Phase - 5

FIITJEE PHASE–V (PHYSICS) CPP
LEVEL-0 (INTERMEDIATE QUESTIONS)
Name: …………………………………… Batch:…………………Date of submission:……………….
ELECTRIC CHARGE & FIELDS
VERY SHORT ANSWER QUESTIONS
1. What is meant by the statement ‘charge is quantized’?

2. Repulsion is the sure test of charging than attraction. Why?
3. How many electrons constitute 1C of charge?
4. What happens to the weight of a body when it is charged positively?
5. What happens to the force between two charges if the distance between them is
a) halved b) doubled?
6. The electric lines of force do not intersect. Why?
7. Consider two charges + q and -q placed at B and C of an equilateral triangle ABC. For this system,
the total charge is zero. But the electric field (intensity) at A which is
equidistant from B and C is not zero. Why?
8. Electrostatic field lines of force do not form closed loops. If they form closed loops then the work
done in moving a charge along a closed path will not be zero. From the above two statements can
you guess the nature of electrostatic force?
9. State Gauss’s law in electrostatics.
10. When is the electric flux negative and when is it positive?
11. Write the expression for electric intensity due to an infinite long charged wire at a distance radial
distance r from the wire.
12. Write the expression for electric intensity due to an infinite plane sheet of charge.
13. Write the expression for electric intensity due to a charged conducting spherical shell at points
outside and inside the shell.
SHORT ANSWER QUESTIONS

1. State and explain Coulomb’s inverse square law in electricity.
2. Define intensity of electric field at a point. Derive an expression for the intensity due to a point
charge.
3. Derive the equation for the couple acting on a electric dipole in a uniform electric field.
4. Derive an expression for the intensity of the electric field at a point on the axial line an electric dipole.
5. Derive an expression for the intensity of the electric field at a point on the equatorial plane of an
electric dipole.
6. State Gauss’s law in electrostatics and explain its Importance.
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CPP- PH(V)- PHY - 2
LONG ANSWER QUESTIONS
1. Define electric flux. Applying Gauss’s law and derive the expression for electric intensity due to an
infinite long straight charged wire. (Assume that the electric field is everywhere radial and depends
only on the radial distance r of the point from the wire.)
2. State Gauss’s law in electrostatics. Applying Gauss law derive the expression for electric intensity
due to an infinite plane sheet of charge.
3. Applying Gauss’s law derive the expression for electric intensity due to a charged conducting
spherical shell at (i) a point outside the shell (ii) a point on the surface of the shell and (iii) a point
inside the shell.
ELECTROSTATIC POTENTIAL & CAPACITANCE

1. Can there be electric potential at a point with zero electric intensity? Give an example.
2. Can there be electric intensity at a point with zero electric potential? Give an example
3. What are meant by equipotential surfaces ?
4. Why is the electric field always at right angles to the equipotential surface ? Explain.
5. Three capacitors of capacitances 1 F, 2F and 3F, are
connected in parallel
(a) What is the ratio of charges?
(b) What is the ratio of potential differences?
6. Three capacitors of capacitances 1F, 2F and 3F are connected in series
(a) What is the ratio of charges?
(b) What is the ratio of potential differences?
7. What happens to the capacitance of a parallel plate capacitor if the area of its plates is doubled?
8. The dielectric strength of air is 3 x 106 Vm–1 at certain pressure, A parallel plate capacitor with air in
between the plates has a plate separation of 1 cm. Can you charge the capacitor to 3 x 106V?

1. Derive an expression for the electric potential due to a point charge.
2. Derive an expression for the electrostatic potential energy of a system of two point ch and find its
relation with electric potential of a charge.
3. Derive an expression for the potential energy of an electric dipole placed in a uniform electric field.
4. Derive an expression for the capacitance of a parallel plate capacitor5. Explain the behaviour of
dielectrics in an external field.
CPP- PH(I)- PHY- 3
1. Define electric potential. Derive and expression for the electric potential due to an electric dipole and
hence the electric potential at a point (a) the axial line of electric dipole (b) on the equatorial line of
electric dipole.
2. Explain series and parallel combination of capacitors. Derive the formula for equivalent capacitance
in each combination.
3. Derive an expression for the energy stored in a capacitor. What is the energy stored when the space
between the plates is filled with a dielectric
(a) with charging battery disconnected?
(b) with charging battery connected in the circuit?
CURRENT ELECTRICITY
1. Define mean free path of electron in a conductor.
2. State Ohm’s law and write its mathematical form.
3. Define resistivity or specific resistivity.
4. Define temperature coefficient of resistance.
5. Under what conditions is the current through the mixed grouping of cells maximum?
6. If a wire is stretched to double its original length without loss of mass, how will the resistivity of the
wire be influenced?
7. Why is manganin used for making standard resistors?
8. The sequence of bands marked on a carbon resistor are: Red, Red, Red, Silver. What is its
resistance and tolerance?
9. Write the color code of a carbon resistor of resistance 23 kilo ohms.
10. If the voltage V applied across a conductor is increased to 2V, how will the drift velocity of the
electrons change?
11. Two wires of equal length, of copper and manganin, have the same resistance. Which wire is
thicker?
12. Why are household appliances connected in parallel?
CPP- PH(V)- PHY - 4
1. Derive an expression for the effective resistance when three resistors are connected in
(i) series (ii) parallel.
2. ‘m’ cells each of emf E and internal resistance ‘r’ are connected in parallel. What is the total emf and
internal resistance ? Under what conditions is the current drawn from mixed grouping of cells a
maximum?
3. Define electric resistance and write it’s SI unit. How does the resistance of a condud vary if
(a)Conductor is stretched to 4 times of it’s (length) (b) Temperature of a conducts is increased.
4. Three resistors each of resistance 10 ohm are connected, in turn, to obtain (i) minim resistance (ii)
maximum resistance. Compute (a) The effective resistance in each case
(b) The ratio of minimum to maximum resistance so obtained.

