-5)
39. To increase the current sensitivity of a moving coil galvnometer by 50 % its resistance is
increased so that the new resistance becomes twice its initial resistance. By what factor does its
Voltage sensitivity change ?
Ans- 25%
40. A rectangular loop of wire of size 2cm × 5 cm carries a steady current of 1A.A straight long wire
carrying 4A current is kept near the loop . If the loop and the wire are coplanar, find
i. The torque acting on the loop.
ii. The magnitude and direction of the force on the loop due to current carrying wire.
Ans- T = o F= 1.6 ×10-5
4A 1A
2 cm
Section C
Short Answer Type Question
1. A stell wire of length L has a magnetic moment M it is then bent into a semicircular arc. What is
the news magnetic movement. ?
2. If a compass needle is placed on the magnetic north pole of the earth,then Row will it behave ?
3. Assuming that earht’s magnetism is due to a large current loop within the earth,what is the plane
of the loop and the direction of current in the loop ?
4. A ber magnet is cut into 2 equal pieces i) along ii) perpendicular to its length. How does its pole
strength and dipole moment change in both cases ?
5. Can you think of a magnetic field configuration with three poles ?
6. One of the two identical bors is definitely magnetised how would you ascertain whether or not
both are magnetised ? If only one is magnetised,how do you find out which one(Using only the
two bers)
7. A current carrying solenoid tends to contract. Why ?
8. Two identical bar magnets. P & Q are placed in identical magnetic fields as shown. Which of
the two p & q is in a) equilibrium b) Stable equilibrium justify your answer
P Q
N S S N
9. A magnetic is held vertically along its length at the equator and then released.Will it strike the
ground head on or fall flat on the ground ? give reason
10. Like poles of nearby magnets repel each other and unlike poles attract each other. Explain this
behaviour in terms of interaction of current loops.
11. Compare diamagnetic, pramagnetic & ferromagnetic materials on the value of their
a) relative permeability
b) susceptibility
12. Following figure shows variation of intensity of magnetisation (I) vs applied magnetic field
intensity (H) for three magnetic materials X and Y and Z
a) Identify X, Y and Z
b) Plot variation of I with temperature for X and Z
Y
X
Z
13. Find work done by the magnetic field on a moving charged particle.
2 5 
 3
 Λx 
14. Two Identical short magnets A and B of magnetic moments on each other are placed at a
distance x with their axes perpendicular to each other.Find the magnetic field at a point midway
between the two dipoles.
15. Find curie constant for a given sample for which χ vs 1/T graph is as shown.
χ
0.6
0.4
0.2
0 2 4 6 8
1 / T ( in 10-3 K-1)
16. A magnet suspended at 300 with the magnetic meridain makes an angle of 450 with the horizontal
What is the actual value of Dip ?
17. If δ 1 and δ 2 are the angles of dip observed in two vertical places at right angles to each other
and δ is the true angle of dip,show that
Cot2 δ = Cot2 δ 1+ Cot2 δ 2
18. Copper sulphate is Paramagnetic with a susceptibility of 1.68 ×10-4 at 293 k. What is its
Susceptibility at 77.4k if it follows curie law ?
19. A short bar magnet placed with its axis at 300 with an external field 800 G experience 0.016
Nm torque.
a. what is the magnetic moments of the magnet ?
b. Find the work done in moving it from its most state to most unstable position.
[4×10-5 J/ T , 0.064 J )
20. A uniform conducting wire of length 12a and resistance R is wound up as a current carrying coil
in the shape of (i) an equilateral triangle of a side (ii) a square of scale a . The coil is connected
to a voltage sources. V0 . Find the magnetic moment of the coils in each case.
Ans 3a 2 I ,3a 2 I
given below.
21. Assertion(A): The centripetal force on the test charge qo is qo vB, where v is the velocity of a
particle and B is the magnetic field.
Reason (R): When a charged particle is fired at right angles to the magnetic field, the radius of its
circular path is directly proportional to the kinetic energy of the particle.
Answer: c
22. Assertion (A): When radius of a circular loop carrying current is doubled, its magnetic moment
becomes four times.
Reason (R): Magnetic moment depends on the area of the loop.
Answer: a
23. Assertion (A): The magnetic field at the ends of a very long current carrying solenoid is half of that at
the centre.
Reason (R): If the solenoid is sufficiently long, the field within it is uniform.
Answer: b
24. Assertion (A): The true geographic north direction is found by using a compass needle.
Reason (R): The magnetic meridian of the earth is along the axis of rotation of the earth.Answer: d
25. Assertion (A): The torque acting on square and circular current carrying coils having equal areas,
placed in uniform magnetic field, will be same.
Reason (R): Torque acting on a current carrying coil placed in uniform magnetic field does not
depend on the shape of the coil, if the areas of the coils are same.
Answer: a
CASE BASED QUESTION
FORCE BETWEEN TWO INFINITELY LONG PARALLEL CURRENTCARRYING
WIRES
Two current-carrying conductors placed near each other will exert magnetic forces on each other. Ampere
studied the nature of this magnetic force and its dependence on the product of magnitude of currents in
both the conductors, on the shape and size of conductors as well as the distances between the conductors.
Using Fleming's left hand rule, it is observed that currents flowing in the same direction attract each other
and currents flowing in the opposite directions repel each other. Thus, force per unit length acting on a
conductor of infinite length is given by
1. A vertical wire carries a current in upward direction. An electron beam sent horizontally towards
the wire will be deflected
(a)towards right (b)towards left (c)upwards (d)downwards
2. A current carrying, straight wire is kept along axis of a circular loop carrying a current. The
straight wire
(a) will exert an inward force on the circular loop.
(b) will exert an outward force on the circular loop.
(c) will not exert any force on the circular loop.
(d) will exert a force on the circular loop parallel to itself.
3. A proton beam is going from north to south and electron beam is going from south to north.
Neglecting the earth's magnetic field, the electron beam will be deflected
(a) towards the proton beam (b)away from the proton beam (c)upwards (d)downwards
4. Consider the situation shown in fig. The straight wire is fixed but the loop can move under magnetic
force. The loop will
(a) remain stationary (b) move towards the wire

(c) move away from the wire (d) rotate about the wire.
Ans: 1 (c) 2 (c) 3 (a) 4 (b)
Unit - ELECTROMAGNETIC INDUCTION & ALTERNATING CURRENTS
MCQ
1. Whenever the flux linked with the circuit changes there is an induced emf in the circuit.This emf
in the circuit lasts.
a) for a very short duration b) for a very short duration C) forever
d) As long as magnetic flux changing
Ans d)
2. Len’z law is essential for
a) Conservation of energy b) Conservation of mass
c) Conservation of Momentum d) Conservation of charge.
Ans a)
3. Inductance play the role of
a) Inertia b) Friction c) Source of emf d) Force
Ans a)
4. The Mutual inductance of two coil depends upon
a) Medium between coils b) Seperation between coils
c) Both on a) and b) d) None of a) and b)
Ans c)
5. A copper ring is held horizontally and a magnet is dropped through the ring with its length along
the axis of the ring. The acceleration of the falling magnet is ___________.
a) equal to that due to gravity
b) less than that due to gravity
c) More than that due to gravity
d) depends on diameter of ring.
Ans b)
6. When the current in a coil changes from 8A to 2A in 3 ×10-2 S, the emf induced in th coil is 8V.
The self inductance of the coil is
a) 0.1H b) 0.2H c) 0.4H d) 0.8H
Ans d)
7. The area of square shaped coil is 10-2 m2 . Its plane is perpendicular to magnetic field of strength
10-3T.The θ B linked with coil is ______________.
a) 10Wb b) 10-5wb c) 10 5wb d) 100wb

Ans b)
8. Electrical energy is transmitted over large distance at high alternating voltages.Which of the
following statement is/ are correct.
a) For a given power level, there is a lower current
b) flower current implies less power loss.
c) It is easy to reduce the voltage at the receiving end using step down transformers.
Ans a) , b) ,d)
9. If an LCR circuit contain L= 8H , C=0.5uF ,R = 100 r in series. Then the resonant
frequency will be
a) 600 rad/s b) 500 rad/s c) 600Hz d) 500Hz
Ans b)
10. The average power dissipation in pure inductance is
1 2 1 2
a) LI b) LI c) 2LI 2 d) O
2 4
Ans d)
11. Which of the following combination should be selected for better tunning of an LCR circuit used
for communication ?
a) R = 20 r , L = 1.5 H , C = 35 µF b) R = 25r , L = 2.5 H , C = 45µF

c) R = 15r , L = 3.5 H , C = 30 µF d) R = 25r , L = 1.5 H , C = 45µF
Ans c)
12. An A.c voltage source E = 200 2 sin 100t, is connected across a circuit containing an Ac
ammeter and a capacitor of C= 1uF.The reading of ammeter is
a) 10mA b) 20 m A c) 40 m A d) 80 m A
Ans b)
13. The average value of ac voltage ( V = V0 Sin wt) over the time interval t =0 to t = π / ω is
Vo Vo 2Vo Vo
a) b) c) d)
π 2π 2π 2
Ans c)
14. The rms value of altenating current shown in fig is
a) 4A b) 2A c) 1A d) 2 2A
Ans b)
Assertion -Reason Questions
a) A and R both are correct and R is correct explanation of A
b) A and R both are correct and R is not correct explanation of A
c) A is correct but R is wrong
d) A is wrong but R is correct
15. A: an A.c(I) of frequency 50 Hz becomes O, 100 times in one seocnd

R: A.c (I) changes direction and becomes zero twice in a cycle.
Ans a)
16. A: A capacitor of suitable capacitance can be used in an Ac circuit in place of the choke
coil
R: A capacitor block DC and allows only AC
Ans b)
17. A: An alternating current does not show any magnetic effect.

R: Alternating current varies with time.
Ans b)
18. A: Only a change of magnetic flux will maintian an induced current in the coil.
R: The presence of large magnetic flux will maintain the induced current in the coil.
Ans c)
19. A: In the phenmenon of mutual induction,self induction of each of the coil persists.
R: Self Induction arise when strength of current in same coil changes.In mutual induction
current is changed in both individual coils.
Ans a)
20: A: When a rod moves in a transverse magnetic field, an emf is inuduced in the rod: the end
becomes magnetic with end A positive.
R: A torentz force evb acts on free electrons , so electrons move from B to A, thus making
end B positive and A negative.
Ans d)
given below.
21. Assertion (A)— The mutual induction of two coils is doubled, if the self-inductance of the primary
or secondary coil is doubled.
Reason(R) — Mutual induction is proportional to self-inductance of primary and secondary
coils.
Answer – C
22. Assertion (A)- Eddy current is produced in any metallic conductor when magnetic flux is changed
around it
Reason (R)— Electric potential determine the flow of charge
Answer – B
23. Assertion (A)- Inductance coil are made of copper
Reason (R) — Induced current is more in wire having less resistance
Answer – A
24. Assertion (A):A capacitor of suitable capacitance can be used in AC circuit in the place of choke
coil
Reason (R) — A capacitor blocks DC and allow only AC
Answer – B
25. Assertion (A): When capacitive reactance is smaller than the inductive reactance in LCR circuit, emf
leads the current.
Reason (R): The phase angle is angle between alternating emf and alternating current of the
circuit.
Answer – B
CASE STUDY QUESTION
A small town with a demand of 800 kW of electric power at 220 V is situated 15 km away from an
electric plant generating power at 440 V. The resistance of the two-wire line carrying power is 0.5&!
per km. The town gets power from the line through a 4000-220 V step-down transformer at a sub-
station in the town.
1.Current flowing through the line is
(a) 200A (b) 100A (c) 30A (d) 15A
2. The line power loss in the form of heat is
(a) 800MW (b) 600MW (c) 1400MW (d) 300MW
3. Total power supplied by the plant, assuming there is negligible power loss due to leakage?(a)
600MW (b) 1000 MW (c) 800 MW (d) 1400MW
4.The characteristics of transformer used at power plant is
(a) 440V-4000V (b) 440V-7000V (c) 7000V-200V (d) 220V-7000V
Anaswers: 1. a 2. b 3. d 4. b
Very Short Answer Question
1. The electric current passing through the wire AB is decreasing. In which direction does the
induced current flow in the closed loop. Justify your answer.
13
14
15
16 Circuit shown here use an air filled parallel plate capacitor. A mica sheet is
now introduced between the plates of capacitor. Explain with reason the
effect on brightness of the bulb B.
17.
18. The power factor of an AC circuit is 0.5 what is the phase difference between voltage and
current in this circuit. ?
Ans π / 3
19. How much current is drawn by the primary coil of a transformer which steps down 220 V to 22
V to operate a device with an impedance of 220V
Ans ( 0.1A , 0.01A)
20. A circular coil of cross-sectional are 200 cm2 and 20 turns is rotated about the vertical diameter
with angular speed of 50 rad/s in a uniform magnetic field of magnitude 3.0 × 10-2T .Calculate
the maximum value of the current in the coil .
600
Ans (I max = mA )
R
SHORT -ANSWER QUESTIONS & NUMERICALS
Q.1. As shown in Fig. a conducting rod Ab moves parallel to X-axis in a uniform magnetic field,
pointing in the positive Z-direction. The end A of the rod gets positively charged. Is this statement
true? Give reason.
Q. 2. Two circular loops are placed with their centres separated by a fixed distance. How would you
orient the loops to have (i) the largest mutual inductance and (ii) the smallest mutual inductance?
Q. 3. Two circular coils, one of radius r and the other of radius R are placed coxially with their centres
coinciding. For R>r, obtain an expression for the mutual inductance of the arrqangement.
Q. 4. A circular coil of radius 10 cm, 500 turns and resistance 2 Ω is placed with its plane perpendicular
to the horizontal component of the earth’s magnetic field. It is rotated about its vertical diameter
through 180 in 0.25 s. Estimate the magnitudes of the emf and current induced in the coil.
Horizontal component of the earth’s magnetic field at the place is 3.0 × 10 −5 T .
(Ans. 3.8 × 10 −3V ,1.9 ×10 −3 A )
Q. 5. A copper rod of length L roates with an angular speed ‘w’ in a uniform magnetic field B. Find the
emf developed between the two ends of the rod. The field is perpendicular to the motion of the
rod.
1 2
(Ans. BL W )
2
Q. 6. A horizontal straight wire 10 m long extending from east to west is falling with a speed of
5.0 m s-1, at right angles to the horizontal component of the earth’s magnetic field, 03.0 × 10 −4
Wb m-2.
(a) What is the instantaneous value of the emf induced in the wire?
(b) What is the direction of the emf?
(c) Which end of the wire is at the higher electrical potential?
(1.5 mV, east to west, eastern end)
Q. 7. What is the maximum value of power factor? When does occur?
Q. 8. Answer the following questions :
(a) For circuits used for transporting electric power, a low power factor implies large power
loss in transmission. Explain.
(b) Power factor can often be improved by the use of a capacitor of appropriate capacitance
in the circuit. Explain.
(c) A lamp is connected in series with a capacitor. Predict your observations for d.c. and a.c.
connections. What happens in each case if the capacitance of the capacitor is reduced?
Q. 9. A uniform magnetic field exists normal to the plane of the paper over a small region of space. A
rectangular loop of wire is slowly moved with a uniform velocity across the field as shown.
Draw the graph showing the variation of (i) magnetic flux linked with the loop and (ii) the induced
e.m.f. in the loop with time.
Q. 10. How does the self inductance of an air core coil change, when (i) the number of turns in the coil is
decreased, (ii) an iron road is introduced in the coil?
A copper coil L wound on a soft iron core and a lamp B is connected to a battery E through a
tapping key K. When the key is closed, the lamp glows dimly. But when the key is suddenly
opened, the lamp flashes for an instant to much greater brightness. Explain.
Q. 11. An a.c. generator consists of a coil of 50 turns and area 2.5 m 2 rotating at an angular speed of 60
rad S −1 in a uniform magnetic fielf B = 0.30 T between two fixed pole pieces. The resistance of
the circuit including that of the coil is 500 Ω .
(i) Find the maximum current drawn from the generator.
(ii) What will be the orientation of the coil with respect to the magnetic fielf to have (a) maxi-
mum (b) zero magnetic flux? Ans.(4.5 A)
Q. 12. The electric current flowing in a wire in the direction B to A is decreasing. What is the direction of
induced current in the metallic loop kept above the wire as shown in Fig.
(Ans. Clockwise)
Q. 13. When an alternating voltage of 220 V is applied across a device X, a current of 0.5 A flows
through the circuit and is in phase with the applied voltage. When the same voltage is applied
across another device Y, the same current flows through the circuit but it leads the applied voltage
by π 2 radian. (i) Name the devices X and Y. (ii) Calculate the curent flowing in the circuit, when
same voltage is applied across the series combination of X and Y.
(Ans. (a) X : Resistor, Y : capacitor (b) 0.35 A)
Q. 14. What will be the readings in the voltmeter and ammeter of the circuit shown in Fig. ?
(Ans. 2A, 0V)

Q. 15. Fig. given below shows how the reactance of a capacitor varies with frequency.
(i) Use the information on graph to calculate the value of
capacity of the capacitor. Xc
(ii) An inductor of inductance ‘L’ has the same reactance

as the capacitor at 100 Hz. Find the value of L. 6
(iii) Using the same axes, draw a graph of reactance

against frequency for the inductor given in part (ii).
2
(iv) If this capacitor and inductor were connected in se-
ries to a resistro of 10 Ω , what would be the imped-
ance of the combination at 300 Hz? 100 Hz 300 Hz
F
(Ans. (i) 2.65 × 10 −4 F , (ii)

9.459 × 10 −3 H (iv) 18.87 Ω )
Q. 16. In fig. given below, a bar magnet moving towards the right or left induces an e.m.f. in the coils (1)
and (2). Find, giving reason, the directions of the induced currents through the resistors AB and
CD when the magnet is moving (a) towards the right, and (b) towards the left.
(Ans. (a) A to B & D to C (b) B to A & C to D)
Q. 17. Fig. below shows two identical rectangular loops (1) and (2), placed on a table along with a
straight long current carrying conductor between them.
(i) What will be the directions of the induced currents in the loops when they are pulled away
from the conductor with same velocity v?
(ii) Will the emfs induced in the two loops be equal?
Justify your answer.
(Ans. (a) Anticlockwise in loop 1 & clockwise in loop 2, (b) No. )
Q. 18. A coil when connected across a 10 V d.c. supply draws a current of 2 A. When it is connected
across a 10 V - 50 Hz a.c. supply, the same coil draws a current of 1 A. Explain why it draws
lesser current in the second case. Hence determine the self inductance of the coil. (Take π = 3 ).
(Ans. L = 0.0282H)
Q.19. A 100 mH inductor, a 20 µF capacitor and a 10 ohm resistor are connected in series to a 100 V,
50 Hz a.c. source. Calculate : (i) Impedance of the circuit at resonance (ii) Current at resonance
(iii) Resonant frequency.
(Ans. 10 Ω , 10 A, 0.0288H)
Q. 20. When 200 volts d.c. are applied across a coil, a current of 2 ampere flows through it. When
200 volts a.c. of 50 cycles are applied to the same coil, only 1.0 ampere flows. Calculate the
resistance, impedance and inductance of the coil. (Ans. 100 Ω , 1.76 H)
Q.21.In the given circuit, the potential difference across the inductor L and resistor R are 120 V and 90
V respectively and the r.m.s. value of current is 3 A. Calculate (i) the impedance of the circuit and
(ii)the phase angle between the voltage and the current.


 Ans.