1. State and explain Kirchhoff’s laws in electricity and apply them to Wheatstone bridge.
2. State the working principle of potentiometer explain with the help of circuit dia how the emf of two
primary cells are compared by using the potentiometer.
3. State the working principle of potentiometer explain with the help of circuit diagram how the
potentiometer is used to determine the internal resistance of the given primary cell.
4. Under what condition is the heat produced in an electric circuit a)directly proportional b) inversely
proportional to the resistance of the circuit? Compute the ratio of the total quantity of heat produced
in the two cases.
5. In a house three bulbs of 100W each are lighted for 4 hours daily and six tube lights of 20W each
are lighted for 5 hours daily and a refrigerator of 400W is worked for 10 hours daily for a month of 30
days. Calculate the electricity bill if the cost of one unit is Rs. 4.00.
CPP- PH(I)- PHY- 5
LEVEL-I(BITSAT/JEEM)
COLOUMBS LAW
1. The dielectric constant K of an insulator can be

(A) –1 (B) 0 (C) 0.2 (D) 5
2. If F is the force between two point charges submerged in a medium of dielectric constant K, then on
withdrawing the medium, the force between the charges becomes
F F
(A) F K (B) FK (C) f (D)
K K
3. With a rise in temperature, the dielectric constant K of a liquid

(A) increases (B) decreases (C) remains constant (D) none of these
4. Two identical metal balls with charges +2Q, and –Q are separated by same distance, and exert a
force F on each other. They are joined by a conducting wire, which is then removed. The force
between them will now be
F F F
(A) F (B) (C) (D)
2 4 8
5. Two identical metallic spheres X and Y have exactly equal masses. X is given a positive charge q
coulomb and Y is given an equal negative charge. Then after charging
(A) masses of X and Y are equal (B) mass of Y is greater than X
(C) mass is not involved (D) mass of X is greater than Y
6. A charge q1 exerts some force on a second charge q2. If a third charge q3 is brought near, then the
force of q1 exerted on q2
(A) will increase in magnitude (B) will decrease in magnitude
(C) both A and B (D) none of these
7. Five balls numbered (1 to 5 are suspended using separate threads. Pairs (1, 2)(2, 4) and (4, 1) show
electrostatic attraction, while pairs (2, 3), (4, 5) show repulsion. Therefore ball 1 must be
(A) neutral (B) made of metal (C) positively charged (D) negatively charged
8. There are two charges +1 micro coulomb and 5 micro coulomb. The ratio of the forces acting on
them will be
(A) 1 : 1 (B) 1 : 25 (C) 1 : 5 (D) 5 : 1
9. An electric charge q exerts a force F on a similar electric charge q separated by a distance r. A third
q
charge is placed mid–way between the two charges. Now, the force F will
4
F F F
(A) become (B) become (C) become (D) remain F
3 9 27
10. Which of the following is a sure test of electrification ?

(A) attraction (B) repulsion (C) induction (D) friction
11. A positive point charge Q is brought near an isolated metal cube

(A) the cube becomes negatively charged
(B) the cube becomes positively charged
(C) the interior becomes positively charged and the surface becomes negatively charged
(D) the interior remains charge free and the surface gets non–uniform charge distribution
CPP- PH(V)- PHY - 6
12. A positively charged glass rod is brought near the disc of uncharged gold leaf electroscope. The
leaves diverge. Which of the following statements is correct?
(A) no charge is present on the leaves
(B) positive charge is induced on the leaves
(C) negative charge is induced on the leaves
(D) positive charge is induced on one leaf and negative on the other
13. A charge Q is divided into two parts q and Q – q and separated by a distance R. The force of
repulsion between them will be maximum when
(A) q = Q/4 (B) q = Q/2 (C) q = Q (D) none of these
14. When 1019 electrons are removed from a neutral metal plate, the electric charge on it is (coulomb)
10q1
(A) 10+19 (B) +1.6 (C) –1.6 (D)
q2
15. Two charged spherical conductors, each of raedius R, are at a distance r from each other. The
charge on the first is +q and on the second is –q. If r > 2R, then the force of attraction is numerically
1 q2 1 q2
(A) equal to 2
(B) more than
40 r 40 r 2
1 q2 r
(C) less than (D) more or less depending upon
40 r 2 R
16. An uncharged metal object M is insulated from its surroundings. A positively charged metal sphere S
is then brought near to M. Which diagram best illustrates the resultant distributions of charge on S
and M ?
++ ––
+ + ++ –– + –
+ – + –
+ + – + S + M
(A) + S +
M (B) –
– + –
+ + – + + –
++ + –
+ + ++ –– + + ++ –– + +
+ – + –
+ + – + + – +
(C) + S + M + (D) + S + M +
– –
+ + – + + – +
++ + – ++ + + – ++
17. Three small spheres, each carrying a charge q are placed on the circumference of a circle of radius
R, forming an equilateral triangle. If we place another charge Q at the centre of the circle, then the
force on Q will be
1 qQ 1 2qQ 1 3qQ
(A) zero (B)  2 (C)  2 (D)  2
40 R 40 R 40 R
18. Three charges, each equal to +2C, are placed at the corners of an equilateral triangle. If the force
between any two charges be F, then the net force on charge will be
(A) 3 F (B) 2 F (C) 2 F (D) 3 F
19. Two identical simple pendulums, A and B, are suspended from the same point. The bobs are given
positive charges, with A having more charge than B, they diverge and reach equilibrium, with A and
B making angles 1 and 2 with the vertical respectively. Which of the following is correct ?
(A) 1 > 2 (B) 1 < 2
(C) 1 = 2 (D) the tension in A is greater than that in B
CPP- PH(I)- PHY- 7
20. Three point charges are placed at the corners of an equilateral triangle. Assuming only electrostatic
forces are acting.
(A) the system can never be in equilibrium
(B) the system will be in equilibrium if the charges rotate about the centre of the triangle
(C) the system will be in equilibrium if the charges have different magnitude and different signs
(D) the system will be in equilibrium if the charges have the same magnitude but different signs
ELECTRIC FIELD & POTENTIAL
1. A solid non–conducting sphere of radius R has electric charge uniformly distributed throughout its
volume. The electric field at distance r(r < R) from the centre varies as
1 1 1
(A) r (B) (C) 2 (D) 3
r r r
2. A cube of side b has charge q at each of its vertices. The electric field at the centre of the cube will
be
q q 32q
(A) 2 (B) 2
(C) 2 (D) zero
b 2b b
3. Three small spheres, each carrying a positive charge q, are placed on the circumference of a circle
of radius r to form an equilateral triangle. The electric field intensity at the centre of the circle will be
3Q 3Q Q
(A) (B) 2 (C) (D) zero
r r 2 r2
4. An electric dipole placed in a non–uniform electric field will experience

(A) only a force (B) only a torque (C) both force & torque (D) neither force nor torque
5. An electric line of force is leaving a charged spherical conductor. What is the angle between the
surface and the electric line of force ?
(A) 0 (B) 30 (C) 45 (D) 90
6. A simple pendulum of time period T is suspended above a large horizontal metal sheet with
uniformly distributed positive charge. If the bob is given some negative charge, its time period of
oscillation will be
(A) > T (B) < T (C) T (D) proportional to its amplitude
7. The electric field inside a spherical shell of uniform surface charge density is
(A) zero (B) outer point
(C) directly proportional to the distance (D) none of the above
8. A proton and an electron are placed in a uniform electric field. Which of the following is correct ?
(A) the electric forces acting on them will be equal
(B) the magnitudes of the forces will be equal
(C) their accelerations will be equal
(D) the magnitudes of their acceleration will be equal

9. If electric field intensity E is along the X–axis, then the equipotential surface are parallel to
(A) XOY plane (B) XOZ plane (C) YOZ plane (D) none of these
10. Electric potential at a point is   x 2 y  yz . The electric field at the point (1, 3, 1) is
(A) 7 units (B) 70 units (C) 49 units (D) 490 units
11. A large isolated metal sphere of radius r carries a fixed charge. A small charge is placed at a
distance d from its surface. It experiences a force which is
(A) independent of r and d (B) proportional to r2 + d2
2
(C) proportional to r (D) inversely proportional to (r2 + d2)
CPP- PH(V)- PHY - 8
12. A hollow metal sphere of radius 0.10 m is charged such that the potential on its surface is 4 V, the
potential at the centre of the sphere is
(A) 0 V
(B) 4V
(C) same as at point 0.10 m away from the surface
(D) same as at point 0.25 m away from the surface
13. A spherical equipotential surface is not possible

(A) for a point charge (B) for a dipole
(C) inside a uniformly charged sphere (D) inside a spherical capacitor
14. An electron which is initially at rest is accelerated through a potential difference of one volt. The
energy acquired by the electron is
(A) 10–19 J (B) 1.6 x 10–19 erg (C) 1.6 x 10–19 J (D) zero
15. A charge of 10 C is moved along an equipotential surface having a potential of 2 V. The work done
is
(A) 10 J (B) zero (C) 2 J (D) 20 J
16. S1 and S2 are two equipotential surfaces on which the potentials are not equal. Which of the
following is incorrect ?
(A) S1 and S2 cannot intersect
(B) S1 and S2 cannot be plane surfaces
(C) in the region between S1 and S2 , the field is maximum where they are closest to each other
(D) a line of force from S1 to S2 must be perpendicular to both
17. In bringing an electron towards to second electron, the electrostatic potential energy of the system
(A) increases (B) decreases (C) remains the same (D) become zero
18. A tin nucleus has charge +50e. If the proton is at a distance of 10–12 m from the nucleus, then the
potential V at this position is [charge on the proton = 1.6 x 10–19 C]
(A) 14.4 x 104 V (B) 7.2 x 104 V (C) 7.2 x 108 V (D) 14.4 x 108 V
 
19. An electric dipole of dipole moment p placed in uniform electric field E will have minimum potential
 
energy if the angle between p and E is
 3
(A) 0 (B)  (C) (D)
2 2
20. A charge q is uniformly distributed over the volume of a sphere of radius R. Assuming the dielectric
constant to be unity throughout, the potential at the centre of the sphere will be
9q 3 1 q 7q 1 q
(A) (B)   (C) (D) 7  
40R 2 40 R 40R 40 R
GAUSS’S LAW
1. A charge Q is placed at the mouth of a conical flask. The flux of the electric field through the flask is
Q Q Q
(A) zero (B) (C) (D) <
0 20 20
2. A point charge q is placed at one corner of a cube of edge a. The flux through each of the cube
faces is
q q q q
(A) (B) (C) (D)
0 160 240 480
CPP- PH(I)- PHY- 9
3. Electric charge is uniformly distributed along a long straight wire of radius 1 mm.
The charge per cm length of the wire is Q coulomb. Another cylindrical surface of
radius 50 cm and length 1 m symmetrically encloses the wire as shown in the
figure. The flux through the cylindrical surface is 1m
Q 100Q 10Q 100Q
(A) (B) (C) (D)
0 0 ( 0 ) (0 )
50m

4. Given: E  (10iˆ  7ˆj)Vm 1 . The electric flux through 1 m2 area in XZ plane is
(A) 10 Vm (B) 7 Vm (C) 100 Vm (D) 49 Vm
5. Q1 and Q2 are the charges inside and outside respectively of a closed surface S. Let E be the
electric field at any point on S and  be the flux of electric field over the closed surface. Which of the
following is in correct?
(A) if Q1 changes, both E and  will change (B) if Q1 changes, E will change but  will not change
(C) if Q1  0 and Q2  0 then E  0 but   0 (D) if Q1  0 and Q2  0 then E  0 but   0

6. Given: E  E0 xiˆ . Consider an imaginary cubical volume of edge  , with its edges parallel to the axis
of coordinates. The charge inside this volume is
1 1
(A) zero (B) 0E0 3 (C) E0  3 (D) 0E03
0 6
7. Due to a charge inside the cube, the electric field is (see figure) Y
0.1m
E x  6001/ 2
x , E y  0, E z  0 . The charge inside the cube is
nearly
(A) 600 C (B) 60 C O X
(C) 7 C (D) 6 C
Z
0.1m
8. A charge q is distributed uniformly on a ring of radius r. A A

sphere of equal radius r is constructed with its centre at the
periphery of the ring (see figure). The electric flux through the
surface of the sphere is O1 O2
q 2q
(A) (B)
0 0
q q
(C) (D) ring B sphere
20 30
(From Q.9 – 12)

A cube has sides of length L = 0.300 m . It is placed with one corner at
the origin as shown in the above figure. the electric field is not uniform,

but is given by E  ( 5.00 N / C.m)xiˆ  (3.00 N/ C.E)zkˆ .
9. Which of the surfaces have zero flux?

(A) S2, S4 and S5 (B) S1, S3 and S4 (C) S1, S2 and S3 (D) S2, S3 and S4
10. The flux passing through the surface S5 will be

2 2 2 2
(A) –0.135 N–m /C (B) –0.054 N–m /C (C) 0.081 N–m /C (D) 0.054 N–m /C
11. Total flux passing through the cube

(A) –0.135 N–m2/C (B) –0.054 N–m2/C (C) 0.081 N–m2/C (D) 0.054 N–m2/C
CPP- PH(V)- PHY - 10
12. The total electric charge inside the cube

(A) –0.135 N–m2/C (B) –0.054 N–m2/C (C) 0.081 N–m2/C (D) 0.054 N–m2/C
13. Total flux passing through the cube

2 2 2
(A) (A+B+C+D)L (B) 2(A+B+C+D)L (C) 6(A+B+C+D)L (D) zero
14. A flat, square surface with sides of length L is described by the equations. x  L, 0  y  L, 0  z  L .
Find the electric flux through the square due to a positive point charge q located at the origin (x = 0,
y = 0, z = 0).
q q q q
(A) (B) (C) (D)
40 60 240 480
 