50
2
( )
Ω, tan −1 4 
3


Q. 22. A horizontal telephone wire 1 km long is lying east-west in earth’s magnetic field. It falls freely to
the ground from height of 10 m. Calculate the emf induced in the wire on striking the ground.Given
BH = 0.32 G..
(Ans. 0.448 V)
Q. 23. In a celling fan, each blade roates in a circle of radius 0.5 m. If the fan makes 20 revolutions
per second and if the vertical component of earth’s field is 8 × 10 −5 Wb m −2 , calculate the p.d.
developed between the ends of each blade.
(Ans. 0.001 T)
Q. 24. Fig. below shows how the reactance of an inductor varies with frequency.
(i) Calculate the value of the inductance of the inductor using the informaton given in the
graph.
(ii) If this inductor is connected in series to a resistor of 8 ohm, find what would be the
impedance at 300Hz?
(Ans. (i) 3.18 × 10 −3 H (ii) 10 Ω
Q. 25. A current of 2.0 A is flowing in the LR-circuit shown in Fig. Find the voltage supplies the a.c.
source and the impedance of the circuit.
(Ans. 260 V, 130 Ω )
Q. 26. An a.c. circuit consists of a 220 V, 50 Hz supply connected across a 100 Ω resistor. What
inductance should be connected in the circuit in series with resistance so that the current is re-
duced to half?
(Ans. 0.55 H)
Q. 27. A 200 V variable frequency a.c. source is connected to a series combination of L = 5 H, C =
80 µF and R = 40 Ω . Calculate (i) angular frequency of the source to get maximum current in the
circuit, (ii) the current amplitude at resonance and (iii) the power dissipated in the circuit.
(Ans. 50 rod S-1, 7.07A, 1000 W)
28 A magnetic field in a certain region is given by B=B0cos(wt) k and a coil of radius a with resistance
k is placed in the x-y plane with its centre at the origin in the magnetic field (fig).Find the magnitude and
the direction of the current at(a, 0, 0) at t = /2w, t = /w and (= 3 / 2w).
(B0AW ,0 ,-B0AW)
29 A conducting wire XY of mass m and negligible resistance slides smoothly on two parallel con-
ducting wires as shown in figure. The closed circuit has a resistance R due to AC AB and CD are
perfect conductors. There is a magnetic field B = B(t)k
(i)Write down equation for the acceleration of the wire XY.

(ii) If B is independent of time, obtain v{t) assuming v (0) = u0
(iii) show that the decrease in kinetic energy of XY equals the heat lost in R.  B 2 L2V B 2 L2 t 
 , V = V0 e − 
 mR mR 
30. When 100v d.c is applied across a coil, a current of 1A flows through it.When 100v a.c of 50 c/s
are applied to the same coil only 0.5A flows.Calculate the resistance the impedance and the
inductane of coil.
31. A circuit draws a power of 550 W from a source of 220 V,50 Hz.The power factor of the circuit
is 0.8. The current in the circuit lags behind the voltage.Shows that a capacitor of about
1 x 10-2 F will have to be connected in the circuit to bring its power factor to unity.
42π
32. A toroidal solenoid with air core has an average radius of 15 cm,area of cross section 12 cm 2 and
has 1200 turns.Calculate the self inductance of the toroid.Assume the field to be unifrom across
the cross section of torroid. (230.4 x 10-4 H)
33. The currents flowing in the two coils of self inductance L1 = 20 mH and L2 = 15 mH are increasing
at the same rate.If the power supplied to the two coils are equals,find the ratio of (i) Induced voltages
(ii)Currents (iii) energy stored in the two coils at a given instant. ( 4/3 , 3/4 , 3/4)
34. A conducting rod held horizontally along East-west direction is dropped from rest from a certain height
near the earth surface.Why should there be an induced in across the end of rod.? Draw a plot showing the
instantaneous variation of emf as a function of time from the instant it began to fall.
35. A resistor R and element X(Capital) are connected in series to an ac source of voltage.The
voltage is found to lead the current in phase by π/4 . If X is replaced by another element Y the voltage
lags behind the current by π/4.
(a) Identify X and Y

(b) When X and Y are connected in series with R to the same source,will the power dissipated in the
circuit be maximum or minimum ? justify. (X inductor, Y Y capacitor maximum due to resonance)
Q36. A solenoid of 500turns /mis carrying a current of 3 A.Its core is iron which has a relative
permeablity of 5000.Determine the magnitude of the magnetic intensity ,magnetisation of the magnetic
field inside the core. ( 1500 A/m , 7.5 × 106 A/m )
Q37. An LC circuit contains a 20mh inductor and a 50 µF Capacitor with an initial charge of 10mc.The
resistance of the circuit is negligible.Let the instant when the circuit is closed be t = 0
a) What is the total energy stored initially ?
b) What is the natural frequency of the circuit ?
c) If a resistor is inserted in the circuit how much energy is eventually dissipated as heat .
(10 J, 159 Hz)
Q38 A square metal wire loop of side 10 cm and resistance 1 ohm is moved with a constant velocity
vo in a uniform magnetic field of induction B = 2Wbm~2 as shown in Fig. 6.19 The magnetic lines are
perpendicular to the plane of the loop (directed into the paper). The loop is connected to a network of
resistors each of value 3 d. The resistance of the loop wires OS and PQ are negligible. What should be
the speed of the loop so as to have a steady current of 1 mA in the loop ? Give the direction of the
current in the loop ? Ans- ( 2m/s) [CBSE.OD 06C]
Q39 A circular loop of radius 0.3 cm lies parallel to a much bigger circular loop of radius 20 cm. The
centre of the small loop is on the axis of the bigger loop. The distance between their centres is 15 cm.
(a) What is the flux linking the bigger loop if a current of 2.0 A flows through the smaller loop ? (b)
Obtain the mutual inductance of the two loops. ( 9.7 × 10-11 W6)
Q40 A series LCR-circuit is connected to an “a.c. source (220 V-50Hz), as shown in Fig.. If the voltages
of the three voltmeters V1 V2 and V3 are 65 V, 415 V and 204 V respectively, calculate:
(i) the current in the circuit,
(ii) the value of the inductor L,
(iii) the value of the capacitor C, and
(iv) the value of C (for the same L) required to produce resonance.
( 0.65 A, 1H,5µF)
15. Under what condition is conduction current same as displacement current. ?
16. Obtain SI unit of displacement current.
17. The charging current for a capacitor is 2.5 A Find the displacement current across its plates
18. A capacitor is fully charged by a d.c source what are the magnitudes of conduction and displace
ment currents ?
19. The em waves consist of oscillating electric & magnetic fields. What is the phase relation
between these oscillations. ?
20. The charge on a paralled plate capacitor varies as q = qo sin 2πvt .The plates are very large
and close together.Find the displacement current through the capacitor.
21. Name any two properties common to all parts of em spectrum.
22. Show that sum of conduction current and displacement current has the same valve everywhere
in the circuit.
23. em waves with wavelength.
a) λ1 are used to detect fracture in bones
b) λ2 are used to treat muscular strain
c) λ3 are used for aircraft navigation
d) λ4 are used in treatment of malignant tumour.

Name the part of spectrum to which these radiations belong and arrange in increasing order
of magnitude.
10. Which of the two ratios A and B is less than,equal to or greater than unity.
υ x ray λvisbile
A= Β=
υ uv λr − rays
11. A small metal ball is charged positively & negatively in a sin υ soidal manner at a frequency of 5
Mhz .Find the displacement current due to this if the maximum charge on the ball is 2 µ c
12. At what rate should the potential difference between the plates of a parallel plate capacitor
of capitance 1 uF be changed to establish a displacement current of IA [106 v/s ]
13. Calculate the peak values of electric and magnetic fields produced by the radiation. coming
from a 100 W bulb at a distance of 3m. Assume that the efficiency of the bulb is 2.5%
[ 4.08 V/m , 1.36 × 10-8 T]
14. em waves travel in a medium at a speed of 2 × 108 m /s . if the relative permeability of the
medium is 1.0. find the relative permitibility of the medium . [ 2.25]
ASSERTION-REASON QUESTIONS
A. Both assertion and reason are True, and reason is the correct explaination . ?
B. Both assertion and reason are True, but reason is not the correct explaination . ?
C. Assertion is True , but reason is False . ?
D. Both assertion and reason are False . ?

1. Assertion: Electromagnetic waves do not require medium for their propagation.
Reason: They can't travel in a medium.
Answer: C
2. Assertion: A changing electric field produces a magnetic field.
Reason: A changing magnetic field produces an electric field.
Answer: B
3. Assertion: X-rays travel with the speed of light.
Reason: X-rays are electromagnetic rays.
Answer: A
4. Assertion: Environmental damage has increased amount of Ozone in atmosphere.
Reason: Increase of ozone increases amount of ultraviolet radiation on earth
Answer: D
5. Assertion: Electromagnetic radiation exert pressure.
Reason: Electromagnetic waves carry both - Momentum & Energy.
Answer: B
6. Assertion: During discharging, there is magnetic field between plates of capacitor.
Reason: Time varying electric field produces magnetic field.
Answer: A
CASE STUDY QUESTIONS TOPIC: ELECTROMAGNETIC WAVES
Q1)Microwave in aircraft navigation
Microwave are used in aircraft navigation. A radar guns out short bursts of microwave and it reflect
back from oncoming aircraft and are detected by receiver in gun. The frequency of reflected wave used
to compute speed of aircraft
1 Q) How are microwave produced?
a) klystron and magnetron valve
b) sudden deceleration of electron in x- ray tube
c) accelerated motion of charge in conducting wire
d) hot bodies and molecules
2 Q) why microwave use for aircraft navigation?
a) due to high wavelength
b) due to low wavelength
c) due to low frequency
(d) due to their frequency modulation power
3 Q) which is use of microwave?
a) in treatment of cancer
(b) to observe changing blood flow
c)used to kill microbes
(d)studying details of atoms and molecule
4 Q) where do microwave fall in electromagnetic spectrum?
a) between u.v region and infrared
b) between gamma and u.v
c)between infrared and radio wave
(d)between gamma and infrared
ANSWER KEY 1)a 3)d 2)b 4)c
Unit - Ray Optics
Code: 12P (10 & 11)
Section A
Choose the correct alternative
1. When a ray of white light enters from air into a glass lens, it undergoes a change in
a) frequency only b) speed only
c) frequency & speed only d) wavelength & speed only
2. A light bulb is placed between two plane mirrors inclined at an angle of 60°. The number of images
formed are
a) 4 c) 6
b) 2 d) 5
3. Two media are separated by a plane surface having speeds of light 2 ×108 m/s & 2.4x108 m/s
respectively. The critical angle for a ray going from first medium to 2nd is
-1
a) sin ½b c) sin–1 5/12
–1
b) sin 5/6 d) sin–1(l/2)
4. An air bubble in water shines because of
a) dispersion b) refraction
c) diffraction d) total internal reflection
5. Two lenses of power +12D & -2D are placed in contact. The focal length of the combination is
a) 10 cm c) 16.6 cm
b) 12.5cm d) 8.33 cm
6. A double convex lens of ml .55 for violet rays & ml .50 for red rays. If the focal length for violet rays
is 20cm, then focal length for red rays will be
a) 6cm c) 20cm
b) 18cm d) 22cm
7. A short linear object of length b lies along the axis of a concave mirror of focal length f at a distance
u from the pole of the mirror. The size of the image is approx equal to
a) b(u-f/)½ b) b(f/u-f)½
c) b(u-4/f) d) b(f/u-f)2
8. A convex lens of u=l .5 has a focal length of 18cm in air. The change in focal length of the lens when
immersed in water (u=1/3) is
a) 18cm b) 72cm
c) 36cm d) 54cm
9. A ray incident on a 50° angled prism of refractive index 2 suffers minimum deviation. The angle of
incidence is
a) 75° b) 0°
c) 45° d) 60°
10. The magnifying power of a telescope can be increased by
a) by increasing focal lengths
b) by fitting eyepiece of higher power
c) by fitting eye piece of lower power
d) by decreasing diameter of the objective lens
UNIT-VI OPTICS
Instructions:?Two statements are given-one labelled Assertion (A) and the other labelled Reason (R).
Select the correct answer to these questions from the codes (a), (b), (c) and (d) as given below.
a) Both A and R are true and R is the correct explanation of A?
b) Both A and R are true but R is NOT the correct explanation of A
c) A is true but R is false
d) A is false and R is also false
Case based Questions (Ray optics)
1) Total internal reflection
(i) What is refractive index of a medium(in terms of speed of light)

a) Speed of light in medium/speed of light in vacuum
b) Speed of light in vacuum/speed of light in medium
c) Speed of light in medium × speed of light in vacuum
d) None of the above.
(ii) In the above diagram, calculate the speed of light in the liquid of unknown
refractive index.
a) 1.2 × 108 m/s
b) 1.4 × 108 m/s
c) 1.6 × 108 m/s
d) 1.8 × 108 m/s
(iii) What is refractive index of a medium(in terms of real and apparent depth).
a) Real depth/ App depth
b) App/ Real depth
c) App ´ Real depth
d) Real + App depth
(iv) What is the relation between refractive index and critical angle for a medium.
a) n = 1/sin ic
b) n = sin ic
c) 1 = n/ sin ic
d) None of the above
Answer:
i) (b)
ii) (d)
iii) (a)
iv) (a)
SECTION - B
1. (a) a short linear object of length b lies along the axis of a concave mirror of focal length f at a
distance u from the pole. What is the size of image?
(b) If object beings to move with the speed V0, what will be the speed of its image?
f 2
[Vi= ( ) V0 ]
4− f
2. A thin rod of length f/3 is placed along the optic axis of a concave mirror of focal length f such that its
image, which is red and elongated, just touches the rod. Calculate the magnification produced by the
mirror.
[3/2]
3. An object is kept in front of a concave mirror of focal length 20 cm. The image formed is three times
the size of the object. Calculate two possible distances of the object from the mirror.
[80/3, 40/3]
4. When an object is placed at a distance of 0.60m from a convex spherical mirror, the magnification
produced is ½. Where should the object be placed to get a magnification of 1/3?
[1.2m]
5. A ray of light incident on an equilateral prism shows minimum deviation of 300. Find the speed of
light through the glass prism.
[2.12 x108m/s]
6. A ray of light passes through an equilateral glass prism such that the angle of incidence equals the
angle of emergence. If the angle of emergence equals ¾ times the angle of the prism, find the refrac-
tive index of glass prism.
[ 2]
7. AB and CD are surfaces of two slabs as shown in the figure. The medium between the slabs has
refractive index 2, refractive index of slab above AB and below CD are 2 and 3 respectively.
Find the minimum angle of incidence at Q so that the ray is totally reflected by both the slabs.
( imin= 600)
8. (a) Light is incident on the prism ABC at angle of
A D
incidence i as shown in figure. Find the value of i
so that the deviation produced by prism ABC is
minimum.
(b)
Another similar prism DCE is now fixed at point 60
0
60
0
C 60
0
600
B E
C, which can rotate about the axis passing
through C and perpendicular to the plane of paper. By what angle will the prism DCE be rotated, so
that the final emergent ray should have minimum deviation? It is given that the refractive index of
material of both the prism is 3 .
(i=600,ACW 600)
9. A tank contains a slab of glass 8 cm thick and R.I =1.6. Above this is a depth of 4.5 cm of a liquid
of R.I = 1.5 and upon this floats 6 cm of water R.I = 4/3. To an observer looking from above, what
is the apparent position of mark on the bottom of the tank?
(6cm from bottom)
10. A point light source is placed on the principal axis of a concave mirror of radius of curvature 30 cm
at a distance of 20cm from its pole. At what distance from the concave mirror should a plane mirror
be kept so that the plane mirror reflects back the light to the point of the location of the source?
(20cm from source)

11. A coin is lying at the bottom of a beaker and a microscope is focuses on it. The microscope is raised
up by 2cm. To what height should the oil of refractive index 1.25 be filled in the beaker so as to bring
coin again into focus?
(10cm)
12. Three rays of light – red(R), green (G) and blue (B)- are incident on the face AB of a right-angled
prism ABC. The refractive indices of the material of the prism for red, green and blue wavelengths
are 13.9, 1.44 and 1.47 respectively. Trace the path of rays through the prism. How will the situa-
tions change, if these rays are incident normally on one of the faces of an equilateral prism?
13. A ray of light is incident at an angle of 600 on one face of a prism, which has an angle of 300. The ray
emerging out of the prism makes an angle of 300 with the incident ray. Show that the emergent ray
is perpendicular to the face through which it emerges and calculate the refractive index of the mate-
rial of the prism. ( 3 )
14. A converging beam of light forms a sharp image on a screen. A lens is placed on the path of the
beam, lens being 10cms from the screen. It is found that the screen has to be moved 8 cm farther
away from the lens to obtain a sharp image. Find the focal length of the lens and state whether it is
concave or a convex lens.
(Concave, 22.5cm)
15. A convex lens has a foal length 25cm. An object placed in front of the lens produces its image at 110
cm. On placing a convex mirror at 10 cm behind the lens, the image coincides with the objects itself.
What is the focal length of the convex mirror?
(50cm)
16. A convex lens of focal length 120 cm in air is immersed in water whose refractive index 4/3. Find the
apparent change in the focal length of the lens.
(60cm)
17. A beam of light converges to a point P. A lens is places in the path of the convergent beam 12cm from
P. At what point does the beam converge if the lens placed is (i) convex lens of focal length 20 cm (ii)
a concave lens of focal length 16cm?
18. A figure divided into squares each of size 1mm2, is being viewed at a distance of 9cm through a
magnifying lens of focal length 10 cm, held close to the eye.
a) What is the magnification produced by the lenses? How much is the area of each square is the virtual
image?
b) What is the angular magnification of the lens?
(1cm2, 2.8)
19. Two lenses of powers 15D and –5D are in contact with each other forming a combination lens
a) What is the focal length of this combination?
b) An object of size 3cm is placed at 30 cm from this combination of lenses. Calculate the position and
size of image formed? (10cm, -1.5cm)
20. A screen is place 90 cm from an object, the image of the object on the screen is formed by a convex
lens at two different locations separated by 20 cm. Determine the focal length of the lens?
(21.4cm)
21. Show that a convex lens produces N times magnified image when the object distances, from the
 f 
lens, have magnitude  f ±  . Where f is the magnitude of the focal length of lens. Find the two
 n
values of object distance from which a convex lens, of power 2.5 D, will produce an image that is the
four times as large as the object?
22. For a converging lens R1 = R2 = 24 cm and refractive index 1.6. (i) Calculate its focal length is air
(ii) if the lens is split vertically into two identical parts, what is the focal length of each part.
(f=20cm, f’=40 cm)

23. Focal length of a plano convex lens is 15cm. The object is placed at A The plane side is silvered.
Find the position of image.
(12cm on left of lens)
24. An equivconvex lens with the radii of curvature of magnitude R each is put over a liquid layer poured
on top of a plane mirror. A small needle, with its tip on the principal axis of the lens, is moved along
the axis until its inverted real image coincides with the needle itself. The distance of the needle from
the lens is measured to be ‘a’. On removing the liquid layer and repeating the experiment the dis-
R (a − b)
tance is found to be ‘b’. Obtain a formula for the refractive index of the liquid. [1+ ]
ab
25. A point source S is placed at a distance of 15cm from a converging lens of focal length 10 cm on its
principal axis. Where should a diverging mirror of focal length 12 cm be placed to that a real image
is formed on the source itself? (6cm right of lens)
26. A point object is placed at a distance of 15cm, from a convex lens. The image is formed on the other
side at a distance of 30 cm from the lens. When a concave lens is place in contact with the convex
lens, the image shifts away further by 30 cm. Calculate focal lengths of two lenses.
(10cm,60cm)
27. A diverging lens of focal length 10 cm are placed coaxially and a converging mirror of focal length
10cm at a separation of 5cm. Where should an object be placed so that a real image is formed at the
object itself?
(60cm from the lens, further away from mirror)
28. In the adjoining figure the direct image formed by the lens (f=10cm) of an object at ÐO and that
formed after reflection from the spherical mirror are formed at the same point O. What is the radius
of curvature of mirror?
Fig for Q. 29 Fig. for Q. 28