15. The electric field E1 at one face of a parallepiped is uniform E2
over the entire face and is directed

out of the face. At the
opposite face, the electric field E2 is also uniform over the
entire face and is directed into that face ( as shown in the
figure). The two faces in question are inclined at 30 from the 6cm
 
horizontal, while E1 and E2 are both horizontal; has a 
magnitude of 2.50 x 104 N/C, and a magnitude of 7.00 x 104 5cm E1
30
N/C. Assuming that no other electric field lines cross the
surfaces of the parallelepiped, determine the net charge
contained within
(A) –67.5 0 C (B) 67.5 0 C (C) 105 0 C (D) –105 0 C
Passage(16 – 17) Y
A cube of side a is placed such that the nearest face which is parallel to a
the y–z plane is at a distance a from the origin. The electric field
components are E x   x1/ 2 , E y  Ez  0 . Calculate
O X
Z
a
16. The flux E through the cube
(A) 2  a5 / 2 (B)   a5 / 2 (C) ( 2  1)  a5 / 2 (D) zero
17. The charge within the cube

(A) 2  a5 / 20 (B)   a5 / 20 (C) ( 2  1)  a5 / 20 (D) zero
Passage(18 – 20)
Two spherical cavities of radii, a and b, are hollowed out from the interior of a R
neutral conducting sphere of radius R. At the centre of each cavity, a point charge a
is placed. Call these charges qa and qb. R , a , b are the charges diverting at the qa
surface of sphere of radius R, the cavity of radius a and the cavity of radius b b
respectively qb
18. Match the table

(i) a (m) q0  q2
4R2
(ii) b (n) qa
4a 2
CPP- PH(I)- PHY- 11
(iii) R (o) qb
4b 2
(A) (i, o), (ii, n), (iii, m) (B) (i, n), (ii, o), (iii, m) (C) (i, m), (ii, o), (iii, n) (D) (i, n), (ii, m, (iii, o)
19. What is the field at a distance r outside the conductor ?

1 qb 1 qa  qb 1 qa
(A)  2 (B) zero (C)  (D) 
40 r 40 r2 40 r 2
20. The electric field inside the cavity of radius a at a distance r from the centre of cavity
1 qa 1 qa 1 qa  qb
(A)  (B) –  (C)  (D) zero
40 r 2 40 r 2 40 r2
CAPACITORS
1. Three equal capacitors, each with capacitance C, are connected as shown in the figure. Then the
equivalent capacitance between A and B is
C 3C
(A) C (B) 3C (C) (D)
3 2 A B C C C
2. The expression for the capacity of the capacitor formed by compound dielectric placed betweent he
places of a parallel plate capacitor as shown in the figure will be (are of plate = A)
0 A 0 A d1 d2
(A) (B)
 d1 d2 d3   d1  d2  d3 
     
K1 K 2 K 3  K1  K 2  K 3 
 A(K1K 2K 3 )  AK1 AK 2 AK 3  K1 K2 K3
(C) 0 (D) 0    
d1d2 d3  d1 d2 d3 
d3
3. The capacity of a parallel plate condenser is 12 pF. If the area of both the plates is doubled and the
distance between them is reduced to half, the capacity of the condenser will be
(A) 124 pF (B) 48 pF (C) 196 pF (D) 126 pF
4. Three capacitors of capacitance 6 F each are available. The minimum and maximum capacitance,
which may be obtained are
(A) 6 F, 18 F (B) 3 F, 12 F (C) 2 F, 12 F (D) 2 F, 18 F
5. The dielectric strength of air of NTP is 3 x 106 Vm–1. Then the maximum charge that can be given in
a spherical conductor of radius 3 m is
(A) 3 x 10–1 C (B) 3 x 10–2 C (C) 3 x 10–3 C (D) 3 x 10–4 C
6. Two metal plates have potential difference of 300 V and are 0.01 m apart. A charged particle of
–15
mass 1.96 x 10 kg is held in equilibrium between the plates of the capacitor. Then the electric field
is
(A) 3 x 102 Vm–1 (B) 3 Vm–1 (C) 3 x 104 Vm–1 (D) 3 x 10–4 Vm–1
7. A parallel plate air capacitor is charged to a potential difference V. After disconnecting the battery,
the distance between the plates of the capacitor is increased using an insulating handle. As a result,
potential difference between the plates
(A) decreases (B) does not change (C) becomes zero (D) increases
8. A parallel plate condenser is filled with two dielectric as shown A
in the figure. area of each plate is Am2 and the separation is d A/2 A/2
metre. The dielectric constants are K1 and K2 respectively. The
capacitance in farad, between A and B, will be d K1 K2
 A  A
(A) 0 (K1  K 2 ) (B) 0 (K1  K 2 )
d 2d
0 A 0 A B
(C) 2(K1  K 2 ) (D) (K1  K 2 )
d 2d
9. To obtain 3 F capacity from three capacitors of 2 F each, they will be arranged

(A) all the three in series
(B) all the three in parallel
(C) two capacitors in series and the third in parallel with the combination of first two
(D) two capacitors in series and the third in series with the combination of first two
10. Eight drops of mercury of equal radii and possessing equal charges combine to form a big drop.
Then the capacitance of bigger drop compared to each individual drop is
(A) 18 times (B) 14 times (C) 2 times (D) 32 times
11. A dielectric material of dielectric constant K introduces half the

length of a parallel plate capacitor. If area of the plates of the K d
capacitor is A and the plate separation is d, then the
capacitance of the arrangement is
20 A  A(1  K)  A(1  K) 30 A
(A) (B) 0 (C) 0 (D)
d d 2d 2d
12. Four capacitors, each of capacity 3 F, are connected as shown in the figure. the A B
ratio of equivalent capacitance between A and B and between A and C will be
(A) 4 : 3 (B) 3 : 4 (C) 2 : 3 (D) 3 : 2
C
13. The two metallic plates of radius r are placed at distance d apart and its capacity is C. If a plate of
r
radius and thickness d is dielectric constant 6 is placed between the plates of the condenser,
2
then its capacity will be
7C 3C 7C 9C
(A) (B) (C) (D)
2 7 3 4
t
14. A parallel plate capacitor has separation t and capacitance 100 pF. If a metallic foil of thickness is
3
introduced between the plates, the capacitance would become (in pF units)
3 2
(A) 3 x 100 (B)  100 (C) 100 (D)  100
2 3
15. The capacities of the capacitors are shown in the figure. the A
equivalent capacitance between the points A and B and the charge 90 volt
on the 6 F capacitor will be
(A) 27 F, 540 F (B) 15 F, 270 F
(C) 6 F, 180 F (D) 15 F, 90 F B
9F 6F 12F
CPP- PH(I)- PHY- 13
16. Between the plates (area = A) of a parallel plate condenser(charge = Q), a plate of thickness t1 and
dielectric constant K1 is placed. In the rest of the space, there is another plate of thickness t2 and
dielectric constant K2. The potential difference across the condenser will be
Q  t1 t  A0  t1 t  Q  K1 K 2  A 0
(A)   2  (B)   2  (C)    (D) K1t1  K 2 t2 
A0  K1 K 2  Q  K1 K 2  A0  t1 t2  Q
17. In the connections shown in the figure, the equivalent capacity