29. A biconvex thin lens is prepared from glass µ =1.5, the two bounding surfaces having equal radii of
25 cm each. One of the surfaces is silvered from outside to make it reflecting. Where should an
object be placed before above lens so that the image is formed on the object itself?
(-12.5cm)
30. An object is approaching a thin convex lens of focal length 0.3m with a speed of 0.01 m/s. Find the
magnitude of rate of change of position and lateral magnification of image when the object is at
distance of 0.4m from the lens.
(0.09m/s, 0.3)
31. A figure divided into squares each of size 1mm2is being viewed at a distance of 9cm through a
magnifying glass (a converging lens of focal length of 10 cm) held close to eye
(i) What is the magnification produced by the lens? How much is the area of each square in the image?
(ii) What is the angular magnification?
(10,1cm2, 2.8)
32. An object is to be seen through a simple microscope of focal length 12 cm. where should the object
be placed so as to produce maximum angular magnification? (8.1cm)
33. How does the revolving power of a microscope affected when

(i) Wavelength of light is decreased
(ii) Diameter of objective lens is decreased
(iii) Focal length of objective lens is increased
(increase, decrease, decrease)
34. An astronomical telescope having an objective of focal length 2m and eye piece of focal length 1 cm
is used to observe a pair of stars with actual angular separation of 0.75. What would be their
observed angular separation as seen through telescope?
(50)
35. The magnifying power of an astronomical telescope in normal adjustments is 80 and length of tube is
20cm. what is the focal length of the objective and eye piece.? (19.75,0.25cm)
36. Using the data given below, state which lenses you use and an eyepiece and the objective to con-
struct telescope and compound microscope. Give reasons
Lense Power Aperture

L1 3D 8cm
L2 6D 1cm
L3 10D 1cm
37. Tower of 100 m tall at a distance of 3km is seen through a telescope having objective of focal length
140cm and eye piece of focal length 5cm. What is the size of final image if it is at a distance of 25cm
from the eye?
(-28cm)
38. An astronomical telescope has an angular magnification of 5 for normal adjustment. The separation
between objective and eyepiece is 36cm. Determine focal lengths of each. (30,6cm)
39. A compound microscope with an objective of 2.0 cm focal length and eyepiece of 4.0cm focal
length has a tube length of 40 cm. calculate the magnifying power, if image is formed at the near point
of the eye. (-5)
40. Two convex lenses of some focal length but aperture 5cm and 10 cm are used as objective lenses in
two astronomical telescopes
(i) ratio of their resolving powers
(ii) intensity of image.
(1/2,1/4)
41. A 40-year-old person requires glasses with lenses of 2D power to read a book at 25 cm. What is his
near point? After few years he finds that he must hold the book 40 cm from his eyes. What is his near
point now and what power does he require now to read a book again at 25cm.
(50cm,200cm,+3.5D)
42. At what angle should a ray of light be incident on the face of a prism of refracting angle 60° so that
it just suffers total internal reflection at the other faces ? The refractive index of.prism is 1.524.
43. A compound microscope has an objective lens of focal length 1.25 cm and eye piece of focal length
5 cm. A small object is kept at 2.5 cm from the objective.If the final image is at infinity,fluid distance
between objective lens and eye piece. (7.5 cm)
44 A light ray falls on a transparent spheres as shown in fig.The ray emerges from the spheres parallel
to line AB.Find the angle of refraction at A if refractive index of glass is ( 30o)
45 A convex lens of focal length 20 cm is placed coarally with a convex mirror of radius of curvature 20
cm.The two are kept 15 cm apart.A point object is placed 40 cm in front of the convex lens.Find the
position of the image formed by this combination draw the ray diagram.
( 16.67 cm away from mirror)
46. A convex lens of focal length 20 cm is placed coaxially with a concave mirror of focal lengths 10
cm at a distance of 50 cm apart from each other.A beam of light coming parallel to the principal axis is
incident on the convex lens.Find the position of final image.Draw ray diagram
(15 cm from concave mirror)
RAY OPTICS
WAVE OPTICS
WAVE OPTICS
Instructions:(Two statements are given-one labelled Assertion (A) and the other labelled Reason (R).
Select the correct answer to these questions from the codes (a), (b), (c) and (d) as given below.(
a) Both A and R are true and R is the correct explanation of A
b) (Both A and R are true but R is NOT the correct explanation of A
c) (A is true but R is false
d) A is false and R is also false
1) Assertion : When a light wave travels from a rarer to a denser medium, it loses speed. The
reduction in speed implies a reduction in energy carried by the light wave. Reason : The energy of a
wave is proportional to velocity of wave.
Correct Answer: D
2) Assertion : No interference pattern is detected when two coherent sources are infinitely close to
each other.(
Reason : The fringe width is inversely proportional to the distance between the two slits.
Correct Answer: A
3) Assertion : For best contrast between maxima and minima in the interference pattern of Young’s
double slit experiment, the intensity of light emerging out of the two slits should be equal.
Reason : The intensity of interference pattern is proportional to square of amplitude.
Correct Answer: B
4) Assertion: In Young’s experiment, the fringe width for dark fringes is different from that for white
fringes.(Reason : In Young’s double slit experiment the fringes are performed with a source of white
light, then only black and bright fringes are observed.
Correct Answer: D
5) Assertion : When a tiny circular obstacle is placed in the path of light from some distance, a bright
spot is seen at the centre of shadow of the obstacle.?
Reason : Destructive interference occurs at the centre of the shadow.?
Correct Answer: C
6) Assertion : Interference pattern is made by using blue light instead of red light, the fringes becomes
narrower.?
Reason : In Young's double slit experiment, fringe width is given by relation ? = ?D/d.
Correct Answer: A
7) Assertion: Diffraction is common in sound but not common in light waves.
Reason: Wavelength of light is more than the wavelength of sound.?
Answer (c)?
8) Assertion: In Young's double slit experiment if wavelength of incident monochromatic light is just
doubled, number of bright fringe on the screen will increase.?
Reason : Maximum number of bright fringe on the screen is directly proportional to the wavelength of
light used.
Answer: (d)?
9) Assertion: In interference and diffraction, light energy is redistributed.?
Reason: There is no gain or loss of energy, which is consistent with the principle of conservation of
energy.?
Answer: (a)
10) Assertion: If complete YDSE (Young's Double Slit Experiment) is dipped in the liquid from the air,
then fringe width decreases.?
Reason: Wavelength of light decreases, when we move from air to liquid. ?
Answer: (a)
CASE BASED QUESTION
Diffraction at a single slit
(i) In the phenomena of Diffraction of light when the violet light is used in the experiment is used instead
of red light then,?
(a) Fringe width increases?(b) No change in fridge width
(c) Fringe width decreases (d) Colour pattern is formed
(ii) Diffraction aspect is easier to notice in case of the sound waves then in case of the light waves
because sound waves
. (a) Have longer wavelength ?
. (b) Shorter wavelength ?
. (c) Longitudinal wave ?
. (d) Transverse waves ?
(iii) Diffraction effects show that light does not travel in straight lines. Under what condition the concepts
of ray optics are valid. ( D = distance of screen from the slit).
. (a) D < Zf
(b) D = Zf
(c) D > Zf
(d) D << Zf
(iv) when 2nd secondary maxima is obtained in case of single slit diffraction pattern, the angular position
is given by
(a) λ (b) λ /2
(c) 3 λ /2 (d) 5 λ /2
Answers: (i) (c)?(ii) (a) (iii) (d) (iv) (d)
Short-Answer Questions
1. What is the effect on the interference fringes in Yaing’s double slit experiment, when
(i.) The source slit is moved closer to the plane of slits
(ii.) The manochromatic source is replaced by source of white light.
2. How does the resolving power of compound Microscope change, when

(i.) refractive index of the medium between object and objective lens increase ?
(ii) frequency of incident light on the objective lens is increased.
(iii.) focal length of objective lens is increased
3. Explain with the reason, how the resolving power of an astronomical telescope will change w
(i.) frequency of incident light on the objective lens is decreased
(ii.) focal length of objective lens is increased
(iii.) aperature of the objective lens is halved.
4. Which of the following waves can be polarised

(i.) x-rays (ii)sound waves ? Give reasons
5. A Partially plane polarised light is passed through a Polaroid. Show graphically the variation of the
transmitted light intensity with angle of rotation of the polarised.
6. Why do we fail to observe the diffraction from a wide slit illuminated by monochromatic light.?
7. Draw a graph to show the variation of intensity with angle in single slit diffraction.
8. Derive an expression for angular width of central maximum and show taht it twice the angular
of the first order secondary maximum.
ANSWER THE FOLLOWING
1. The number of waves in a 4cm thick strip of glass is the same as in 5cm thick water layer, when the
same monochromatic light travels in them. If the refractive index of water is 4/3, what will be that of
glass (5/3)
2. The absolute refractive index of air is 1.0003 and wavelength of yellow and light in vacuum is
6000A0. Find the thickness of the air column, which will contain one more wavelength of yellow light
than in the same thickness of vacuum. (2mm)
3. In a two-slit experiment with monochromatic light, fringes are obtained on a screen placed at some
distance D from the slits. If the screen is moved 5x10-2m towards the slits, the change is fringe width
is 3 x10-5 m. If the distance between the slits is 10-3m, calculate the wavelength of the light used.
(6000A0)
4. Two sources S1 and S2 emitting light of 600n m are placed. A detector moved on the line S1P that is
perpendicular to S1S2.
(i) what would be the minimum and maximum path difference at the detector as it moved along the line
S1P.
(ii) Locate the positon of farthest minimum detected. (0.1mm,1.7cm)
5. A slit of width ‘d’ is illuminated by red light of wavelength 6500A . For what value of ‘d’ will
0
(i) the first minimum fall at an angle of diffraction of 300 and

(ii) the first maximum fall at an angle of diffraction of 300.
(1.3x10-6m,1.95x10-6m)
6. Two ‘crossed’ Polaroids A and B are placed in the path of a light beam. In between these, a third
Polaroid C is placed whose polarization axis makes an angle θ with the polarization axis of the
Polaroid A. If the intensity of light emerging from the Polaroid A is I0, then show that the intensity of
light emerging from Polaroid B will be ¼ I0 sin22 θ .
7. Find the thickness of a plate, which will produce a change in optical path equal to half the wave-
length λ of the light passing through it normally. The refractive index of the plate is µ .
 λ 
Ans.  
 2(µ −1) 
8. In an experimental set up similar to Young’s double slit experiment to observe interference of light
Here SS1-SS2= λ /4
Write the condition of

(i) constructive P
S1
(ii) destructive, interference at any point P in terms of path difference.
S
∆ =S2P – S1P S2
Does the central fringe observed in the above setup lie above or below
O? Give reasons in support of your answer.
λ λ λ
( + ∆ = nλ , + ∆ = (2n − 1)
)
4 4 2
9. A Polaroid examines two adjacent two adjacent plane polarized light beams A and B whose planes
of polarization are mutually at right angles. In one position of the Polaroid, the beam B shows zero
intensity. From this position a rotation of 300 shows the two beams of equal intensities. Find the
intensity ratio IA/IB of the two beams. (1:3)
10. Two wavelengths of sodium light 590nm, 596nm are used, in turn, to study the diffraction-taking
place at a single slit of aperture 2 x10-4m. the distance between the slit and the screen is 1.5m.
Calculate the separation between the positions of first maximum of the diffraction pattern obtained in
the two cases.
(6.75mm)
11. A double – slit apparatus is immersed in a liquid of refractive index 1.33. It has slit separation of 1.0
mm, and distance between the plane of slits and screen is 1.33m. A parallel beam of light whose
wavelength in air is 6300A0 illuminates the slits.
(i) Calculate the fringe-width
(ii) One of the slits of the apparatus is covered by a thin glass sheet of refractive index 1.53. Find the
smallest thickness of the sheet to bring the adjacent minimum on the axis.
(0.63mm,1575A0)
12. A narrow monchromatic beam of light of intensity I is incident on a glass plate. Another glass plate is
kept close to the first one and parallel to it. Each plate reflects 25% of the incident light and transmits
the remaining. Calculate the ratio of the minimum and maximum intensity in the interference pattern
obtained after reflection from each plate. (I min/Imax = 1/49)
13. How does the width and intensity of central maxima change when distance between slit and screen
of a single sit diffraction setup is made double? [ Linear width = double, Angular width = same,
intensity = half ]
14. How does the width and intensity of central maximum changes when width of Slit is made half is the
single sit diffraction setup?
( Linear width = half, Angular width = half, intensity = one fourth)
15. Light of wavelength 520 nm passing through a double slit, produces interference pattern
of relative intensity vs deflection angle θ . as shown in the figure Find the seperation ‘d’ between the
slits.
-2
[1.98 x 10 mm]
16. Two identical narrow slits s1 and s2 are illuminated by light of wavelength from a point source p as
shown..If the light is then allowed to fall on a screen and if n is a integer,the condition for destructive
at Q is -
(A) (L -L ) = (2n +1) λ /2 (B) (L -L )= (2n +1) λ/2
1 2 3 4
(C) (L + L ) - (L +L ) = n λ (D) (L + L ) - (L +L ) = (2n +1) λ /2 [ (Ans) D]

1 2 2 4 1 3 2 4
17 Two point source separated by 5 micrometer emit light of wavelength 2 micrometer in phase.
A circular wire of radius 20 um is placed around the source as shown in fig.
State which of the points out of A,B,C and D will be dark/bright A

[Ans A,C : Bright 20
B,D Dark] micrometer
D B
S S
1 2
C
18. Two monochromatic (λ =a/5) and coherent sources of EM waves are placed on the x-axis at the
points ( 2a,0) and (-a,0), A detector moves in a circle of radius R(>> 2a) whose centre is at the
origin.How many maximas will be detected by the detector during one circular revolution ?
[Ans 60]
19. In a young’s Double slit experiment (YDSE) first maxima is observed at a fixed point P on the
screen.Now the screen is continuously moved away from the plane of slits.The ratio of intensity
at point P to the intensity at point O (Centre of the screen)
(A) Remains Constant -p
(b) keeps on decreasing O
(c) First decreases and then increases
(d) First decreases and then becomes constant

[Ans- C]
20. In YDSE using monochromatic light of wavelength λ the intensity of light at a point on the screen
where the path difference is λ is K units.What is the intensity of light at a point where path difference
is λ ? k
 
3 4
21. In a double slit interference experiment,the two coherant beams have slightly different intensities.I
and I +δ I δ( I << I).Show that the resultant intensity at the maxima is nearly 4I while at the minima is
nearly
[δI]2
4I
22. White light is used to illuminate two slits in young’s double slit experiment.The seperation between
the slit is b,and the screen is at a distance d (d>>b) from the slits.At a point on the screen directly
in front of one the slits,which wavelengths are missing ?
2 2 2
Ans b , b , b -
d 3d 5d
23. The intensity at the central maxima (O) in a Young’s double slit experiment is I .If the distance OP
0
equals one-third of the fringe width of the pattern,show that the intensity at point P would be I0
4
24. (a) Light passes through two polaroids P1 and P2 with pass axis of making an angle θ with the pass
axis of P . For what value of θ is the intensity of emergent light zero?
1
(b) A third polaroid is placed between P1 and P2 with its pass axis making the angle β with the pass
axis of of P .Find the value of β for which the intensity of light emerging from P is I0 , where
1 2
I0 is the intensity of light on the polaroid P 8
1
0 0
(90 ,45 )
-2
25. Two sources S and S emitting light of wavelength 600 nm are placed at a distance 10 cm apart.
1 2
A detector is moved along line S P which is perpendicular to S S (A)What is the minimum and
2 1 2
maximum path difference at the detector as it is moved along the line S P ?
-2 1
(b) Locate the position of the farthest minimum. ( 10 0;1.7 cm)
26. In a double slit experiment with monochromatic light, fringes are obtained on a screen palced at
some distance from the slits. If the screen is moved by 5 × 10-2m towards the slits, the change in fringe
width is 3 ×10-5m. if the distance between slits is 10-3m, calculate the wavelength of light used.
Unit - Semiconductors
Code - 12P (12)_
1. In figure given, assuming the diodes to be ideal
(a) D1 is forward biased and D2 is reverse biased and hence current flows from A to B.
(b) D2 is forward biased and D1 is reverse biased and hence no current flows from B to A and vice
versa.
(c) D1 and D2 are both forward biased and hence current flows from A to B.
(d) D1 and D2 are both reverse biased and hence no current flows from A to B and vice versa.
Answer/Explanation
Answer: b
2. Which specially fabricated p-n junction diode is used to detect light intensity
a) LDR b) Photodiode c) LED d) Solar Cell
Ans b)
3. The output of the given circuit in figure is given below.
(a) would be zero at all times.

(b) would be like a half-wave rectifier with positive cycles in output.
(c) would be like a half-wave rectifier with negative cycles in output.
(d) would be like that of a full-wave rectifier.
Answer/Explanation
Answer: c
Explaination:
(c) Explanation:
When the diode is forward biased, the resistance of pn junction diode will be low then current in the
circuit is maximum. In this situation, a maximum potential difference will appear across resistance
connected in a series of circuit. This result into zero
________________________________________
4. Electrical conductivity of a semiconductor
(a) decreases with the rise in its temperature.
(b) increases with the rise in its temperature.
(c) does not change with the rise in its temperature.
(d) first increases and then decreases with the rise in its temperature
Answer/Explanation
Answer:
Explaination:
(b) With temperature rise, the conductivity of semiconductor increases.
________________________________________
5. The forbidden energy band gap in conductors, semiconductors and insulators are EG1,EG2 and EG3
respectively. The relation among them is
(a) EG1 = EG2 = EG3
(b) EG1 < EG2 < EG3
(c) EG1 > EG2 > EG3
(d) EG1 < EG2 > EG3
Answer/Explanation
Answer:
Explaination:
(b) In insulators, the forbidden energy gap is very large, in case of semiconductor it is moderate and in
conductors the energy . gap is zero.
________________________________________
6. In an insulator, the forbidden energy gap between the valence band and the conduction band is of the
order of __________ .
Answer/Explanation
Answer:
Explaination: 5 eV
7. A n-type semiconductor is
(a) negatively charged.
(b) positively charged.
(c) neutral.
(d) none of these
Answer/Explanation
Answer: c
Explaination:
(c) n-type semiconductors are neutral because neutral atoms are added during doping.
8. In the half-wave rectifier circuit shown. Which one of the following waveforms is true for VCD the
output across C and D?
Answer/Explanation
Answer: b
Explaination:
(b) Half wave rectifier rectifies only the half cycle of the input ac signal and it blocks the other half.
9. A full-wave rectifier circuit along with the input and output voltages is shown in the figure The contri-
bution to output voltage from diode 2 is
(a) A, C
(b) B, D
(c) B, C
(d) A, D
Answer/Explanation
Answer: b
Explaination:
(b) In the positive half cycle of input ac signal diode D1 is forward biased and D2 is reverse biased so
in the output voltage signal, A and C are due to D1. In negative half cycle of input ac signal, D2 con-
ducts, hence output signals B and D are due to D2
________________________________________
10 In an n-type silicon, which of the following statements is true.