between A and B will be 6F
(A) 10.8 F (B) 69 F
(C) 15 F (D) 10 F A 9F 24F 12F B
18F
C1= 6F
18. The effective capacitance between points X and Y is
(A) 24 F (B) 18 F
(C) 12 F (D) 6 F C3= 6 F C2= 6F
X C5=20F Y
C4= 6F
A
2C 2C
19. The effective capacity between A and B of the given network is
(A) 3C (B) 2C 2C
(C) C (D) C/3 C
C C
B
20. In the circuit shown in figure, the potential difference across the 3
F capacitor is V. The value of V is 3F 6F
(A) 20 V (B) 40 V 2F
(C) 45 V (D) 60 V
60V
A B
CURRENT ELECTRICITY
1. V–I graphs for parallel and series combination of two metallic v B

resistors are as shown in the figure. which graph represents A
parallel combination ?
(A) A (B) B
(C) A and B both (D) neither A nor B
I
2. The current in the arm CD of the network in the B

I1 I2
figure
(A) I1 + I2 (B) I2 + I3 A
(C) I1 + I3 (D) I1 – I2 + I3 I3
3. AB is a wire of uniform resistance. The R 80 
galvanometer G shows no current when the
length AC = 20 cm and CB = 80 cm. The
resistance R is equal to
(A) 2  (B) 8  C
(C) 20  (D) 40 
A B
C
4. What is the ammeter reading in the circuit of the 10V

figure ?
(A)0.25 A (B) 0.5 A
(C) 1.0 A (D) 2.0 A
5
A
5
5. Five resistances are connected as shown in the 2.5 

B
figure. the effective resistance between A and B
is 10 
10 10 7.5  1
(A)  (B) 
3 7
(C) 40  (D) 45  A
9
6. The figure, represents a part of closed circuit.

The potential difference (VA – VB) is 3A – + 1 6
(A) 24 V (B) 0 V
(C) 6 V (D) 18 V A 3V B
7. A uniform wire of resistance 20  having resistance 1 /m resistance

between M and N is 1.8 , then the length of the shorter section is
(A) 2 m (B) 5 m M N
(C) 1.8 m (D) 18 m
8. Fifty identical cells each having emf. E, and internal resistance r are B
connected as shown in the figure. the potential difference between
points A and B is
(A) 4 E (B) 2 E
(C) E (D) zero
A C
9. Two resistors of resistance 200 k and 1 M 200k  x 1M

respectively form a potential divider with outer junctions
maintained at potentials of +3 V and –15 V. What is the +3V –15V
potential at the junction X between the resistors?
(A) + 1 V (B) 0 V (C) –0.6 V (D) –12 V
CPP- PH(I)- PHY- 15
10. What is the current flowing through 2 resistance shown 4
in the figure ? 1
2E 2
(A) 2 E (B)
7
E E
(C) (D) E
7
11. The value of current I in the circuit shown in the 60 

figure is I
(A) 0.1 A (B) 0.5 A 15  5
1 1
(C) A (D) A 10 
3 6 1A 1A

12. A and B are two points on a uniform ring of resistance R. AOB = , where O is A B
the centre of the ring. The equivalent resistance between A and B is 
r r
R R (2  ) 
(A) 2
(2  ) (B) 2
(2  1) (C) R (D) R
4 4 4 2 O
13. Two cells of emfs E1 and E2 (E1 > E2) are connected as shown in the figure. When a potentiometer is
connected between A and B, the balancing length of the potentiometer wire is 300 cm. On
E
connecting same potentiometer between A and C, the balancing length is 100 cm. The ratio 1 is
E2
(A) 3 : 1 (B) 1 : 3 A B C
(C) 2 : 3 (D) 3 : 2 E E1 2
14. Five resistances are connected as shown in the

2 3
figure. the equivalent resistance between A and C is
10
(A)  (B) 22  A 7 C
3
(C) 15  (D) 10.6  4 6
15. The equivalent resistance between points A and B in the

circuit shown in the figure is 2R
(A) 5 R (B) 2 R A R 2R B
R 6R
(C) (D) Q
2 5
16. A cell of negligible emf of 2 V is connected to a series combination of 2 , 3  and 5 . The

potential difference in volt between the terminals of 3  resistance will be
(A) 0.6 V (B) 2/3 V (C) 3 V (D) 6 V
17. In the circuit shown in the figure, the total resistance between R R
X
points X and Y is R0. The value of resistance R is
R
(A) R0 (B) 0 R R0
3
R0 Y
(C) (D) 3 R0
2
18. The effective resistance between A and B in the 1
network of figure is
4 3 1 1
(A)  (B)  1
3 2 1
8 A B
(C) 7 (D)  1 1
7
19. The equivalent resistance between A and B in the network in 3

figure is
4 3 8 4
(A)  (B) 
3 2 A 2 6 B
6
(C) 3 (D) 2
20. In the circuit shown here, E1 = E2 = E3 = 2 V and R1 = R2 = 4 . E1 R1

The current flowing between points A and B through battery E2
is E2
(A) zero (B) 2A from A to B A B
(C) 2A from B to A (D) none of the above
E3 R2
CPP- PH(I)- PHY- 17
LEVEL-I(BITSAT/JEEM)
ANSWERS
COLOUMBS LAW
1. D 2. B 3. B 4. D
5. B 6. D 7. A 8. A
9. D 10. B 11. D 12. B
13. B 14. B 15. B 16. D
17. A 18. D 19. C 20. A
ELECTRIC FIELD & POTENTIAL
1. A 2. D 3. D 4. C
5. D 6. B 7. A 8. B
9. C 10. A 11. D 12. B
13. B 14. C 15. B 16. B
17. A 18. B 19. A 20. B
GAUSS’S LAW
1. C 2. C 3. B 4. B
5. D 6. B 7. C 8. D
9. B 10. A 11. B 12. A
13. D 14. C 15. A 16. C
17. C 18. B 19. C 20. A
CAPACITORS
1. C 2. B 3. D 4. D
5. C 6. C 7. D 8. B
9. C 10. C 11. C 12. B
13. B 14. B 15. A 16. B
17. D 18. D 19. A 20. B
CURRENT ELECTRICITY
1. A 2. B 3. C 4. D
5. A 6. D 7. A 8. D
9. B 10. B 11. A 12. A
13. D 14. A 15. C 16. A
17. B 18. D 19. A 20. B
LEVEL-II(JEEA)
Name: …………………………………… Batch:…………………Date of submission:……………
ELECTROSTATICS
1.COULOMB’S LAW
1. Two identical pith balls are charged by rubbing against each other. They are suspended from a
horizontal rod through two strings of length 20 cm each, the separation between the suspension
points being 5 cm. In equilibrium, the separation between the balls is 3 cm. The tension in the string
is ______. The charge on each ball has a magnitude 2.0  10 8 C .
(A) 8.2 102 N (B) 6.2 102 N (C) 8.2 103 N (D) 6.2 103 N
2. Two particles A and B, each having a charge Q, are placed a distance d apart. Where should a
particle of charge q be placed on the perpendicular bisector of AB so that it experiences maximum
force?
d d d d
(A) (B) (C) (D)
2 3 2 2 3 3
3. A point charge is placed at a distance r from one edge of a line charge of length l and charge Q
uniformly distributed over the whole length. The force on point charge is
Qq Qq Qq  
 1  1  (D) None of these
(A) (B) (C)  2 
4peo r  l r  l 2 4peo  r r  l2 
4peo r  
 2
4. Four equal charges, each +q are placed at the four corners of a square of side a. Then the coulomb
force experienced by one charge due to the rest of three is
(2 2  1)Kq2 3Kq2 2 2Kq2
(A) (B) (C) (D) zero
2a2 a2 a2
5. The vector form of coulomb’s law is