(a) Electrons are majority carriers and trivalent atoms are the dopants’
(b) Electrons are minority carriers and pentavalent atoms are the dopants.
(c) Holes are minority carriers and pentavalent atoms are the dopants.
(d) Holes are majority carriers and trivalent atoms are the dopants.
Answer
Answer: c
11. If a small amount of antimony is added to germanium crystal

(a) its resistance is increased
(b) it becomes a p-type semiconductor
(c) there will be more free electrons than holes in the semiconductor,
(d) none of these.
Answer
Answer: c
12. The dominant mechanism for motion of charge carriers in forward and reverse biased silicon p-n
junction are
(a) drift in forward bias, diffusion in reverse bias
(b) diffusion in forward bias, drift in reverse bias
(c) diffusion in both forward and reverse bias
(d) drift in both forward and reverse bias
Answer
Answer: b
13. In an unbiased p-n junction, holes diffuse from the p-region to n-region because
(a) free electrons in the n-region attract them
(b) they move across the junction by the potential difference
(c) hole concentration in p-region is more as compared to u-region.
(d) all of these
Answer
Answer: c
14. Region without free electrons and holes in a p-n junction is

(a) n-region
(b) p-region
(c) depletion region
(d) none of these
Answer
Answer: c
15. Which of the following statements is incorrect for the depletion region of a diode?
(a) There the mobile charges exist.
(b) Equal number of holes and electrons exist, making the region neutral.
(c) Recombination of holes and electrons has taken place.
(d) None of these
Answer
Answer: a
16. Potential barrier developed in a junction diode opposes the flow of

(a) minority carrier in both regions only
(b) majority carriers only
(c) electrons in p region
(d) holes in p region
Answer
Answer: b
17. The breakdown in a reverse biased p-n junction diode is more likely to occur due to
(a) large velocity of the minority charge carriers if the doping concentration is small
(b) large velocity of the minority charge carriers if the doping concentration is large
(c) strong electric field in a depletion region if the doping concentration is small
(d) none of these
Answer
Answer: b
18. What happens during regulation action of a Zener diode?

(a) The current through the series resistance (Rs) changes.
(b) The resistance offered by the Zener changes.
(c) The Zener resistance is constant.
(d) Both (a) and (b)
Answer
Answer: d
19. A zener diode is specified as having a breakdown voltage of 9.1 V, with a maximum power dissipa-
tion of 364 mW. What is the maximum current the diode can handle?
(a) 40 mA
(b) 60 mA
(c) 50 mA
(d) 45 mA
Answer
Answer: a
20. In a half wave rectifier circuit operating from 50 Hz mains frequency, the fundamental frequency in
the ripple would be
(a) 25 Hz
(b) 50 Hz
(c) 70.7 Hz
(d) 100 Hz
Answer
Answer: b
21. Assertion - A-p type semiconductor has net positive charge on it.
Reason : P type impurities atom has positive charge carriers in it .
Ans D
22. Assertion - A p-n junction diode can be used even at UHF.
Reason : Reaction of p-n junction diode increases as frequecny increases.
Ans C
23. Assertion - The energy gap between the valence band and the conduction band is greater in
silicon than in germanium
Reason : thermal energy produces few minority carriers in silicon than in germanium
Ans A
24. Assertion -A p-n junction with reverse bias can be used as a photo diode to measure light inten
sity
Reason- In a reverse bias condition , the current is small but it is more sensitive to change in
intensity of light.
Ans A
25. Assertion - The electrical conductivity of n type semiconductor is higher then p type semiconduc
tor at a given tempearture and voltage applied.
Reason-The mobility of electrons is higher than holes.
Ans A
Two statements are given – One labeled assertion (A) and other labeled reason (R).
Select the correct answer to these questions from the codes (a), (b), (c) and (d) as
given below:
b) Both A and R are true but R is not the correct explanation of A.
c) A is true but R is false.
d) A is false but R is true.
26. Assertion (A): A Pure semiconductor has negative temperature coefficient of resistance.
Reason (R): On raising the temperature, more charge carriers are released, conductance increases
and resistance decreases.
27. Assertion (A): At a fix temperature, silicon will have a minimum conductivity when it has a smaller
accepter doping.
Reason (R): The conductivity of and intrinsic semiconductor is slightly higher than of a lightly doped
p-type.
28. Assertion (A): The electrons in the conduction band have higher energy than those in the valance
band of a semi-conductor.
Reason (R): The conduction band lies above the energy gap and valance band lies below the energy
gap.
29. Assertion (A): The energy gap between the valance band and conduction band is greater in silicon
than a germanium.
Reason (R): Thermal energy produces fewer minority carriers in silicon than in germanium.
30. Assertion (A): p- n junction diode can be used even at ultra-high frequencies. Reason (R): Capacitative
reactance p- n junction diode increases as frequency increases.
CASE STUDY BASED QUESTIONS ELECTRONIC DEVICES

1. SEMICONDUCTOR :
A pure semiconductor germanium or silicon, free of every impurity is called intrinsic semiconductor. At
room temperature, a pure semiconductor has very small number of current carriers (electrons and holes)
.Hence its conductivity is low.
When the impurity atoms of valance five or three are doped in a pure semiconductor, we get respectively
n- type or p- type extrinsic semiconductor. In case of doped semiconductor ne nh=ni2. Where ne and nh
are the number density of electron and hole charge carriers in a pure semiconductor. The conductivity of
extrinsic semiconductor is much higher than that of intrinsic semiconductor.
Q (1). Which of the following statements is not true?

a. The resistance of intrinsic semiconductor decreases with increase of temperature.
b. Doping pures Si with trivalent impurities gives p- type semiconductors.
c. The majority charges in n- type semiconductors are holes.
d. A p-n junction can act as semiconductor diode.
Q (2). The impurity atoms with which pure Si should be doped to make a p- type semiconductor is
a. Phosphorus
b. Boron
c. Arsenic
d. Antimony
Q (3). Holes are majority charge carriers in
a. Intrinsic semiconductors.
b. Ionic Solids
c. p- type semiconductors
d. Meta
Q (4). At absolute zero, Si acts as
a. Non- metal
b. Metal
c. Insulator
d. None of these
Answers
1. (c) The majority Charge carriers in n-type semiconduch as holes
2. (b) BORON
3. (c) p-type semiconductors
4. (c) Insulators
SHORT ANSWER TYPE QUESTIONS
Q.1 What is the conductivity of a semi conductor at absolute zero?
(Zero)
Q.2 Name two factors on which electrical conductivity of a pure semiconductor at a given tempera-
ture depends.
(i) The width of the forbidden energy band (ii) Intrinsic charge carrier concentration.
Q.3 Why does a semiconductor get damaged when a heavy current flows through it?
Q.4 Name any one element, other that ‘As’ and ‘Sb’, which can be used as impurity with germanium
to form n-type semiconductor.
Phosphorous (P).
Q.5 How does the junction width change, when a p-n junction is forward biased?
Q.6 How does potential barrier cahnge when a p-n junction is forward biased? ?
Q.7 The forbidden energy gaps in insulators, semiconductors and conductors are EG1 , EG2 and EG3
repectively. Arrange them in ascending order.
Q.8 Can we take one slab of p-type semiconductor and physically join it to another n-type semicon-
ductor to get p-n junction?
Q.9 How does the thickness of the depletion layer in a p-n diode very with increase in reverse bias?
Q.10 Draw and explain the output waveform across the load resistor R, if the input waveform is as
shown in the given figure.
Q.11 In the following circuits, if the input waveform is as shown in the figure, what will be the output
waveform, across R in Fig. (a & b) ? Assume that the diode is ideal.
Q.11 In the following diagrams, indicate which of the diodes are forward biased and which are reverse
biased.
12. The semiconductor material used to fabricate a photo diode has energy gap of 1.2 eV
using calcualtion show whether it can detect light of wavelength 400 nm.
Ans Yes
13. A pure semiconductor material has electron-hole concentration of 2 × 1016 m-3 when doped
by a pentavalent density charged to 8 ×1021 m-3
i) Which type of semiconductor is prepared .
ii) What is the new hole concentrated
(Ans n type , 5 × 1010 m-3)
14. Assuming that diodes D1 and D2 used in the elecric circuit are ideal, find out the value of
current flowing through 2 r resistor.
Ans=0.4A
DUAL NATURE OF RADIATION
MCQ
1. Light of frequency 1.9 times the threshold frequency is incident on a photosensitive material. If the
frequency is halved and intensity is doubled, the photocurrent becomes
(a) quadrupled
(b) doubled
(c) halved
(d) zero
Answer/Explanation
Answer: d
Explaination: (d) As vi = 0.95 v0. No photoelectric emission takes place.
2. Threshold wavelength for a metal having work function W0 is X. What is the threshold wavelength
for the metal having work function 2W0?
(a) 4ë
(b) 2ë
(c) ë/2
(d) ë/4
Answer/Explanation
Answer: c
3.. Radiations of frequency v are incident on a photosensitive metal. The maximum K.E. of the photo-
electrons is E. When the frequency of the incident radiation is doubled, what is the maximum kinetic
energy of the
photoelectrons?
(a) 2E
(b) 4E
(c) E + hv
(d) E – hv
Answer/Explanation
Answer: c
Explaination: (c) Using Einstein’s photoelectric equation hv – w0 = E
4. Maximum kinetic energy (Ek) of a photoelectron varies with frequency (v) of the incident radiation as
Answer/Explanation
Answer: d
Explaination: (d) Using Einstein’s photoelectric equation hv = hv0 + Ek
5. The stopping potential V0 for photoelectric emission from a metal surface is plotted along y-axis and
frequency v of incident light along x-axis. A straight line is obtained as shown. Planck’s constant is given
by
(a) slope of the line
(b) product of the slope of the line and charge on electron
(c) intercept along y-axis divided by charge on the electron
(d) product of the intercept along x-axis and mass of the electron
Answer/Explanation
Answer: b
Explaination: (b) Using Einstein’s photoelectric equation
6. The energy of photon of wavelength 450 nm is

(a) 2.5 × 10-17 J
(b) 1.25 × 10-17 J
(c) 4.4 × 10-19 J
(d) 2.5 × 10-19 J
Answer/Explanation
Answer: c
7. The kinetic energy of an electron is 5 eV. Calculate the de broglie wavelength associated with it. (h =
6.6 × 10-34 Js, me = 9.1 × 10-31 kg)
(a) 5.47 Å
(b) 10.9 Å
(c) 2.7 Å
(d) None of these
Answer/Explanation
Answer: c
Explaination:
8. The slope of the stopping potential versus ‘ frequency graph for photoelectric effect is equal to
(a) h
(b) he
(c) h/e
(d) e
Answer/Explanation
Answer: c
Explaination:
(c) Using Einstein’s equation for photoelectric effect
10. Work function of three metals A, B and C are 4.5 eV, 4.3 eV and 3.5 eV respectively. If a light of
wavelength 4000 Å is incident on the metals then
(a) photoelectrons are emitted from A.
(b) photoelectrons are emitted from B.
(c) photoelectrons are emitted from C.
(d) photoelectrons are emitted from all the metals.
Answer/Explanation
Answer: d
11. Which of the following figure represents the variation of particle momentum and associated de
Broglie wavelength?
Answer/Explanation
Answer: d
12. According to Einstein’s photoelectric equation the plot of the kinetic energy of the emitted photo-
electrons from a metal vs the frequency of the incident radiation gives a straight line whose slope
(a) depends on the nature of the metal used.
(b) depends on the intensity of the radiation.
(c) depends both on the intensity of the radiation and the metal used.
(d) is the same for all metals and independent of the intensity of the radiation.
14. For a given kinetic energy which of the following has smallest de Broglie wavelength?
(a) Electron
(b) Proton
(c) Deutron
(d) a-particle
Answer/Explanation
Answer: d
Explaination:
(d) Since de Broglie wavelength
particle, mass of ?-particle is maximum

15. A particle is dropped from a height H. The de Broglie wavelength of the particle as a function of
height is proportional to
Answer/Explanation
Answer: d
16. A proton, a neutron, an electron and an a-particle have same energy. Then their de Broglie wave-
lengths compare as
(a)λp = λn > λe > λα
(b) λα < λp = λn < λe
(‘C) λe < λp = λn > λα
(d) λe = λp = λn = λα
Answer/Explanation
Answer: b
17. In photoelectric effect what determines the maximum velocity of electron reacting the collector?
(a) Frequency of incident radiation alone
(b) Work function of metal
(c) Potential difference between the emitter and the collector

(d) All of these
Answer/Explanation
Answer: d
Explaination: (d) As per Einstein’s photoelectric equation
18. A Proton and an a-particle have the same de Broglie wavelength. What is same for both of them?
(a) Mass
(b) Energy
(c) Frequency
(d) Momentum
Answer/Explanation
Answer: d
19. The wavelength of a photon needed to remove a proton from a nucleus which is bound to the
nucleus with 1 MeV energy is nearly [NCERT Exemplar]
(a) 1.2 nm
(b) 1.2 × 10-3 nm
(c) 1.2 × 10-6 nm
(d) 1.2 × 101 nm
Answer/Explanation
Answer: b
20. An electron is moving with an initial velocity v = v0i and is in a magnetic field B = B0 j. Then, its de
Broglie wavelength [NCERT Exemplar]
(a) remains constant.
(b) increases with time.
(c) decreases with time.
(d) increases and decreases periodically.
21. Assertion :- If frequency of Incident light is doubled, the kinetic energy of photoelectron is also
doubled.
Reason : The kinetic energy of photoelectron is directly proportional to frequency of Incident Light
Ans- d
22. Assertion : on increasing the frequency of light the photocurrent remains unchanged.
Reason : The photocurrent is independent of frequently but dpends only on intensity of incident light.
Ans -a)
23. Assertion : Photoelectric process is instantaneous process.
Reason: When photon of energy ( hw) greater than work function of metal ( ϕ 0 ) are incident on a
metal, the electrons from metal the electrons from metal are emitted with no time lag
Ans -a)
24. Assertion :- Photoelectric effect demonstrates the wave nature of light .
Reason : The number of photoelectron is proportional to the wavelength of Incident light
Ans - d)
25. Assertion : In the process of photoelectric emission all emitted electrons have the same kinetic
energy.
Reason : According to Einstein’s equation E=hw- ϕ
Ans - d)
CASE STUDY
1. The photoelectric emission is possible only if the incident light is in the form of packets of energy,
each having a definite value, more than the work function of the metal. This shows that light is not of
wave nature but of particle nature. It is due to this reason that photoelectric emission was accounted by
quantum theory of light.
Q1. Packet of energy are called (a)electron
(a) quanta (c)frequency (d)neutron
Q2. One quantum of radiation is called (a) meter (b) meson (c) photon (d) quark
Q3. Energy associated with each photon

(a) hc (b) mc (c)hv (d) hk
Q4. Which of the following waves can produce photo electric effect
(a) UV radiation (b) Infrared radiation (c). Radio waves (d) Microwaves
Q5. Work function of alkali metals is

(a)less than zero (b) just equal to other metals
(c) greater than other metals (d) quite less than other metals
Answer
Q1.(b) Q2.(c) Q3.(c) Q4.(a) Q5.(d)
Answer
Answer: a
ANSWER THE FOLOWING
Q1 On what factors does the work function of a metal depend?
Q2 What is the freqauency associated with a photon of energy 3.3 × 10 −10 J ?
Ans. 5 × 10 −23 Hz .
Q.3 If the wavelength of an electromagnetic radiation is doubled, what will happen to the energy of
photons?
Q.4 If the maximum kinetic energy of electrons emitted in a photo-cell is 5 eV, what is the stopping
potential?
Ans. 5V
Q.5 What is the effect on the velocity of photoelctrons, if the wavelength of incident light is de-
creased?
Q.6 Calculate the work function of a metal in eV if its threshold wavelength is 6800 Aoand h = 6.62
× 10 − 27 ergs.
Q.7 Define the terms threshold frequency and stopping potential in relation to the phenomenon of
photoelectric effect. How is the photoelectric current affected on increasing the (i) frequency (ii)
intensity of the incident radiations and why?
Q.8 What is photo-electric effect? Write Einstein’s photoelectric equation. Explain how it enables us
to understand the
(i) linear dependence, of the maximum kinetic energy of the emitted electrons, on the
frequency of the incident radiation.
(ii) existence of a threshold frequency for a given photoemitter.
(iii) independence of the maximum energy of emitted photo-electrons from the
intensity of incident light.
Q.9 Two beams, one of red light and the other of blue light, of the same intensity are incident on a
metallic surface to emit photoelectrons. Which one of the two beams emits electrons of greater
kinetic energy?
Q.10 Work function of a aluminium is 4.2 eV. If two photons each of energy 2.5 eV are incident on its
surface, will the emission of electrons take place? justify your answer.
Q.11 Two metals A, B have work functions 2 eV and 4 eV respectively. Which metal has a lower
threshold wavelength for photoelectric effect?
o
Q.12 What is the de Broglie wavelength (in A ) associated with an electron accelerated through a
potential of 100 V?
Q.13 State how in a photo-cell, the work function of the metal influence the kinetic energy of emitted
electrons.
(a) If the intensity of incident radiation is doubled, what changes occur in
(i) the stopping potential and
(ii) the photoelectric current?
(b) If the frequency of the incident radiation is doubled, what changes occur in the
(i) stopping potential and
(ii) photoelectric current?
Q.14 Sketch a graph between frequency of incident radiations and stopping potential for a given pho-
tosensitive material. What information can be obtained from the value of intercept on the potential
axis?
A source of light of frequency greater than the threshold frequency is placed at a distance of 1
m from the cathode of a photo-cell. The stopping potential is found to be V. If the distance of the
light source from the cathode is reduced, explain giveing reasons, what change will you observe
in the
(i) photoelectric current,
(ii) stopping potential?
Q.15 An α − particle and a proton are accelerated through the same potential difference. Calculate
the ratio of linear momenta acquired by the two.
Ans. 2 2 :1
Q. 16 Mention the significance of Davission-Germer experiment. An α − particle and a proton are
accelerated from rest through the same potential difference V. Find the ratio of de-Broglie wave-
lengths associated with them.
Ans. 1: 2 2
Q. 17 The work function of caesium is 2.14 eV. Find (a) the threshold frequency for caesium, and (b)
the wavelength of the incident light if the photocurrent is brought to zero by a stopping potential of
0.60 eV.
Ans. (a) 5.16 × 1014 Hz

(b) 453.7 nm
Q. 18 The threshold frequency for a certain metal is 3.3 × 1014 Hz. If light of frequency 8.2 × 1014 Hz is
incident on the metal, predict the cut of voltage for photoelectric emission. Given 6.63 × 1014 Js
and e = 1.6 × 10 −19 C.
Ans. 2.03 V
Q. 19 Light of frequency 7.21× 1014 Hz is incident on a metal surface. Electrons with a maximum speed
of 6.0 × 10 5 m/s are ejected from the surface. What is the threshold frequency for photoemission
of electrons?
Ans. 4.74 × 1014 Hz.

Q. 20 Threshold wavelength for photoelectric emission is 5000 A0. Will the photoelectrons be emitted
when this material is illuminated with monochromatic from 1 watt ultrviolet lamp?
Q.21 If photoelectrons are to be emitted from a potassium surface with a speed of 6× 106 ms-1, what
frequency of radiation must be used? (Threshold frequency for potassium is 4.22 × 1014 Hz,
−31
h = 6.6 × 10 −32 Js and me = 9.1× 10 kg ).
Ans. 6.7 ×1014 Hz .