     q1q2  
   
1 q q2 1 q q 1
(A) F  .  1  (B) F  .  1 2 r1  r2 (C) F  r1  r2
4peo r  r 2 4peo r  r 2 4peo r  r 3

2 1 1 2 1 2
(D) None of these
6. Three charges each of +1C are placed at 1,0,0 ,  2,1,1 and  3,0,0 , then force on the charge
placed at 1,0,0 is
9   1 1   9   1 1  
(A) 9  10 i    j  k  (B) 9  10 i    j  k 
  3 3 8 
    3 3 4 
 
   
  1 1   
(C) 9  109 i     j  k  (D) None of these
  3 3 8  
 
7. Five balls, numbered 1 to 5 are suspended using separate threads. Pairs 1,2,2,4 and  4,1 show
electrostatic attraction, while pairs 2,3 and  4,5 show repulsion. Therefore, ball 1 must be:
(A) positively charged (B) negatively charged (C) neutral (D) made of metal
CPP- PH(I)- PHY- 19
8. Three charges, each of +q, are placed at the vertices of an equilateral triangle. The charge needed
at the incentre of the triangle for the charges to be in equilibrium is
q q
(A) – (B) + (C) + 3 q (D) – 3 q
3 3
9. A total charge of 20 C is to be divided into two parts for maximum coulombian repulsion. The charge
should be divided into
40 20
(A) 15 C, 5 C (B) 10 C, 10 C (C) C, C (D) 12 C, 8 C
3 3
10. Three equal charges each +q are placed on the corners of an equilateral triangle of side a. Then the
coulomb force experienced by one charge due to the rest of the two is
Kq2 2Kq2 3 Kq2
(A) 2 (B) (C) (D) zero
a a2 a2
2. ELECTRIC FIELD
1. Electric field just outside the spherical conducting shell whose surface charge density is  is ______
  2 
(A) (B) (C) (D)
20 0 0 30
2. Four point charges q , q , 2Q and Q are placed in order at the corners of A,B,C and D of a square.
q
If the field at the midpoint of CD is zero, the value of is
Q
5 2 2 5 5
(A) 1 (B) (C) (D)
2 5 2
3. A charged sphere of diameter d , density r is immersed in oil of density . There is uniform electric
field E directed vertically upward such that the sphere is suspended in oil. Charge on the sphere is
_____ . Assume viscous force is absent.
d3 (   )g d3 (   )g d3 (   )g d3 (   )g
(A) (B) (C) (D)
3E 2E 6E 12E
4. A point charge q  1C and mass 1 kg is projected with a speed

E
u  10 m/s in the perpendicular direction of uniform electric field strength
100 V/m. The equation of trajectory of particle is
x
(A) y 2  2 x (B) y  2 x 2 (C) y 2  4 x (D) y  4x 2 O u
5. A particle of charge q and mass m moves rectilinearly under action of an electric field E  a  b x .
Here, a and b are positive constants and ' x ' is the distance from point where the particles were
initially at rest, then
b a
(A) amplitude of particle’s oscillations is (B) amplitude of particle’s oscillations is
a b
b qb
(C) mean position of particle’s oscillations is at x  (D) maximum acceleration is
a m
6. Two rings of radii 2 cm and 5 cm, charged with charge density of 5 C/m and 16 C/m are placed

co-axially, centered at same point. The distance of point from centre, along the axis where  E  0
is
(A) 3 (B) 3 (C) 5 (D) none of these
7. Charge Q is distributed uniformly on length ' l ' of a wire. It is bent in form of semicircle. The electric
field strength near the centre of arc is
Qp Q Q Q
(A) (B) (C) (D)
2 2 2
4eo l 4peo l 2peo l 2eo l2
8. A block of mass ' m ' and charge ' q ' is placed a smooth horizontal table which terminates in a
vertical non conducting wall at a distance ' d ' from the block. A horizontal electric field E towards
right is switched on. Assuming elastic collision, the time period of motion is
2dm 4dm 8dm 10dm
(A) (B) (C) (D)
Eq Eq qE Eq
9. For a finite line of charge with linear charge density l , the electric field at a
point shown is given by +
l l +
(A) sin a  sin b i  cos a  cos b j x a
4peo x 4peo x +
b
l  +
(B) cos a  cos b i  sin a  sin b j 
4peo x  +
l  l 
(C)  sin a  sin b i  cos a  cos b j  (D)
 cos a  cos b i  sin a  sin b j 
4peo x 4peo x 
10. Electric field because of a disc of charge on a point on the axis at a distance ' x ' from its centre is
(areal charge density is s , radius is ' R ' )
       
  x  (B)   1  x  (C)   1  R  (D)   1  R 
(A) 1  2       
2 o  x  R2  2 o  x2  R 2  2 o  x2  R 2  2 o  x2  R 2 
   
11. 1m C charge is placed at point 1, 2, 4 . The electric field at a point P 0,4,3 is ______ N/C.
(A) 38.42i  230.52j  38.42k (B) +38.42i  38.42j  230.52 k
(C) 38.42i  38.42j  230.52
k (D) None of these
12. A circular wire loop of radius R carries a total charge ' q ' distributed uniformly over its length. A small
length x  R is cut off. The electric field at the centre due to remaining wire is ______
q qx qx qx
(A) (B) (C) (D)
4p 2 eo R 2 4peo R 3 8peo R 3 8p 2 eo R 3
13. A positively charged sphere suspended with a silk thread is slowly pushed in a ++ ++
+
metal bucket. After its insertion the lid is closed. What will be the electric field ++ ++
intensity inside when the sphere has touched the bucket? s is the surface
charge density of sphere.
s s
(A) zero (B) (C) (D) None of these
2eo eo
CPP- PH(I)- PHY- 21
14. Three identical positive charges Q are arranged at the vertices of an equilateral triangle. The side of
the triangle is ' a ' . The intensity of the field at the vertex of a regular tetrahedron of which the
triangle is the base is _______
1  3Q  1  2Q  1  3Q  1  6Q 
(A)   (B)   (C)   (D)  
4o  a 
2  4o  a 
2  4o  2a 
2  4o  a2 
15. A ball of mass 2kg, charge 1C is dropped from top of a high tower. In space electric field exist in
horizontal direction away from tower which varies as E = (5 – 2x) 106 V/m. Find maximum horizontal
distance ball can go from the tower.
(A) 2.5 cm (B) 2.5 m (C) 5 cm (D) 5 m
16. An electric line of force in x -y plane is given by x 2  y 2  1 . A particle with unit positive charge,
initially at rest at the point x  1,y  0 in the x – y plane:
(A) will not move at all
(B) will move along the straight line
(C) will move along the circular line of force
(D) information is insufficient to draw any conclusion
17. Consider equal and oppositely charged large parallel plates, with charge
+σ σ
density   . A small charge qo is moved along the rectangular path ABCDA  
D C
where side AB = x and side BC = y, then the correct statement(s) is (are)  
q x  
(A) work done by electric field along path AB is positive and equal to o .
o  
(B) work done by electric field along path BC is zero.  
A B
(C) work done by electric field along the path ABCDA is zero  
(D) All of these
18. An electric charge of + 5 C is placed at a distance of 2m from another charge of – 5 C. The
electric field at the mid–point of the line joining them will be
(A) zero (B) 9000 V m–1 (C) 90000 V m–1 (D) 4500 V m–1
19. A pendulum bob of mass 10 mg and carrying 9.8 x 10–9 C is suspended in a horizontal uniform
electric field of 1000 Vm–1. The string of the pendulum lies inclined to the vertical at an angle
(take g = 9.8 m/s2)
(A) 30o (B) 45o (C) 60o (D) 0o
–5 –13
20. The electric field required to just support a water droplet of mass 10 g, which has a charge of 10
C, is
7 –1 3 –1 6 –1 5 –1
(A) 10 V m (B) 9.8 x 10 V m (C) 10 V m (D) 9.8 x 10 V m
3. ELECTRIC POTENTIAL ENERGY
1. Four charges q 1  1C, q 2  2C, q 3  3C and q 4  4C are kept on the q4 q3
vertices of a square of side 1m. The electric potential energy of this system of
charges is _______ 1m
(A) 7.62 102 J (B) 8.62 102 J (C) 7.62 104 J (D) 8.62 104 J 1m
q1 q2
2. Two point charges q 1  q 2  2C are fixed at x1   3m and x2  3m as y
shown in figure. A third particle of mass 1g and charge q 3  4C is q3 y = 4m
released from rest at y = 4.0m. Find the speed of the particle as it reaches
the origin.
(A) 3.2 m/s (B) 4.2 m/s (C) 5.2 m/s (D) 6.2 m/s
q2 q1
x
x2 = -3m x1 = 3m
3. Find the work done by some external force in moving a charge q  2C from infinity to a point
where electric potential is 10 4 V .
(A) 20 mJ (B) 2 mJ (C) 0.2 mJ (D) 200 Mj
4. Two conducting spheres of radii R1 and R2 are charged with charges Q1 and Q2, respectively. On
bringing them in contact, there is
(A) no change in the energy of the system
(B) an increase in the energy of the system if Q1R2  Q 2R1
(C) always a decrease in the energy of the system
(D) a decrease in the energy of the system if Q1R2  Q 2R1
5. A particle A of mass m and charge Q moves directly towards a fixed particle B, which has charge Q.
The speed of A is v when it is far away from B. The minimum separation between the particles is not
proportional to
1 1 1
(A) Q2 (B) 2 (C) (D)
v v m
6. The electric field strength at a distance r from the centre of a charged sphere of radius R is E. If r >
R, how much work will be done in bringing a test charge q0 from infinity to that point
1 1
(A) q0RE (B) q0RE (C) q0rE (D) q0Re
2 2
7. Two identical rings, each of radius r, are co–axially placed. The distance between their centres is r.
Same charge Q is placed on each ring. The work done in moving a test charge from the centre of
one ring to that of the other is
1 2 q0 O 1 ( 2  1)q0 O 1 2 q0 O
(A) (B) zero (C) (D)
40 r 40 2r 40 ( 2  1)r

8. Point charge q moves from point P to point S along the path PQRS in a uniform electric field E
pointing parallel to the positive direction of x–axis. The coordinates of the point P, Q, R and S are
(a, b, 0) (2a, 0, 0), (0, –b, 0) and (0, 0, 0) respectively. The work done by the field in the above
process is given by
Eqm
(A) qEa (B) – qEa (C) qEa 2 (D)
2t
9. A charged particle of mass m and charge q is released from rest in an electric field of constant
magnitude E. The kinetic energy of the particle after time t is
2E2 t 2 E2 q2 t 2 Eq2m Eqm
(A) (B) (C) 2
(D)
mq 2m 2t 2t
–8
10. A ball of mass 1 g and charge 10 C moves from a point A whose potential is 600 V to the point B
–1
whose potential is zero. Velocity of the ball at the point B is 20 cms . The velocity of the ball at the
point A is
(A) 16.7 cms–1 (B) 16.7 ms–1 (C) 2.8 cms–1 (D) 2.8 ms–1
CPP- PH(I)- PHY- 23
11. A particle A has charge +q and particle B has charge +4Q with each of them having the same mass
m. When allowed to fall from rest through the same electric potential difference, the ratio of their
v
speed A will become
vB
(A) 1 : 2 (B) 2 : 1 (C) 1 : 4 (D) 4 : 1
12. Figure shows three points. X, Y and Z forming an equilateral triangle of