Q.22 An electron and a photon each have a wavelength of 1.00 nm. Find
(a) their momenta,
(b) the energy of the photon, and
(c) the kinetic energy of electron.
(Take h = 6.63 × 10 −34 Js )
Ans. (a) 6.63 × 10 −25 kg m/s

(b) 1.24 Kev
(c) 1.51 ev.
o
Q.23 Light of wavelength 3500 A is incident on two metals A and B. Which metal will yield photoelec-
trons if their works functions are 4.2 eV and 1.9 eV respectively?
Ans. Metal B.
Q. 24 Red light, however bright, cannot cause emission of electrons from a clean zinc surface. But even
weak ultraviolet radiations can do so. Why?
Draw the variation of maximum kinetic energy of emitted electrons with the frequency of incident
radiation on a photosensitive surface. On the graph drawn, what do the following indicate (i)
slope of the graph and (ii) intercept on energy axis?
Q.25 It is difficult to eject out an electron from copper than sodium. Which of the two metals has
greater work function and which has greater threshold wavelength?
Ans. Sodium
Q. 26 Light of frequency 1.5 times the threshold frequency is incident on a photosensitive material. If the
frequency is halved and intensity is doubled, what happens to photoelectric current?
Q. 27 Out of microwaves, ultraviolet rays and infra-red rays, which radiations will be most effective for
emission of electrons frim a metallic surface?
Q. 28 An electron is accelerated through a potential difference of 300 V. What is its energy in electron
volt?
Ans. 300 eV.
Q. 29 In an experiment on photoelectric effect, the following graphs were obtained between the photo-
electric current (I) and the anode potential (V). Name the characteristic of the incident radiation
that was kept constant in this experiment.
Ans. The frequency of the incident radiation is kept constant in the experiment.
Q. 30 How will be photoelectric current change on decreasing the wavelength of incident radiation for
a given photosensitive material?
Ans. No change.
Q.31 Work function of Na is 2.3 eV. Does sodium show photoelectric emission for light of wavelength
o
6800 A ?
Ans. No
Q.32 If the frequency of incident light on a metal surface is doubled, will the kinetic energy of the
photoelectrons be doubled? Give reason.
Ans. E2 = 2 E1 + Wo .
Q. 33 The work function for a certain metal is 4.2 eV. Will this metal give photoelectric emission for
incident radiation of wavelength 330 nm?
Ans. No.
34. From the graph between frequency of incident light and maximum kinetic energy(Ek) of emitted
photoelectron. Find the values of threshold frequency and work function
(Ek)
i) Threshold frequency f=10x1014 HZ = 1015 HZ

ii) value of intercept OC gives value of work function, φ0 = 4eV.
35. Which metal, P or Q, has the greater value of work function? What does the slope of the line
depict?
a) Threshold frequency f0 for metal surface Q has greater value, hence work function of metal Q
has a greater value.
h
b) The slope of V0-f0 graph depicts the value of .
e
1
36. Two lines A and B are shown in the graph between de Broglie wavelength ( λ ) and (V is
V
the accelerating potential) for two particles, having the same charge. Which of the two repre-
sents the particle of heavier mass?
Ans: The slope of graph A is less. Since charge of both particles is same, it means that mass of particle
A is more.
 h 
∵ slope = 
 2me 
37. Show graphically how the stopping potential for a given photosensitive surface varies with the
frequency of the incident radiation.
38. What do the slope of the graph and intercept on energy axis indicates?
i) slope of the graph = Plancks Constant h.

ii) Intercept of the graph on the energy axis gives the value of work function O. Intercept on
frequency axis gives threshold frequency.
39 A small plate of a metal (work function = 1.17 eV) is placed at a distance of 2 m from a
monochromatic light source of wave length 4.8 x 10-7m and power 1.0 watt.The light falls normally
on the plate .
(a) Find the no of photons striking the metal plate per sq.m per sec.
(b) If a constant uniform B of strength 10-4 T is applied paralled to the metal surface,find the radius of
the largest circular path followed by the emitted photoelectrons
Ans (a) 4.8 x 10 16
(b) 4 cm
40. The potential energy of a particle of mass m is given by V(x) = E0 is given by

V(x) = E0 for 0 < x < 1
=0 for x>1
λ1 and 2λare the de-Broglie wavelength of the particle when 0 < x < 1 and x>1 respectively.If the
total energy of particle is 2E0 , Find λ 1/λ 2
Ans
2
ATOMS AND NUCLEI
1. If the radius of inner most electronic orbit of a hydrogen atom is 5.3 * 10~n m, then the radii of n = 2
orbits is
(a) 1.12 Å
(b) 2.12 Å
(c) 3.22 Å
(d) 4.54 Å
Answer
Answer: b
2. The diagram shows the energy levels for an electron in a certain atom. Which transition shown
represents the emission of a photon with the most energy?
(a) I
(b) II
(c) III
(d) IV
Answer
Answer: c
3. In a hydrogen atom, the radius of nth Bohr orbit is rn. The graph between log(rn/r1) and log n will be
Answer
Answer: a
4. The transition from the state n = 5 to n = 1 in a hydrogen atom results in UV radiation. Infrared
radiation will be obtained in the transition
(a) 2 ? 1
(b) 3 ? 2
(c) 4 ? 3
(d) 6 ? 2
Answer
Answer: c
5. The hydrogen atom can give spectral lines in the Lyman, Balmer and Paschen series. Which of the
following statement is correct?
(a) Lyman series is in the infrared region.
(b) Balmer series is in the visible region.
(c) Paschen series is in the visible region.
(d) Balmer series is in the ultraviolet region.
Answer
Answer: b
6. Which of the relation is correct between time period and number of orbits while an electron is resolv-
ing in an orbit?
Answer
Answer: c
A radioactive element has half-life period 1600 years. After 6400 years what amount will remain?
Answer/Explanation
Answer: b
Explaination:
6. Ratio of the radii of the nuclei with mass numbers 8 and 27 would be
Answer/Explanation
Answer: c
7. A radioactive nucleus emits a beta particle. The parent and daughter nuclei are
(a) isotopes
(b) isotones
(c) isomers
(d) isobars
Answer/Explanation
Answer: d
8. In the disintegration series
the values of Z and A respectively will be

(a) 92, 236
(b) 88, 230
(c) 90, 234
(d) 91, 234
the values of Z and A respectively will be
(a) 92, 236
(b) 88, 230
(c) 90, 234
(d) 91, 234
Answer/Explanation
Answer: d
9. A nucleus A X emits an ?-particle. The resultant nucleus emits a ?-particle. The respective atomic
and mass numbers of the daughter nucleus will be
(a) Z - 3, A - 4
(b) Z - 1, A - 4
(c) Z - 2, A - 4
(d) Z, A - 2
Answer/Explanation
Answer: b
Explaination:
10. In the nuclear reaction
What does X stand for?

(a) Electron
(b) Proton
(c) Neutron
(d) Neutrino
Answer/Explanation
Answer: d
Explaination:
(d) By conservation of mass A = 0, and by conservation of charge Z = 0, Hence X is neutrino.
Completion Type Questions

1. The angle of scattering ? for zero value of impact parameter b is ____________.
Answer: 1800.
Applying and Evaluating
2. The frequency spectrum of radiation emitted as per Rutherford's model of atom is ____________.
Answer: Continuous.
Remembering
3. The scattering angle will decreases with the _________ in impact parameter.
Answer: Increase
Understanding
4. An alpha particle contains _______ protons and _______neutrons.
Answer: Two, two.
Remembering
5. According the Rutherford's model of an atom, the most of space in atom is _________.
Answer: Empty.
Understanding
6. The radius of an atom is about _______m and that of nucleus is ________m.
Answer: 10-10 m and 10-15 m.
Remembering
7. The Rutherford's model of an atom cannot explain the characteristics ________ spectrum emitted by
H-atom.
Answer: Line?Understanding?8. The force responsible for scattering of alpha particle with target
nucleus is ___________. Answer: Electrostatic force?Remembering?9. The SI unit of impact parameter
is _________.?Answer: Meter.?Remembering
10. If the size of first orbit of hydrogen atom is 0.5 Å, the size of 2nd orbit of hydrogen atom would be
_______________.
o?Ans. 2 A { r n2 }
Applying and Evaluating
115
11. When an electron jumps from an outer stationary orbit of energy E2 to an inner stationary orbit of
energy E1, the frequency of radiation emitted = _______________.
Ans. E2 E1 h
Remembering?12. According to de Broglie a stationary orbit is that which contains an
_______________ number
of de -Broglie waves associated with the revolting electron
Ans. Integral
Remembering
13. _______________ is a physical quantity whose dimensions are the same as that of Planck's
constant.
Ans. Angular momentum
Applying
14. Energy possessed by an electron for ( n )th orbit is _______________.
Ans. Zero
Understanding
15. _______________series of hydrogen spectrum which lies in the visible region electromagnetic
spectrum.
Ans. Balmer
16. Assertion : The total energy of an electron revolving in any stationary orbit is negative .
Reason : Energy can have positive or negative values.
Ans-b
17. Assertion : Bohr’s postulate states that the electrons in stationary orbit around the nucleus do not
radiate.
Reason : According to classical physics all moving electrons radiate.
18. Assertion : A neutrino is chargeless and has a spin.

Reason : Neutrino exists inside the nucleus
Ans- C
19. Assertion : The elements produced in the fission are radioactive.
Reason : The fragments have abnormally high proton to neutron ratio .
Ans C
20. Assertion : β -particles have continous energies starting from zero to a certain maximum value.
Reason : The total energy released in decay of a radioactive elements is shared by electron
and neutrino.The sum of energies and neutrino is constant.
Ans - C
Bohr’s Atomic Model
To study about atom various scientists perform various experiments and sug-
gest various models of an atom with some explanation. For example,
Thomson gives the “plum pudding” model in which he said the atom consists
of a positive material known as “pudding” with some negative materials
(“plums”) distributed throughout. Later, famous scientist, Rutherford gives
Rutherford’s model of the atom after performing an Alpha Particle scattering
experiment.
This model is a modification of the earlier Rutherford Model. According to this
model, an atom consists of a small, positively-charged nucleus and negatively-
charged electrons orbiting around it in an orbital. These orbital can have differ-
ent sizes, energy, etc. And the energy of the orbit is also related to its size, I.e
The lowest energy is found in the smallest orbit. So if the electron is orbiting in
nth orbit then we will study about its Velocity in nth orbital, Radius of nth
orbital, Energy of electron in nth orbit, etc. Energy is also emitted due to the
transition of electrons from one orbit to another orbit. This energy is emitted in
the form of photons with different wavelengths. This wavelength is given by
the Rydberg formula. When electrons make transitions between two energy
levels in an atom various spectral lines are obtained. The emission spectrum of
the hydrogen atom has been divided into various spectral series like Lyman
series, Balmer series, Paschen series Etc.
Q1. The formula which gives the wavelength of emitted photon when electron jumps from higher
nergy state to lower was given by
a) Balmer
b) Paschen
c) Lymen
d) Rydberg
Q2. What is true about Bohr’s atomic Model
a) His model was unique totally different from other
b) His model is a modification of Rutherford atomic model.
c) His model is a modification of Thomson atomic model.
d) None of the above
Q3. Bohr’s atomic model is applicable for

a) All types of atoms
b) Only for hydrogen atom
c) For hydrogen like atoms
d) For H2 gas.
Q4. The cause of rejection of Rutherford atomic model was

a) It was totally wrong
b) It could not justify its stability
c) Rutherford was unable to explain it
d) None of the above.
Answer : Q1 – d; Q2 – b; Q3 – c; Q4 – b
ANSWER THE FOLLOWING
Q.1 The Rutherford α - particle scattering experiment shows that most of the α - particles pass
through almost unscattered while some of the them are scattered through large angles. What
information does it give about the structure of atom
Q.2 What was the main conclusion of Rutherford’s experiment on the scattering of alpha particles by
thin foils?
Q.3 What are the values of impact parameter for a head-on collision?
Q.4 The total electrical energy of an electron in the first excited state of hydrogen atom is about -3.4
eV. What is the potential energy of the electron in this state?
Ans. -6.8 eV.
Q.5 What is the potential energy of an electron when it is far away from the nucleus?
Ans. Zero.
Q.6 Name the series of hydrogen spectrum which has least wavelength.
Ans. Lyman series.
Q.7 Out of three radiations of wavelengths 8000A0, 5000A0 and 1000A0, which one corresponds to
Lyman series of hydrogen spectrum?
Ans. 1000A0, because Lyman series lies in the ultraviolet region of the spectrum.
Q.8 Identify the nuclides X and Y in the nuclear reactions:
11 1 8
B + H → Be + X
5 1 4
14 0
C →Y + e
6 −1
Q.9 What do you mean by the fact that binding energy of helium nucleus is 28.17 Me V?
Q.10 A radioactive substance decays to 1/32th of its initial activity in 25 days. Calculate its half life.
Ans. 5 days.
Q.11. What is the significance of the negative energy of electron in the orbit?
Q.12 What is Bohr’s quantisation condition for the angular momentum of an electron in an atom?
13 .6
Q. 13 How much is the energy possessed by an electron for n = ∞ ,[ E n = − eV = 0 . ]
n2
Q.14 The energy of an electron in the nth orbit is given by En = -13.6/n2 eV. Calculate the energy
required to excite an electron from ground state to the second excited state.
Ans. 12.09 eV.
Q.15 Using the Rydberg formula, calculate the wavelength of the four spectral lines in the Balmer series
of the hydrogen spectrum.
Ans. 6575A0, 4870A0, 4348A0, 4109A0.
Q. 16 The wavelength of the second line of the Balmer series in the hydrogen spectrum is 4861 A0.
Calculate the wavelength of the first line.
Ans. 6562A0.
238 239
Q.17 U on absorbing a neutron goes over to U . This nucleus emits an electron to go over
92 92
to neptuium which on further emitting an electron goes to plutonium. How would you represent
the resolting plutonium?
Ans.
1 0 0
238 + e 239 + e
−1 239 − e
−1 239
U  →
0
U  → Np  
 → Pu
92 92 93 94
Q.18 The half-life period of a radioactive substance is 30 days. What is the time taken for 3/4th of its
original mass to disintegrate?
Ans. 60 days.
7
Q.19 When Li is bombarded with a certain particle, two alpha particles are produced. Identify the
3
bombarding particle.
Q.20 A heavy nucleus X of mass number A = 240 and binding energy per nucleon 7.6 MeV is split into
two nearly equal fragments Y and Z of mass numbers A1 = 110 and A2 = 130. The binding energy
of each one of these nuclei is 8.5 MeV per nucleon. Calculate the total binding energy of each of
the nuclei X, Y and Z and hence the energy Q released per fission in Mev.
Ans. 1824 MeV, 935 MeV, 216 MeV.
4 3
Q.23 Calculate the binding energy per nucleon (in MeV) He and He . comment on the difference of
2 2
these binding energies and its significance in relation to α -decay of the nuclei.
1 1 3
(Given : mass of H = 1.00783 u, mass of n = 1.00867 u, mass of He = 3.01664 u, mass of
1 0 2
4
He = 4.00387 u)
2
Ans. 6.83 MeV and 2.39 meV.

Q.24 The half-life, of a given radioactive nuclide, is 138.6 days. What is the mean life of this nuclide?
After how much time will a given sample of this radioactive nuclide get reduced to only 12.5% of
its initial value?
Ans. 199.58 days and 415.8 days
238 238
Q.25 The half life of U against α -decay is 1.5 × 1017 S . What is the activity of a sample of U
92 92
having 25× 10 20 atoms?
Ans. 11550 dps.
90
Q.26 The half-life of Sr is 28 years. What is the disintegration rate of 15 mg of this isotope?
38
Ans. 2.13 Ci.
1 1 P
Q.27 In the nuclear reaction H → n + X Find P, Q and hence identify X.
1 0 Q
Q. 28 Calculate the binding energy of an α -particle in MeV. Given:

mp (mass of proton) = 1.007825 amu,
mn (mass of neutron = 1.008665 amu,
Mass of He nucleus = 4.002800 amu,
1 amu = 931 MeV.
Ans. 28.097 MeV.
6
Q. 29. A neutron is absorbed by α Li nucleus with subsequent emission of an alpha particle. Write the
3
corresponding nuclear reactin. Calculate the energy released in this reaction.
6 4 1
Given: m ( Li) = 6.015126 amu ; m ( He) = 4.0026044 amu ; m ( n) = 1.0086654 amu ;
3 2 0
3
m ( H) = 3.016049 amu
1
Ans. Q = 4.78 MeV.

Q.30 A radioactive isotope has half-life of T years. How long will it take the activity to reduce to (a)
3.125%, (b) 1% of its original value?
Ans. (i) 5 T years.
(ii) 6.65 T years.
60
Q. 31 Obtain the amount of Co necessary to provide a radioactive source of 8.0 mCi strength. The
27
60
half-life of Co is 5.3 years.
27
Ans. 7.123 ×10 −6 g .
Q.32 The nucleus Ne23 decays by β -emission. Write down the β -decay equation and determine the
maximum kinetic energy of the electrons emited from the following data :
23 23
m( Ne) = 22.994466 amu ;m ( Na) = 22.989770 amu.
10 11
23 23 0
Ans. Ne → Na + e+ 00ν + Q
10 11 -1
4.374 MeV.
Q.33 The Q value of a nuclear reaction A + b → C + d is defined by
Q = (mA + m b - mC - md ) c2
Where the masses refer to nuclear rest masses. Determine from the given data whether the fol-
lowing reactions are exothermic or endothemic.
1 3 2 2
(i) H + H → H + H
1 1 1 1
12 12 20 4
(ii) C+ C→ Ne + He
6 6 10 2
1 2
Atomic masses are given to be :m ( H ) = 1.007825 amu ; m ( H ) = 2.014102 amu
1 1
3 12 20
m ( H ) = 3.016049 amu ; m( C ) = 12.000000 amu ; m ( Ne ) = 19.992439 amu
1 6 10
4
m ( He ) = 4.002603 amu
2
Ans. (i) Q = -4.033 MeV Endothermic

(ii) Q = 4.618 MeV Exothermic
239 235
Q. 34 The fission properties of Pu are very similar to those of U. The average energy released
94 92
per fission is 180 MeV. How much energy, in MeV, is released if all the atoms in 1 kg of pure
239
Pu undergo fission?
94
Ans. 4.54 × 10 26 MeV.
Q. 35 Find the Q-value and the kinetic energy of the emitted α -particle in the α -decay of
226
(a) Ra.
88
220
(b) Rm/
86
226 222 220
Given m( Ra) = 226.02540 amu, m ( Rn) = 222.01750 amu, m ( Rn) = 220.01137 amu,
88 86 86
216
m( Po) = 216.00189 amu.
84
6 7
Q. 36 (a) Two stable isotopes of lithium Li and Li have respective abundances of 7.5% and 92.5%.
3 3
These isotopes have masses 6.01512 amu and 7.01600 amu respectively. Find the atomic weight
of lithium.
10 11
(b) Boron has two stable isotopes, B and B . Their respective masses are 10.01294 amu
5 5
10
and 11.00931 amu, and the atomic weight of boron is 10.811 amu. Find the abundances of B
5
11
and B.
5
Ans. (a) 6.941 amu

(b) 19.9%, 80.1%.
37. The energy levels of an atom are shown in the figure. Which one of the transition will result in the
emission of a photon of wavelength 275nm?
Ans- If λ =275nm, then energy of photon,

hc
E= = 4.5ev
λ
Electron transition takes from Oev to 4.5 ev
E1- E2= 0-(-4.5)= + 4.5 ev
Transition B will result in the emission of a photon of wavelength 275nm.
38. Draw the graph showing the distribution of the kinetic energy of electrons emitted during beta decay.
238
Ans U decays by emitting an - particle to form an isotope of thorium(Th).
92
U → 234
238
92 90TH + 2 He
4
39. Draw the energy level diagram showing the emission ofβ -particles followed by two-rays by gamma
nucleus of 2760Co
LIST OF PRACTICALS
[PHYSICS]
CLASS – XII
SECTION A
1. To determine resistance per cm of a given wire by plotting a graph of potential difference versus
current.
2. To find resistance of given wire using metre bridge and hence determine the specific resistance of its
material.
3. To verify the laws of combination (series/parallel) of resistances using metre bridge.
4. To compare EMF’s of two given primary cell using a potentiometer.
5. To determine the internal resistance of a given primary cell using potentiometer.
6. To determine the resistance of given galvanometer by half deflection method and find its figure of
merit.
7. To find frequency of the a.c. mains with a sonometer.
SECTION B
1. To find the focal length of a convex lens by plotting graphs between u and v or between 1/u and
1/v.
2. To find the focal length of a concave lens, using a convex lens.
3. To determine angle of minimum deviation for a given prism by plotting a graph between the angle of
incidence and angle of deviation and find refractive index of the material of the prism.
4. To find the value of v for different values of u in case of concave mirror and to find the focal l
ength.
5. To find the focal length of a convex mirror, using a convex lens.
6. To find the refractive index of a liquid by using (i) concave mirror, (ii) convex lens and plane mirror.
7. To draw the I-V characteristic curve of a p-n junction diode in forward bias and reverse bias.
8. To draw the characteristic curves of a Zener diode and determine its reverse breakdown voltage.
OHM’S LAW
AIM:To establish current voltage relationship (Ohm’s Law) for a given resistance using an ammeter
and voltmeter and to find out the unknown value of resistance and resistance per unit length of the
wire.
APPARATUS:A voltmeter, an ammeter, unknown resistance, rheostat, key, battery and connecting
wires.
THEORY :Ohm’s Law states that when a steady current flows through a conductor the ratio of potential
difference between the ends of the conductor and current flowing through it is constant, provided that the
physical condition of the conductors, such as length, temperature etc. does not change. If V is the potential
difference and I is the current, then
I ∝V
Or V/I= Constant (R)

R is the resistance of the conductor
CIRCUIT DIAGRAM
PROCEDURE:
1. Clean the ends of the conducting wires with the help of sand paper in order to remove any insulating
coating on them.
2. Arrange the apparatus according to the circuit diagram as shown.
3. Note the zero correction of ammeter and voltmeter, if any.
4. Insert the key k and slide the rheostat contact starting from the left end to the right end. Note down
the observations in the ammeter and voltmeter.
5. Go on increasing the current step by step with the help of rheostat and take least six sets of observations.
Tabulate all the observations.
6. Draw the graph by plotting voltmeter reading (V) along the X axis and ammeter reading (I) along the
Y axis.
OBSERVATIONS:
Range of ammeter = …0……A to ……..A
Least count of ammeter= ……………A
Range of voltmeter = …0….V to ……..V
Least count of voltmeter= …………V
Least count of metrescale = ………..m
Length of the given wire = ……….m
GRAPH:
CALCULATIONS:
RESULT :1. The graph between V and I is a straight line hence V / I = constant. The
value of unknown resistance is ________ Ω .
2. The resistance per unit length of the wire is _________ Ω .m-1
PRECAUTIONS:
1. The ends of the wire should be neat and clean.

2. The connections should be tight.
3. The key should be inserted only while taking observations as excessive flow of current
causesunnecessary heating of the wire.
4. A low resistance rheostat should be used.
SOURCES OF EROR:
1. The connections may be loose.
2. The wire used may not be of uniform crossection.
3. The ratio of V / I may not be constant due to heating caused by passage of current for longer interval
of time.
4. High resistance rheostat may be used.
METRE BRIDGE
AIM :To find an unknown resistance using Wheatstone bridge (meter bridge) and hence determine the
specific resistance of its material.
APPARAUS :Meter bridge, galvanometer, resistance box, one way key, a cell, unknown resistance,
connecting wires and jockey.
THEORY:Meter bridge is a form of Wheatstone bridge, under balanced conditions.
P/Q=R/X
For a meter bridge, the expression becomes X = (R (100- L )) / L
The specific resistance of the material of a given wire is
where r is the radius of the wire and l is the length of thexπ

wir,
r 2 X is unknown resistance, R is known
p=
resistance and L is balancing length. l
PROCEDURE:
1. Find the average diameter of the wire with a screw gauge. From this, obtain the radius of the wire.
2. Arrange the apparatus and assemble it according to the circuit diagram.
3. Close the key and test the connection. Take out 1 or 2 ohms resistance from the resistance box and
touch the jockey at two ends of the wire (A & C). If the deflection in the galvanometer is in opposite
direction, the connections are correct.
4. Move the jockey over the wire and fine the position for which the galvanometer shows zero deflec-
tion. Note the value of R from the resistance box.
5. Repeat step 4 for three more values of R.
OBSERVATIONS:
Least count of the screw gauge (L.C.) = —————mm
Zero error of the screw gauge = ——————mm
Least count of meter scale= —————-cm
Length of the wire, l = ————cm
Diameter of wire
CALCULATIONS
xπr 2
ρ = =
l
RESULT:
1. Unknown resistance of the wire is ________ohms.
2. The resistivity of the material of the given wire is _________&!m
PRECAUTIONS:
1. The balance point must be confined to the middle region of the wire (40-60 cm).
2. In the resistance box the plug must be tight.
3. The jockey should not touch the wire, when it is moved to and fro.
4. Keep the key of the battery closed only when the reading is being taken and open it immediately after
that.
SOURCES OF ERROR:
1. The meter bridge wire may not be of uniform area of cross section throughout its length.
2. The thick copper strips at the two ends of the wire offer some resistance. They are called end
resistances; the errors due to them are called end errors.
3. As current passes through the wire, it gets heated and its resistance can change.
4. The length measurements may have error if the meter bridge wire is not taut.
METRE BRIDGE (Series and parallel combination)
AIM :To verify the laws of combination of resistances (series and parallel) using a metre bridge.
APPARAUS:Meter bridge, galvanometer, two different resistances, resistance box, one way key, a cell
or a battery eliminator, unknown resistance, connecting wires and jockey.
THEORY:When two resistances R1 and R2 are connected in series, the resistance of the combination Rs
is given by, Rs= R1 + R2
When connected in parallel, the resistance Rpof the combination is given by
Rs l lR
CIRCUIT DIAGRAM: = , Rs =
R 100 − l 100 − l
Series combination:
1 1 1
= + lR
R p R 1 R 2 Rp =
(100 − l )
lr
R =
− l)
p
( 100
Parallel Combination:
PROCEDURE:
1. Set up the apparatus as shown in the circuit diagram 1.
2. Insert only R1 in the left gap. Remove some plugs from the resistance box to get suitable value of
resistance R. Obtain the null point on the metre bridge wire by sliding the jockey on the wire.
3. Calculate the experimental value of R1. Repeat for two different values of R.
4. Insert only R2 in the left gap and repeat steps 2 and 3
5. Repeat the experiment by connecting R1 and R 2.in series. Calculate the experimental value of the
equivalent resistance of combination of resistances.
6. Repeat the experiment by connecting resistances R1 and R2 in parallel.
l l
l l
l l
l l
Calculations:
1. The theoretically expected value of the series combination of resistances is
Rs = R1 + R2 =
2. The theoretically expected value of the parallel combination of resistances is
lR
Rp =
(100 − l )
RESULT:
Series combination: The theoretical expected resistance = ——————— and the experimentally ob-
tained resistance = ——————————
Parallel combination: The theoretical expected resistance = ——————— and the experimentally
obtained resistance = ——————————
PRECAUTIONS:
1. In the resistance box the plug must be tight.
2. The balance point must be confined to the middle region of the wire (40-60 cm).
3. The jockey should not touch the wire, when it is moved to and fro.
4. Keep the key of the battery closed only when the reading is being taken and open it immediately
1 1 1
= +
after that. RP R1 R2
SOURCES OF ERROR:
1. The meter bridge wire may not be of uniform area of cross section throughout its length.
2. The thick copper strips at the two ends of the wire offer some resistance. They are called end
resistances; the errors due to them are called end errors.
3. As current passes through the wire, it gets heated and its resistance can change.
4. The length measurements may have error if the meter bridge wire is not taut.
5. POTENTIOMETER-COMPARISON OF EMF’S OF TWO CELLS

AIM : To compare the emf of two given primary cells by using potentiometer
APPARATUS: Leclanche cell, Daniel cell, potentiometer, rheostat, galvanometer, connecting wires, bat-
tery, jockey, keys. Ammeter, two way key
THEORY : If steady current is maintained by a battery through a wire of uniform
area of cross section then potential difference (V) is directly proportional to length (L).
Therefore V ∝L
According to principle of potentiometer
Emf of a cell E= k L, where k is the potential gradient and L is balancing length
Then for two different cells, it can be written
E1 / E2 = L1 / L2
PROCEDURE:
1. Arrange the apparatus as shown in the circuit diagram.
2. Insert the plug in one way key K and put one of the cells i.e. E1 in the circuit by inserting the plug in
the gap (K1). Now press the jockey over the end A of the wire and note the direction of current
in the galvanometer,. Now repeat the same at the other end and note the direction. If the direction
is opposite then the connections are correct.
3. Now move the jockey over the wire and obtain a point, where there is no deflection. Note the
length of wire, let it be L1.
4. Similarly obtain the null point for the cell E2, let it be L2.
5. Repeat the experiment (2, 3, 4) by changing resistance with the help of the rheostat.
OBSERVATIONS:
Least count of meter scale =_________cm
S No Balancing length for Balancing length for E1 / E2 = L1 / L2

E1 (Leclanche Cell) L1 E2 (Daniel Cell) L2
(cm) (cm)
1.
2
3
CALCULATIONS:
Mean E1/E2 =
RESULT: The ratio of two cells (Leclanche to Daniel) E1 / E2 =_______
PRECAUTIONS:
1. The emf of the auxiliary battery E should be grater than either of the two cells E1 and E2
2. A low resistance rheostat should be used.
3. Press the jockey gently.
4. The current should remain fixed for each set of observations with the two cellls.
SOURCES OF ERROR:
1. The potentiometer wire may not be uniform.
2. The resistance of wire may change due to change in temperature.
POTENTIOMETER- INTERNAL RESISTANCE OF A CELL

AIM
To determine internal resistance of a given primary cell using potentiometer.
APPARATUS
Leclanche cell, potentiometer, rheostat, galvanometer, connecting wires, battery, jockey, keys, Amme-
ter, two one way keys
THEORY
If steady current is maintained by a battery through a wire of uniform area of cross section the potential
difference (V) is directly proportional to length (L).
Therefore
Internal resistance of the cell is,
r is internal resistance, R is external resistance, L1 is balancing length when key K2 is switched off and
L2 is balancing length when key K2 is switched on.
Procedure
1. Arrange the apparatus as shown in the circuit diagram.
2. Insert the plug in one way key K1 while key k2 is off , now press the jockey over the end A of the
wire and note the direction of current in the galvanometer,. Now repeat the same at the other end
and note the direction. If the direction is opposite then the connections are correct
3. Now move the jockey over the wire and obtain a point, where there is no deflection.Note the
length of wire, let it be L1
4. Similarly obtain the null point with key k2 plugged on, let it be L2.
5. Repeat the steps (2, 3, 4) by changing resistance with the help of the rheostat
Calculation
Show calculation for individual internal resistances.
Mean value of internal resistance is …………………….
RESULT: The internal resistance of given cell is _______
PRECAUTIONS:
1. The emf of the auxiliary battery E should be greater than either of the cell.
2. Always measure length from point A i.e. the point at which positive terminals of battery are
connected and measure this length upto the balance point.
3. Press the jockey gently. Against the potentiometer wire.
4. The current should remain fixed for each set of observations.
5. Insert K1 and K2 only when readings are taken otherwise the wires may get heated up due to
continuous flow of current and may also affect the internal resistance of the cell.
SOURCES OF ERROR:
1. The potentiometer wire may not be uniform.
2. Brass strips at the ends may have a finite resistance.
3. Emf of the auxiliary battery producing the drop of potential along the wire may not be constant
throughout the course of the experiment.
4. Heating of the potentiometer wire by current may introduce some error.
FREQUENCY OF AC MAINS
AIM : To find the frequency of ac mains using a sonometer.
APPARATUS : Sonometer, half kg weights, two wooden bridges, horse shoe magnet.
THEORY : If a sonometer wire of length L, mass per unit u, be stretched between two wedges by a
force T (tension), is once plucked from the middle and then released, it will execute transverse vibrations
with a fundamental frequency
Where L is the distance between two bridges
PROCEDURE:
1. Arrange the apparatus according to the circuit diagram.
2. Adjust the secondary of the transformer to 4 V and place ½ kg on the hanger and
then switch on the ac mains.
3. Adjust the distance between the bridges till the amplitude of vibration of the
sonometer wire between the bridges becomes maximum. Measure the length of
the wire between the two bridges. This is the resonant length.
4. Repeat the experiment for at least four sets of observations by increasing load in
the hanger. STEP DOWN TRANSFORME
OBSERVATIONS:
Mass per unit length of wire µ =___________g/cm
L.C. of meter scale=__________________cm
Standard Value of frequency of ac mains fo= 50 Hz
TABLE
CALCULATIONS- Show calculations for each frequency
Mean frequency of ac mains f= _________Hz;

 f − f0 
Percentage error =   ×100
 f0 
Result: Experiment value of frequency of ac mains f = ____________ Hz
PRECAUTIONS
1. The sonometer wire should be uniform and free from kinks.
2. While increasing the tension of the wire, be careful that the wire is not stretched beyond
elastic limit.
3. The bridges should have sufficient height so as to support the sonometer wire properly.
4. Pulley should be frictionless otherwise tension in the string may not be equal to suspended
weights in hanger.
SOURES OF ERROR
1. The tension on the two sides of the bridges may not be the same.
2. The wire is not of uniform composition.
3. The expression for determination of frequency ( RS )

G =assumes that the wire is perfectly flexible. Hence
due to rigidity of wire some error will be there. ( R − S )
RESISTANCE OF GALVANOMETER BY HALF DEFLECTION

AIM:To determine the resistance of galvanometer by half deflection method and to find its figure of
merit.
APPARATUS: Galvanometer, voltmeter, ammeter, battery, two one way keys, resistance box (0- 10 k Ω
), resistance box (0-200 Ω ).
THEORY:
1. Using half deflection method the resistance of galvanometer is given by
Where R is the resistance in series with galvanometer and S is shunt resistance.
2. The figure of merit
 E 1
k = 
 R + G θ
Where E is the emf of the cell, θ is the deflection produced in a galvanometer of resistance G. When a
resistance R is used in used in series with the circuit.
R (0 - 10 k Ω)
S (0 - 100 Ω)
E
K=
(R + G)θ
( A / div )
Mean value of G= _________.....ohm
Mean value of K = ____________A / Division
RESULT:
a) The experimental value of resistance of the given galvanometer is_________ohm.
b) The figure of merit of the given galvanometer is_____________A/div.
PRECAUTIONS:
1. The cell or battery used in the circuit should be of constant emf.
2. Before closing the keys K1 and K2 all the plugs of the resistance boxes R and S should be
tightly fitted and checked.
3. The deflection in the galvanometer should be an even number of divisions than and as large as
possible.
4. The value of R should be very large as compared to the value G.
SOURCES OF ERROR:
1. The resistance of the coils in the resistance box used may not exactly be the same as marked.
2. The plugs in the resistance box may be loose which will produce large error in the observations.
3. The emf of the battery may not be constant.
REFRACTIVE INDEX OF PRISM

AIM: To determine the angle of minimum deviation for a given prism by plotting a graph between
angle of incidence and angle of deviation and hence calculate refractive index of the material of the
prism.
APPARATUS: Drawing board, sheets of white paper, drawing pins, pencil, protractor, scale,
graph paper.
THEORY : The refractive index ì of the material of prism is given by
Where A is angle of prism and δ min is angle of minimum deviation
A + δ min
sin( )
µ= 2
sin( A / 2)
PROCEDURE:
1. Fix the white sheet of paper in the drawing board. Place the prism and draw its boundary with
the help of a sharp pencil.
2. Draw a normal N on the face AB and draw an incident ray PQ making an angle of incidence i
say 350.
3. Fix two pins p1 and p2 on the incident line PQ.
4. Now see the images P1 and P2 through the face AC. Fix other pins P3 and P4 in such a way
that these two pins and the images of pins P1 all appear in the same line.
5. Remove the pins P3 and P4 and join their positions to obtain the emergent ray RS.
6. Measure the angle of deviation 8 corresponding to this angle of incidence.
7. Measure the angle of deviation δ by repeating the above steps for 400 , 45o and so on.
8. Plot a graph taking angles of incidence along X axis and then corresponding angles of deviation
along Y axis.
i → Angle of incidence
e → Angle of emergence
δ → Angle of emergence
r1 & r 2 → Ang le of refractio n
OBSERVATION:
Angle of prism = _________
Least count of protractor = _________
Calculation: Graph between angle of incidence and angle of deviation.
Angle of minimum deviation=………….
RESULT:
1. As angle of incidence is increased, angle of deviation decreases, becomes minimum and then
increases. The minimum value of angle of deviation is _________
2. Refractive index of the material of the prism is ì =__________
PRECAUTIONS:
1. Alpins should be fixed vertically to the plane of paper.
2. The angle of incidence should be between 300 and 600
3. The distance between pins should be at least 8 cm.
4. The position of the prism should not be disturbed for a given set of observations.
5. Same angle of prism should be used for all observations.
SOURCES OF ERROR:
1. The pins are not fixed vertically.
2. Prism is disturbed while taking observations.
3. There may be an error in measuring the values of the angles.
CONVEX LENS
AIM : To find the focal length of a convex lens by plotting of graphs u and v
and between 1/u and 1/ v.
APPARATUS : Convex lens, lens, two needles, three uprights, one clamp, an optical
bench.
THEORY: The position of the image formed by a convex lens depends upon the
position of object with respect to the lens.
Where of focal length, u object distance, v image distance
PROCEDURE:
1. Find the rough focal length of convex lens by focusing a sharp, clear and inverted image of
the distant object on the screen.
2. Place object needle at a distance greater than 2F from the lens. See its inverted image on the
other side of the lens. Now adjust the image such that the parallax between the image of the
object needle and image needle is removed. The parallax is to be removed tip to tip.
3. Note the position of the lens, object needle and image needle.
4. Repeat the above steps for different positions of object needle by placing it beyond 2F and
between F and 2F.
5. Draw the graph between (a) u & v (b) 1/u & 1/v.
OBSERVATIONS:Rough length of convex lens = _____cm ,
L.C. of optical bench = ______ cm
Calculation of focal length by graphical methods.
(i) u-v graph. Draw a line OA making an angle of 450 with either axis. Draw AB and AC
perpendicular on X- and Y- axes, respectively. Coordinates of point A must be (2f,
2f).
or
(ii) 1/u and 1/v Graph
RESULT:
The focal length of a given convex lens is
(i)___________cm from u and v graph.
(ii)___________cm from 1/u and 1/v graph.
PRESCAUTIONS:
1. The uprights must be vertical.
2. The tips of object needle and image needle must be at the height as the center of convex lens.
3. The cross movement of uprights should be used so that image of object needle is in line with the
image needle.
4. Parallax must be removed tip to tip.
SOURCES OF ERROR:
1. The convex lens is very thick.
2. The principal axis of the lens may not be parallel to the optical bench scale.
3. Parallax is not removed tip to tip.
1. FOCAL LENGTH OF CONCAVE LENS
AIM: To find the focal length of a concave lens using a convex lens.
APPRATUS: An optical bench with four uprights, concave lens, two holders, two optical needles.
THEORY: Let I be the real image of an object O formed by lens L1. If a concave lens L2 is placed
between the positions I and L1 in such a way that the real image of O is now formed at I’ then the image
I’ is the virtual formed by concave lens L2 for object I. Hence focal length can be calculated as
Where f focal length of concave lens. u object distance and v image distance.
PROCEDURE:
1. Mount an object needle O in the first upright, the given convex L1 in the second upright and the
image needle I in the fourth upright. Leave the third upright for mounting concave lens later.
2. Adjust the height so that tips of the object and image needles are at same level as the centre of lens
L1.
3. Keep the object needle O beyond the rough focal length of lens L1. Look for the real inverted
image of O from the other size and with the help of image needle I.
4. Mount the given concave lens in the third upright in between L1 and I. The distance between L1
and L2 is suitably adjusted. Look from the side of needle I and move it gradually away from L2 till
there is no tip to tip parallax between the image and image needle I’. Note the position of concave
lens L2 and image needle I’. This is one set of observations.
5. Change the position of concave lens L2 and repeat step 4 and take at least four observations.
OBSERVATIONS:
Rough length of convex lens = _____cm
L.C. of optical bench = ______ cm
Calculations.
Calculate (Show calculation for each value of f )
Mean focal length f = ______ cm
RESULT:
Focal length of given concave lens = _____ cm
PRECAUTIONS:
1. The uprights must be vertical
2. The tips of object needle and image needle be at the same height as the centre of convex lens.
3. The cross movement of uprights should be used so that image of object needle is in line with the image
needle.
5. Focal length of convex lens should be smaller than the focal length of concave lens
SOURCE OF ERROR:
1. The convex lens is very thick.
2. The principal axis of the lens may not be parallel to the optional parallel to the optical bench scale.
CONCAVE MIRROR
AIM: To find the value of v for different values of u in case of concave miror and calculate the focal length
.
APPARATUS:An optical bench with three uprights, concave mirror, a mirror holder, two optical needles.
RAY DIAGRAM:
THEORY(Formula Used):
Where,f= focal length of mirror.

u =object distance and v= image distance.
PROCEDURE:
1. Find the rough focal length of concave mirror by focusing a sharp, clear and inverted image of
the distant object on the screen.
2. Clamp the concave mirror on an upright and mount it vertically near one end of the optical
bench.Move an object on the optical bench back and fourth so that its image is formed at the same
height.
3. Place another needle in front of concave mirror and adjust the height of the tips of these pins.
4. Move one needle away from the mirror and place it almost at 2F.An inverted image of same size
as the needle should be visible.
5. Now place a piece of paper on one of the needle and take this as object . Place this needle be-
tween F and 2F.
6. Locate the image of the needle using other needle and remove the parallax between the image and
object.Note the values of u and v.
7.Repeat the experiment for at least three different positions of the object and determine the corre-
sponding values of v.
OBSERVATIONS: Rough length of concave mirror = _____cm,L.C. of optical bench = ______

cm
CALCULATIONS:Mean focal legth
Result: The Focal length of given concave mirror = _____ cm f1 + f 2 + f 3

f =
3
PRESCAUTIONS:
1. The uprights must be vertical.
2. The tips of object needle and image needle must be at the height as the center of concave
mirror.
3. The cross movement of uprights should be used so that image of object needle is in line
with the image needle.
SOURCES OF ERROR:
1. The upright may not be vertical.
2. The principal axis of the mirror may not be parallel to the optical bench scale.
1. Focal length of Convex Mirror
AIM: To find the focal length of a convex mirror using a convex lens.
APPARATUS: A convex lens, convex mirror, optical bench, two needles, four uprights, two holder.
THEORY:
An object AB is placed at point P2 in front of a thin convex lens such that its real, inverted and magni-
fied image A2B2 is formed at position C on the other side of the lens [Fig. (a)]. Now a convex mirror is
introduced between the convex lens and point C and so adjusted that the real and inverted image A2B2
coincides with the object AB at point P2 [Fig.(b) ]. This is possible if the light rays starting from the tip
of the object, after passing through the lens, fall normally on the reflecting surface of the convex mirror
and retrace their path. Any normal ray (perpendicular) to a spherical surface has to be along the radius
of that sphere so that point C must be the centre of curvature of the convex mirror. Therefore, the
distance P C is the radius of curvature R and half of it would be the focal length of the convex mirror.
That is,
f=
PROCEDURE:
1. Find the approximate focal length of the given thin convex lens.
2. Place the uprights mounted with pin P1 (object pin), convex lens LL, and convex mirror MM on
the horizontal optical bench.[Fig. (a)].
3. Place the object pin P1 from the convex lens LL at a distance slightly greater than the focal length
of the lens. Adjust the position of the convex mirror MM till the light rays reflected back from the
mirror pass through the lens and form a real and inverted image coinciding with the object pin P1, as
shown in Fig.(a). Remove the parallax between the image and object pins.
4. Read the position of uprights holding the object pin P1, convex lens LL, and convex mirror MM2
and record the observations in the observation table.
5. Remove the convex mirror from its upright and fix image pin P2 on it. Using the method of parallax
and without changing the position of lens LL and object pin P1, adjust the position of image pin P2
on the other side of the lens so that it coincides with the real and inverted image of the object pin P1
formed by the convex lens [Fig.(b)]. Note the position of the image pin.
Repeat the experiment by changing the separation between the pin P1 and lens L L’ and the mirror
MM2. In this manner, take four sets of observations
OBSERVATIONS
Least count of optical bench = ……..cm
Observation table
CALCULATIONS:
Mean focal length of convex mirror f= ……………………………..
RESULT: The focal length of the given convex mirror is………………
PRECAUTIONS:
1. The uprights supporting the pins, lens and mirror must be rigid and mounted vertically.
2. The apertures of the given convex lens and convex mirror should be small, otherwise the image
formed will be distorted.
3. Eye should be placed at a distance of about 25 cm or more from the image pin.
4. Optical bench should be horizontal. The tips of pins,centre of convex lens and pole of the
mirror should be at the same horizontal level.
SOURCE OF ERROR:
1. The tip of the inverted image of the object pin should just touch the tip of the image pin and
must not overlap. This should be ensured while removing the parallax.
2. Personal eye defects may make removal of parallax tedious.
The convex mirror should preferably be front-coated. Otherwise multiple reflections may take
place
Refractive Index of Liquid
AIM: To find the refractive index of a liquid using plane mirror and a convex lens.
APPARATUS: A convex lens, plane mirror, transparent liquid, optical needle, iron stand with bars and
clamp arrangement, meter scale.
THEORY:Let’s add small amount of water on a plane mirror and place a convex lens over it. This forms
a plano-concave lens of water between the lower surface of convex lens and plane mirror.
Let fl and fg are the focal lengths of water lens and convex lens respectively, then focal length of the
combination is:
Let f l and fg are the focal lengths of water lens and convex lens respectively, then focal length
of the combination is:
1 1 1
= +
F fl fg
The focal length of the plano-concave lens is
1 1 1
= − .....( i )
f l F fg
From Lens Maker’s formula,
As R1 = R and R2 = infinite (for water lens.)
The refractive index of water is,
1 For glass lens, µ = 1.5

fl
Now using Lens maker’s formula, =
Therefore, refractive index of water is,
PROCEDURE:
(a) For Focal length of the convex lens

1. Take a convex lens and find its rough focal length.
2. Take a plane mirror and place it on the horizontal base of iron stand.
3. Place the convex lens on the plane mirror.
4. Screw the optical needle tightly in the clamp of the stand and hold it horizontally above
the lens at a distance equal to its rough focal length.
5. Bring the tip of the needle to the vertical principle axis of the lens, so that the tip of
the needle appears to touch the tip of its image.
6. Move the needle up and down and remove parallax between the tip of the needle and
the tip of its image.
7. Measure the distance between the tip of the upper surface of the lens using a plumb
line and a meter scale.
8. Also measure the distance between the tip and the surface of the plane mirror.
(b) For Focal length of the combination of lens
9. Take a few drops of transparent liquid on the plane mirror and put the convex lens over
it with its same face about as before.
10. Repeat steps 6, 7 and 8.
11. Record your observation as given below.
OBSERVATION:
1. Rough focal length of convex lens =______ cm.
2. Least count for meter scale =................. cm
CALCULATION:
1 1
=
fg R
1 1 1
= −
fl F f g
fg
µ = 1+
fl
RESULT: The refractive index of a given liquid is_________.
PRECAUTIONS:
1. The needle should be kept horizontal and principal axis of the mirror should be vertical.
2. Eye should be kept at a distance of distinct vision while removing the parallax.
3. Parallax may not be removed tip to tip.
SOURCES OF ERROR:
1. Liquid may not be quite transparent.
2. The parallax may not be fully removed.
P-N JUNCTION DIODE
AIM: To draw the characteristic curve in forward bias and reverse bias of a P-N junction diode.
APPRATUS: P-N junction diode, battery, rheostat, resistance, milliammeter, voltmeter, wires.
THEORY:
Forward biased diode: A diode is said to be forward

Fg biased if its P-end is at higher potential with
respect to N-end.
Reverse biased diode: A diode is said to be reverse biased if its P-end is at lower potential with
respect to N-end.
Forward Biased P-N Junction
Reverse Biased P-N Junction
PROCEDURE:
For Forward Bias
1. Make the connection as shown in the figure for forward bias.
2. Adjust the rheostat of the potential divider arrangement to a minimum value and slowly increase
the potential difference across the diode by varying the rheostat of the potential divider. Note the
reading in voltmeter and corresponding reading of ammeter.
3. Vary the potential difference so as to have 10 to 15 observations.
4. Plot the graph taking V along X axis.
For Reverse Bias
1. Make the connection as shown in the figure for reverse bias.
1. Repeat the step 2, 3, and 4 as above for reverse bias.
OBSERVATIONS:
1. Forward Bias
(i) Least count of milliammeter = ____________mA
(ii) Range of milliammeter = ……………………….. mA
(iii) Least count of voltmeter = ____________V
(iv) Range of voltmeter = …………………… V
GRAPH:
L
D
RUSULT: In forward bias of a P-N junction diode, with increase in bias voltage, the forward current
increases slowly in the beginning and then rapidly.
In the reverse bias of a P-N junction diode, when reverse bias voltage increases, initially there is a very
small reverse current flow, which remains almost constant with bias. But when reverse bias voltage
increases to sufficiently high value, the reverse current suddenly increases to a large value.
PRECAUTIONS:
1. All the connections should be tight.
2. Voltmeter should be connected in parallel and ammeter in series.
3. The positive of the battery should be connected to the p-end and negative to n-end of the p-n
junction of diode to have forward bias and vice versa for reverse bias.
4. The potential differential across the diode should be varied slowly.
5. Zero error must be noted properly, if any.
SOURCE OF ERROR
1. The diode is not suitably biased.
2. Current is passed through the diode for longer duration
ZENER DIODE
AIM : To draw the characteristic of a Zener diode and to determine its reverse breakdown voltage.
APPARATUS : p-n junction Zener diode, power supply with potential divider 0-100 in rheostat, mi-
crometer, voltmeter.
THEORY: When a reverse bias is applied to a p-n junction diode the reverse current in the diode is
almost zero. On increasing the reverse bias to a certain value, the reverse current increases sharply. The
reverse voltage applied to the diode at this stage is called Zener voltage.
PROCEDURE:
1. Assemble the various components of the circuit according to the figure.
2. Move the slider of the rheostat so that voltage supply to the Zener diode is minimum.
3. Increase the reverse bias applied to the Zener diode gradually by moving the slider of the rheostat.
Read the values from voltmeter and ammeter.
4. After a certain voltage, there is a sudden increase in the reverse current. This voltage is called
Zener voltage.
5. Take 15 -20 readings by varying voltage across the diode in steps.
6. Plot a graph between reverse bias voltage (V) along X axis and current (I) along Y axis.
OBSERVATIONS:
Least count of voltmeter = ____________V.
Least count of ammeter = _____________ µ A.
GRAPH:
RESULT:The Zener voltage for the given diode is____________volt.

PRESCAUTIONS:
1. All the connections should be tight.
2. Voltammeter should be connected in parallel and ammeter in series.
3. The positive of the battery should be connected to the n-end and negative to the p-end of the
diode to have reverse bias.
4. The potential difference across the diode should be varied slowly.
SOURCES OF ERROR:
1. The diode is not reverse biased.
2. Current is passed through the diode for longer duration.
Same as pn-junction diode
SUBJECT: PHYSICS
ASSESSMENT: PRE-MIDTERM
Maximum marks : 70 Time Limit : 3 hrs
(1) All questions are compulsory. There are 33 questions in all.

(2) This question paper has five sections: Section A, Section B, Section C, Section D and Section E.?
(3) Section A contains ten very short answer questions and four assertion reasoning MCQs of 1 mark
each, Section B has two case based questions of 4 marks each, Section C contains nine short
answer questions of 2 marks each, Section D contains five short answer questions of 3 marks
each and Section E contains three long answer questions of 5 marks each.?
(4) There is no overall choice. However internal choice is provided. You have to attempt only one of
the choices in such questions.
SECTION-A
1. Draw the graph showing the velocity acquired by an electron starting from rest and moving
through potential difference V. (1)
2. Write the dimensions of electrical conductivity. (1)
3. Write the expression, in a vector form, for the ? Lorentz magnetic force F on a charge -q moving?
with velocity V in a magnetic field B . What is the direction of the magnetic force? (1)
4. A battery of 16V and internal resistance 2 is connected to an external resistance R. Calculate
the value of current so that power in the circuit is maximum. (1)
5. An charge q μ C is placed at the centre of a cube of side 0.1m. Then calculate the electric flux
diverging from each face of this cube. (1)
6. μ
A carbon resistance is having a following coding: green, orange, black, gold. Write the resistance
of resistor. (1)
7. What will be the path of a charged particle moving in a uniform magnetic field at any arbitrary
acute angle? Why? (1)
8. Four charges as shown in figure are placed at the corners of a square of side length a. What will
be the direction of electric field at the centre of square (1)
9. When a current is passed in a conductor,30C rise in temperature is observed. If the strength of

current is made thrice, then what will be the rise in temperature? (1)
10. The electric field required to keep a water drop of mass m just to remain suspended, calculate
the charge of the drop. (1)
For question numbers 11, 12, 13 and 14, two statements are given-one labelled Assertion (A)
and the other labelled Reason (R). Select the correct answer to these questions from the codes
(a), (b), (c) and (d) as given below.?
b) Both A and R are true but R is NOT the correct explanation of A
c) A is true but R is false?
d) A is false and R is also false (1×4)
11. Assertion: Electric current whose magnitude and direction reverses periodically with time is
known as alternating current. ?
Reason: In a complete cycle of AC, the mean value of AC will be zero.
12. Assertion (A): No work is done in moving a test charge around a circular arc of radius r at the
centre of which another point charge q is located. ?
Reason(R): No work is done in moving a test charge from one point to another over an
equipotential surface. ?
13. Assertion: If North-pole of a bar magnet is pushed towards the coil, the pointer in the galva
nometer deflects, indicating the presence of electric current in the coil.
Reason: The relative motion between the magnet and the coil that is responsible for generation
(induction) of electric current in the coil.
14. Assertion: Through the same current flows through the line wires and the filament of the bulb
but the heat produced in the filament is much higher than that in line wires.
Reason: The filament of bulbs is made of a material of high resistance and a high melting point.
SECTION-B
Questions 15 and 16 are Case Study based questions and are compulsory. Attempt any
4 sub parts from each question. Each question carries 1 mark.
15. Lamps in a circuit and their brightness:
Two tungsten lamps with resistances R1 and R2 respectively at full incandescence are connected first in
parallel and then in series in a lighting circuit of negligible internal resistance. In a series circuit, the output
current of the first resistance flows into the input of the second resistor therefore the current is same in each
resistor. In parallel circuit, all the resistor leads on one side of the resistors are connected together and all
the leads on the other side are connected together. The energy dissipated per unit time is the power
dissipated. It is the power loss, called ohmic loss, which heats up the coil of an electric bulb to incandes-
cence. It is given that R1 > R2 (1×4)
a. Which lamp will glow more brightly when they are connected in parallel?
A Bulb having lower resistance B Bulb having higher resistance
C Both the bulbs D Data is not sufficient
b. If the lamp of resistance R2 burns out in series circuit, and the lamp of resistance R1 alone is plugged
in, will the illumination increase or decrease?
A Illumination will remain same B Illumination will increase
C Illumination will decrease D It is not possible to predict from the given information
c. If the lamp of resistance R1 in parallel circuit now burns out, how will the illumination produced
change?
A Net illumination will increase B Net illumination will decrease
C Net illumination remain same D Net illumination will reduce to zero
d. The total power consumed when they are connected in series
16. MOVING COIL GALVANOMETER

The moving coil galvanometer is made up of a rectangular coil that has many rums and it is usually made of
thinly insulated or fine copper wire that is wounded on a metallic frame. The coil is free to rotate about a
fixed axis. A phosphor-bronze strip that is connected to a movable torsion head is used to suspend the coil
in a magnetic field.
i) Moving coil galvanometer is used to detect

a) potential difference
b) electric current
c) electric resistance
d) electric field
ii) Shape of magnets used to produce magnetic field in moving coil galvanometer
a) Plane
b) convex
c) concave
d) none of the above
iii) Phosphorous bronze wire used because it has
a) high melting point
b) low temperature coefficient of resistance
c) high restoring torque per unit twist
d) low restoring torque per unit twist
iv) A galvanometer can be converted in to ammeter by connecting
a) low resistance in tenet
b) high resistance in tenet
c) low resistance in parallel
d) high resistance in parallel
SECTION-C
17. Three Point charges Q1 =+ 10 μ C, Q2 =+ 50 μ C and Q3 are separated as shown in the figure
below. What is the electrostatic charge on particle 3, if the net electrostatic force on particle 2 is zero?
(2)
18. The strength of magnetic induction at the center of a current carrying circular coil is B1 and at a point on
its axis at a distance equal to its radius from the center is B2. Find the value of B1 /B2. (2)
OR
An element of length 1 cm along x - axis is placed at origin and carries a large current I = 10 A in positive
X -direction. What is the magnitude and direction of magnetic field on positive Y- axis at 0.5m from
origin? (2)
19. A potentiometer wire of length 100 cm having a resistance of 10 Ω is connected in series with a
resistance and cell of emf 2V of negligible internal resistance. A source emf of 10 mV is balanced
against a length of 40 cm of potentiometer wire. What is the value of the external resistance R conected
in circuit? (2)
20. A parallel plate capacitor is charged to a potential difference V by D.C. Source. The capacitor is
then disconnected from the source. if the distance between the plates is halved, state with reason
how the following will change : (i) electric field between plates and (ii) energy stored in the capacitor.
(2)
21. Using Kirchhoff's rules determine the value of unknown resistance R in the circuit so that no current
flows through 4 Ω resistance. Also find the potential difference between A and D. (2)
A cylindrical metallic wire is stretched to increase its length by 10%. Calculate the percentage increase
in its resistance. (2)
22. A long straight wire carrying a current of 25 A rests on a table as shown in the figure. Another wire
PQ of length 1 m, mass 2.5 g carries the same current but in the opposite direction. The wire PQ is free
to slide up & down. To what height will PQ rise? (2)
23. An electric dipole is held in a uniform electric field. (i) Using suitable diagram show that it does not
undergo any translatory acceleration, and (ii) Derive an expression for torque acting on it. (2)
24. A metal rod consumes power P on passing current. Find power consumed if metal rod is cut into halves
and joined in parallel to the same source. When electrons drift in a metal from lower to higher potential,
does it mean that all free electrons of the metal are moving in the same direction? Explain.
OR
A steady current flows in a metallic conductor of non- uniform cross section. State which of the quantities
current, current density, electric field and drift velocity remain constant? Draw a graph to show the varia-
tion of resistivity of copper with temperature. (2)
25. A current is set up in a long copper pipe. Calculate the magnetic field (i) inside (ii) outside the pipe?
SECTION-D
26.Two cells of emf 1V and 2V and internal resistances 2 Ω and 1 Ω respectively are connected in (i)
series, (ii) parallel. What should be the external resistance in the circuit so that the current through the
resistance be same in the two cases? In which case is more heat generated in the cells? (3)
OR
A copper wire of length 3m and radius r is nickel plated till its radius becomes 2r. What would be the
effective resistance of the wire, if specific resistance of copper and nickel are ρ c and ρ n respectively?
(3)
27. Derive an expression for capacitance of parallel plate capacitor of area A and plate separation d, if
a dielectric slab of thickness t(t<d) is introduced between the plates. (3)
OR
Define dielectric constant of a medium. Explain how the polarization of dielectric reduces the electric
field inside the dielectric. What is the relation between polarization and reduced value of electric field?
28. (i) Two wires of the same material having lengths in the ratio 1:2 and diameter 2:3 are connected in
series with an accumulator. Compute the ratio of potential difference across the two wires
(ii) Why does Resistance increase in series combination and decrease in parallel combination? (3)
OR
Two students A and B perform an experiment on potentiometer separately using the circuit diagram
shown here. Keeping other things unchanged
(i) A decreases the value of resistance R
(ii) B increases the value of resistance S in the set up.
How would these changes affect the position of null point in each case and why? (3)
29. (a) Why does a solenoid contract when a current is passed through it ?
(b) A wire of length 0.04 m carrying a current of 12 A is placed inside a solenoid, making an
angle of 300 with its axis. The field due to the solenoid is 0.25 T. Find the force on the
wire. (3)
30. A charge of 8 µC is distributed uniformly on the surface of a sphere A of radius 1 cm.It is covered
by a concentric, hollow conducting sphere B of radius 5cm.(i)Find the electric field at a point 2cm
away from the Centre. (ii) A charge of 12 µC is placed on the hollow sphere B. Find surface
charge density on the outer surface of hollow sphere B. (3)
SECTION-E
31. (i) Write the expression for the magnetic moment M due to a planar square loop of side l carrying a
steady current I in vector form.
As shown in figure this loop is placed in a horizontal plane near a long straight conductor carrying a
steady current I1 at a distance l. Give reason to explain that the loop will experience a net force but no
torque. Find the expression for the net force acting on the loop.
(ii) Equal currents are flowing through two infinitely long parallel wires. What will be the magnetic field at
a point midway when currents are flowing in same direction? (5)
OR
(i) (a) A point charge q moving with speed v enters a uniform magnetic field B that is acting into the
plane of the paper as shown in figure. What is the path followed by the charge q and in which
plane does it move?
(b) How does the path followed by the charge get affected if its velocity has a component parallel to
B?
(c) If an electric field E is also applied such that the particle continues moving along the original
straight line path, what should be the magnitude and direction of the electric field E?
(ii) A particle of mass m and charge q moves at right angles to a uniform magnetic field. Plot a graph
showing the variation of the radius of the circular path described by it with the increase in its charge.
Justify your answer. (5)
32. (i) Derive condition for balanced Wheatstone bridge. Why is Wheatstone bridge (or metre bridge)
method considered unsuitable for the measurement of very low resistances?
(ii) A battery of internal resistance r is connected to the network of resistances as shown in the
figure. Calculate the current drawn from the battery, if ε =2V and R=2 Ω (5)
OR
(i) Explain the term drift velocity of electrons in a conductor. Derive the expression for the current
through a conductor in terms of drift velocity.
(ii) Find the drift velocity of electrons if current flowing through a copper wire of cross- section area
1mm2 is 2A. Assume that each atom of copper contributes one electron. (Given density of Cu=9
g/cm3, atomic weight of Cu=63u and Avagadro's number= 6x1023).
33. (i) Define electric flux. Write its S.I. unit. Using Gauss's to derive expression for electric field inten
sity at a point due to a uniformly charged infinite plane sheet if surface charge density is ?.
(ii) A uniform line charge with linear density λ lies along the y-axis. What flux crosses a spherical
surface centered at the origin with r = R? (5)
OR
(i) Derive the expression for the energy stored in a parallel plate capacitor. Hence obtain the
expression for the energy density of electric field.
(ii) Find the ratio of the potential difference that must be applied across the parallel and the series
combination of two capacitors C1 and C2 with their capacitances in the ratio 1:3 so that the
energy stored in the two cases, becomes the same. (5)
CLASS XII
PHYSICS
MID TERM 2020
MM-70 TIME:3HOURS
General Instruction
(1) All questions are compulsory. There are 33 questions in all.
(2) This question paper has five sections: Section A, Section B, Section C, Section D and Section
E.
(3) Section A contains ten very short answer questions and four assertion reasoning MCQs of 1
mark each, Section B has two case-based questions of 4 marks each, Section C contains nine
short answer questions of 2 marks each, Section D contains five short answer questions of 3
marks each and Section E contains three long answer questions of 5 marks each.
(4) There is no overall choice. However internal choice is provided. You have to attempt only one
of the choices in such questions.
Section -A
1. A given rectangular coil OLMN of area A, carrying a given current I, is placed in a uniform magnetic
field in given figure. What is the magnitude and direction of torque experienced by this coil?
2. Find the potential difference (VA – VB) between the points A and B in the given figure.
3. A variable resistor R is connected across a cell of emf ∈ and internal resistance r. Plot a graph to
show the variation of the current as a function of R.
4. How is the power transmission and distribution over long distances done with the use of transform
ers?
5. Why does a solenoid contract when a current is passed through it?
6. The plot of the variation of potential difference across a combination of three identical cells in series,
versus current is shown below. What is the emf and internal resistance of each cell? What is the
internal resistance of each cell?
7. Sketch a schematic diagram depicting electric and magnetic fields for an electromagnetic wave
propagating along the Z-direction.
8. A ray of light travelling from glass to air undergoes total internal reflection. Find critical angle in terms
of the speed of light.
9. If eight similar charge drops combine to form a big drop. what is the ratio of capacitance of bigger
drop to that of smaller drop?
10. A vertical wire carrying a current in the upward direction is placed in a horizontal magnetic field
directed towards north. What is the direction of force?
In questions 11 to 14, a statement of assertion is followed by a statement of reason. Choose
the correct option
11. Assertion: A current flows in a conductor only when there is an electric field within the conductor.
Reason: The drift velocity of electron in presence of electric field decreases.
(A) If both assertion and reason are true and reason is the correct explanation of assertion.
(B) If both assertion and reason are true but reason is not the correct explanation of assertion.
(C) If assertion is true but reason is false.
(D) If both assertion and reason are false.
12. Assertion: The electrostatic potential energy is independent of the manner of which the
configuration is achieved.
Reason: Electrostatic field is conservation field.
13. Assertion: Magnetic field lines are continuous and closed.
Reason: Magnetic monopole does not exist.
14. Assertion: When a charged particle moves in a circular path. It produces electromagnetic wave.
Reason: Charged particle has acceleration.
SECTION-B
Question 15 and 16 are case study-based questions and are compulsory. Each question has four
parts of 1 mark each.
15. Mutual Inductance between the two coils is defined as the property of the coil due to which it opposes
the change of current in the other coil, or you can say in the neighboring coil. When the current in the
neighboring coil changes, the flux sets up in the coil and because of this, changing flux emf is induced in the
coil called Mutually Induced emf and the phenomenon is known as Mutual Inductance. The value of
Mutual Inductance (M) depends upon the following factors:
1. Number of turns in the secondary or neighboring coil
2. Cross-sectional area
3. Closeness of the two coils
When on a magnetic core, two or more than two coils are wound, the coils are said to be mutually
coupled. The current, when passed in any of the coils wound around the magnetic core, produces flux
which links all the coils together and also the one in which current is passed. Hence, there will be both self-
induced emf and mutual induced emf in each of the coils. The best example of the mutual inductance is the
transformer, which works on the principle of Faraday's Law of Electromagnetic Induction. Faraday's law
of electromagnetic induction states that " the magnitude of voltage is directly proportional to the rate of
change of flux." which is explained in the topic Faraday's Law of Electromagnetic Induction.
a. The phenomenon due to which there is an induced current in one coil due to current in a neighbouring
coil is?
A. Electromagnetism
B. Susceptance
C. Mutual inductance
D. Steady current
b. Mutual inductance between two magnetically coupled coils depends on
A. Permeability of the core material
B. Number of turns of the coils
C. Cross sectional area of their common core
D. All of the above
c. Which of the following is unit of inductance?
A. Ohm B. Henry C. Ampere turns D. Webers/meter
d. If in an iron cored coil the iron core is removed so as to make the air cored coil, the inductance of the
coil will be
A. More B. Less C. The same D. None of these
16. The lens maker's formula relates the focal length of a lens to the refractive index of its material and
the radii of curvature of its two surfaces. This formula is used to manufacture a lens of particular focal
length from the glass of a given refractive index. For this reason, it is called the lens maker's formula.
a. For a plano-convex lens of radius of curvature 10 cm the focal length is 30 cm. If the refractive index
of the material of the lens is
(A).2.0 (B).1.33 (C).1.66 (D).1.5
b. An image is formed on the screen by a convex lens when upper half part of lens is covered with
black paper then
(A) half image is formed (B) full image is formed
(C) intensity of image is enhanced (D) all of the above
c. A convex lens of power +6D is in contact with a concave lens of power -4D. What will be the focus
length and nature of the combined lens?
(a) Concave, 25 cm (b) Convex, 50 cm
(c) Concave, 20 cm (d) Convex, 100 cm
d. In a convex lens of focal length f, the minimum distance between an object and its real image must be
(a) 3f (b) 4f (c) 3f/2 (d) 2f
SECTION -C
17. A particle having a charge of 20 ?C and mass 20 ?g moves along a circle of radius 5.0cm under the
action of a uniform magnetic field of 1.0 T. When the particle is at a point P, a uniform electric field
E is switched on and it is found that particle continues on the tangent through P with a uniform
velocity. Find the electric field.
18. Answer the following questions:
(i) When electrons drift in a metal from lower to higher potential, does it mean that all free elec
trons of the metal is moving in the same direction?
(ii) Manganin and constantan are used in making standard resistance coils. Why?
OR
A storage battery of emf 8.0 V and internal resistance 1.5 Ω is being charged by a 120 V d.c. supply using
a series resistance of 14.5 Ω
(i) Find charging current in the circuit.
(ii) What is the terminal voltage of the battery during charging?
19. Derive an expression for the potential energy of two-point charges q1 and q2, separated by distance
r in an external electric field E.
20. A concave lens made of a material of refractive index n1 is kept in a medium of refractive index n2.
A parallel beam of light is incident on the lens. Trace the path of rays of light parallel to the principal axis
incident on the concave lens after refraction when: (i) n1>n2, (ii) n1 = n2.
OR
Which two of the following lenses, L1 L2and L3will you select as objective and eyepiece for constructing
best possible compound microscope? Give reason to support your answer.
Lenses Power(P) Aperture (A)

1 6D 1 Cm
2 3D 8 Cm
3 10D 1Cm
21. A charge of 8mC is located at the origin. Calculate the work done in taking a small charge of
-2x10-9C from point A (0,0,3) to a point b (0,4cm,0) via a point C (0,6cm,9cm).
22. An alternating voltage = 200 Sin 377t volt is applied across an inductance L having a resistance of
∋
1.0 ohm. The maximum current is found to be 10 A. Find the value of L.
23. A proton has spin and magnetic moment just like electron. Why then its effect is neglected in
magnetism of material? How does the magnetic moment of revolving electron change when The
frequency of revolution is halved?
24. Derive condition of balance of a Wheatstone bridge.
OR
Two cells of emf 1V and 2V and internal resistances 2 Ω and 1 Ω respectively connected in (i) series, (ii)
parallel. What should be the external resistance in the circuit so that the current through the resistance be
same in the two cases?
25. An electric dipole is held in a uniform electric field. (i) Using suitable diagram show that it does not
undergo any translatory acceleration, and(ii) Derive an expression for torque acting on it.
SECTION-C
26. Calculate the electric and magnetic fields produced by the radiation coming from a 100 W bulb at a
distance of 3 m. Assume that the efficiency of the bulb is 2.5% and it is a point source.
27. Draw the circuit diagram to determine the internal resistance of a primary cell using a potentiometer.
Obtain an expression for the internal resistance.
28. The current flowing through an inductor of self-inductance L is continuously increasing. Plot a graph
showing the variation of
(i) Magnetic flux versus the current
(ii) Induced emf versus dI/dt
(iii) Magnetic potential energy stored versus the current.
OR
(a) Starting from the expression for the Lorentz magnetic force acting on the free charge carriers of a
conductor moving in a perpendicular magnetic field, obtain the expression for the motional emf induced.
(b) Hence deduce the expressions for the power delivered by the source and the power dissipated as
Joule heat.
29. Establish the relation between electric field and electric potential at a point. Draw the equi-potential
surface for an electric field pointing in +Z direction with its magnitude increasing at constant rate along -Z
direction.
30. A beam of light consisting of red, green and blue colours is incident on a right- angled prism ABC.
The refractive indices of the material of the prism for the above red, green and blue wavelengths are 1.39,
1.44 and 1.47 respectively. Which one of the three rays will emerge out of the face AC of prism? Give
reason to support your answer. Trace the path of these rays after passing through face AB.
1 1 1
Derive the lens formula, = − for a concave lens, using the necessary ray diagram.
SECTION-D
31.(a)Describe the working principle of a moving coil galvanometer. Why is it necessary to use (i) a radial
magnetic field and (ii) a cylindrical soft iron core in a galvanometer? Write the expression for current
sensitivity of the galvanometer.
(b) Can a galvanometer as such be used for measuring the current? Explain.
(c) One voltmeter has 1000 Ω resistance and another voltmeter has a resistance of 4000 Ω .Which one
of the two will you prefer to measure a potential difference across a resistance of 500 Ω
OR
(a)State ampere circuital law.
(b) A straight thick long wire of uniform cross-section of radius a is carrying a steady current I. The current
is uniformly distributed across the cross-section. Apply Ampere's circuital law to calculate the magnetic
field at a point 'r' in the region for (i) r < a and (ii) r > a.
(c) Draw a graph Showing the dependence of B (r) on r.
32.(a) In a series LCR circuit connected to an ac source of variable frequency and voltage
V=Vm sin ωt , draw a plot showing the variation of current (I) with angular frequency ( ω ) for
two different values of resistance R1 and R2 (R1 > R2). Write the condition under which the
phenomenon of resonance occurs.
(b) Define the term Sharpness of Resonance. Calculate the quality factor of a series LCR circuit
with L = 4.0H, C = 1 µF F and R = 20 Ω .
OR
(a) Draw a labelled diagram of a step-down transformer. State the principle of its working. Express the
turn ratio in terms of voltages.
(b) Find the ratio of primary and secondary currents in terms of turn ratio in an ideal transformer. How
much current is drawn by the primary of a transformer connected to 220 V supply when it delivers power
to a 110 V - 550 W refrigerator?
33.(a) Derive the expression for capacitance of a Parallel plate capacitor without any dielectric medium
between the plates.
(b) A parallel plate capacitor with air as a dielectric has capacitance C. A slab of dielectric constant K,
having same thickness as the separation between the plates is introduced so as to fill one fourth of the
capacitor as shown in the figure. Find the new capacitance.
OR
(a) State Gauss's law .Using Gauss's law, deduce an expression for the electric field intensity at any point
due to a thin, infinitely long wire of linear charge density ? C/m.
(b) A cube which each side a is kept is an electric field given by E = Cxiˆ (as is shown in the figure) where,
C is a positive dimensional constant. Find out.
(i) The electric flux through the cube , and
(ii) The net charge inside the cube.

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Cycle Topic:: Current Electricity

Physics Electric current, flow of electric charges in a

Dual Nature of Matter and Radiation

B. Evaluation Scheme for Practical Examination:

* Practical record (experiments & activities) 6 Marks

3. The electric field in a region can be expressed as

(Ans.11.7 2 × 103 N/C)

if the potential at centre, VC = 0? (Ans. q4 = 0)

(i) magnitude of the charge on the dipole, and

A is given a positive potential of 10 V, and the other surface of B is earthed.

(i) the electric flux throught the cube. (5 × 10-4 Vm)

68 A charge Q is distributed uniformly on a ring of radius r. A sphere of equal radius r is constructed

MULTIPLE CHOICE QUESTIONS

(b) The value of electric field inside a charged capacitor is (R)

CASE STUDY BASED QUESTION

8. The resistance of a coil used in a platinum-resistance thermometer at 0 C is 3.00 Ω and at

(Ans. 19.1 Ω , 14.5v)

(Ans. V1 > V2 > V3 )

If the galvanometer deflection at the end B is

(Ans. R = 2 Ω , 0.5 A, 0.5A)

(i) What is the emf of each cell used?

(A) 3 Ù (B) zero (C) 6 Ù (D) 3/2 Ù

(A) 40 Ù (B) 20 Ù (C) 30 Ù (D) 10 Ù

Completion Type Questions

19. (i) Conductance is reciprocal of (a) Conductivity

20 . In the given circuit if reading of A1 is 2.4 A then

(i) Reading of A3 (a) 1.6A

Assertion -Reason Questions ( 16 to 18)

(5A, clockwise direction)

[(a. 3x105 m/s) (b. helical) (c.0.5m) (d. 2.1x10-5s)]

36. A galvanometer having 30 divisions has a current sensitivity of 20 microampere . It has a

(a) remain stationary (b) move towards the wire

Ans: 1 (c) 2 (c) 3 (a) 4 (b)

10-3T.The θ B linked with coil is ______________.

a) 10Wb b) 10-5wb c) 10 5wb d) 100wb

a) R = 20 r , L = 1.5 H , C = 35 µF b) R = 25r , L = 2.5 H , C = 45µF

a) A and R both are correct and R is correct explanation of A

b) A and R both are correct and R is not correct explanation of A

c) A is correct but R is wrong

d) A is wrong but R is correct

15. A: an A.c(I) of frequency 50 Hz becomes O, 100 times in one seocnd

17. A: An alternating current does not show any magnetic effect.

(Ans. 3.8 × 10 −3V ,1.9 ×10 −3 A )

(Ans. 2A, 0V)

(ii) An inductor of inductance ‘L’ has the same reactance

(iii) Using the same axes, draw a graph of reactance

(Ans. (i) 2.65 × 10 −4 F , (ii)

(Ans. (a) Anticlockwise in loop 1 & clockwise in loop 2, (b) No. )

(ii)the phase angle between the voltage and the current.

(Ans. (i) 3.18 × 10 −3 H (ii) 10 Ω

(Ans. 50 rod S-1, 7.07A, 1000 W)

(i)Write down equation for the acceleration of the wire XY.

(a) Identify X and Y

b) λ2 are used to treat muscular strain

c) λ3 are used for aircraft navigation

d) λ4 are used in treatment of malignant tumour.

C. Assertion is True , but reason is False . ?

D. Both assertion and reason are False . ?