sides in an uniform electric field of strength F. A unit positive test
charge is moved from X to Y, from Y to Z, and from Z back to X. Which
one of the following correctly gives the work done against electrical
forces in moving the charge along the various parts of this path?
X to Y Y to Z Z to X
o o
(A) + Es + Es cos 60 – Es cos 60
o o
(B) 0 – Es cos 60 + Es cos 60
o o
(C) + Es + Es cos 60 – Es cos 60
o
(D) 0 – Es cos 60 + Es cos 60o
13. A particle of mass 0.002 kg and a charge 1 C is held at rest on a frictionless horizontal surface at a
distance of 1 m from a fixed charge of 1 mC. If the particle is released, it will be repelled. The speed
of the particle when it is at a distance of 10 m from the fixed charge is
(A) 60 ms–1 (B) 75 ms–1 (C) 90 ms–1 (D) 100 ms–1
14. Three charges Q, +q and +q are placed at the vertices of a right angled
isosceles triangle as shown in the figure. The net electrostatic energy of the
configuration is zero if Q is equal to
q 2q
(A) (B) (C) – 2q (D) + q
1 2 2 2
15. Two identical thin rings, each of radius R metre, are co–axially placed at a distance R metre apart Q1
coulomb and Q2 coulomb are the charges uniformly spread on the two rings. The work done in
moving a charge q from the centre of one ring to that of the other is
q(Q1  Q2 )( 2  1) 2q(Q1  Q 2 ) q(Q1  Q2 ) /( 2  1)
(A) zero (B) (C) (D)
2 40r 4 0R 2 40R
16. A, B, C, D, P and Q are points in a uniform electric field. The potentials at these points are V(A) = 2
V. V (P) = V (B) = V (D) =5 V. V(C) =8 V. The electric field at P is
(A) 10 V m–1 along PQ (B) 5 V m–1 along PC (C) 15 2 V m–1 along PC (D) 5 V m–1 along PA
17. Two small spheres, each carrying a charge q, are placed R metre apart. If one of the spheres is
taken around the other one in a circular path, then the work done will be equal to
(A) force between them xR (B) force between them l 2 nR
(C) force between them x2nR (D) zero
18. In bringing an electron towards to second electron, the electrostatic potential energy of the system
(A) increases (B) decreases (C) remains the same (D) becomes zero
4. ELECTRIC POTENTIAL
1. If sphere-1 with a charge q touches to a uncharged sphere-2, of half the radius of 1, charges on
q q q 2q 2q q q 4q
them are (A) , (B) , (C) , (D) ,
2 2 3 3 3 3 5 5

2.  
An electric field E  20iˆ  30ˆj N /C exists in the space. If the potential at the origin is taken to be
zero, the potential at (2m, 2m) is _________

(A) 100 V (B) 100 V (C) 50 V (D) 50 V
 
3. An electric field E  iAx exists in the space, where A  10 V /m 2 . Take the potential at (10 m, 20
m) to be zero. The potential at the origin is ________
(A) 100 V (B) 200 V (C) 400 V (D) 500 V
4. A charge q  10C is distributed uniformly over the circumference of a ring of radius 3m placed on
x-y plane with its centre at origin. Find the electric potential at a point P(0, 0, 4m).
(A) 1.8 kV (B) 18 kV (C) 2.8 kV (D) 28 kV
5. Find potential difference VAB between A(0, 0, 0) and B(1m, 1m, 1m)in an electric field

E  3x 2 yiˆ  x 3 ˆj
(A) 1 volt (B) 2volts (C) 3 volts (D) 4 volts

6. Find the potential function V  x, y  of an electrostatic field E  2axyiˆ  a x 2  y 2 ˆj, where a is a
 
constant.
ay 2 ay 2 ay 2 ay 2
(A) Vo  ax 2 y  (B) Vo  ax 2 y  (C) Vo  ax 2 y  (D) Vo  ax 2 y 
3 3 3 3
a
7. A spherical distribution of charge consists of uniform charge density, 1 from r = 0 to r  and a
2
a a
uniform charge density  2 from r  and r = a. The potential at r  is ________
2 2
a2 a2 a2
(A) 1  22  (B) 21  92  (C) 1  3 2  (D) None of these
24o 24o 8o
8. A charge q is distributed uniformly on the surface of a sphere of radius R. It is

covered by a concentric hollow conducting sphere of radius 2R . Find the
charge on outer surface of hollow sphere if it is earthed. R q
q q
(A) (B)  (C) q (D) zero 2R
2 2
9. In the above problem if the thickness of the outer sphere is considerable, find the charge on outer
surface of hollow sphere if it is earthed.
q q
(A) (B)  (C) q (D) zero
2 2
10. Eight mercury droplets having a radius of 1mm and a charge of 0.066 pC each merge to form one
droplet. Its potential is:
CPP- PH(I)- PHY- 25
(A) 2.4 V (B) 1.2V (C) 3.6V (D) 4.8V
11. Two spheres having radii of 5 cm and 10 cm bear identical charges of 6.6 nC. Find the potentials of
spheres after they have been connected by a conductor. Assume that the spheres are at large
distance from each other.
(A) 396 V (B) 600 V (C) 792 V (D) 1200 V

12. The electric field E in the given situation is constant in both magnitude
2
and direction. Consider a path of length d at an angle   60o with
d 
respect to field lines shown in figure. The potential difference between E
o
points 1 and 2 is: 60
1
E Ed E 3
(A) (B) Edcos60o (C) (D) cos 60o
o o d
dcos60 cos 60
 D

 
13. For the isolated charged conductor shown in figure, the potentials at 




 

points A,B,C and D are VA , VB ,VC and VD respectively, then: 



C 
 
(A) VA  VB  VC  VD (B) VD  VC  VB  VA 
 A 
 B 

(C) VD  VC  VB  VA (D) VD  VC  VB  VA ’ 
  

14. A solid conducting sphere having a charge Q is surrounded by an uncharged concentric conducing
hollow spherical shell. Let the potential difference between the surface of the solid sphere and that
of the outer surface of the hollow shell be V. If the shell is now given a charge of 3Q, the new
potential difference between the same two surfaces is:
(A) V (B) 2V (C) 4V (D) 2V
15. A charged soap bubble of radius r is in equilibrium. If T is the surface tension of soap solution, then
potential of the soap bubble is:
8To 8Tr 8Tr
(A) (B) (C) 8Tro (D)
r o o
16. Two conducing spheres of radii R1 and R2 are charged with charges Q1 and Q2 respectively. On
bringing them in contact there is:
(A) always a decrease in energy of the system
(B) an increase in the energy of the system if Q1R2  Q2R1
(C) no change in the energy of the system
(D) a decrease in energy of the system if Q1R2  Q2R1
17. Choose the correct relation regarding potential. Here A,B,C and D all    
are at equal distance from point O. then: A q O +q B
(A) VA  VB  VC  VD (B) VC  VD  VA  VB
(C) VA  VC  VD  VB (D) VB  VC  VD  VA 
D
C
18. Figure shows three spherical and equipotential surfaces A,B and C round a point B
A
charge q . The potential difference VA  VB  VB  VC . If t1 and t 2 are the
distances between them then: q   t1 
 t 
(A) t1  t 2 (B) t1  t 2 (C) t1  t 2 (D) t1  t 2 2
5.DIPOLES
1. Two charges +10 m C and 10m C are separated by a distance of 4 m. The magnitude of dipole
moment is
(A) 80 (B) 40 (C) 400 (C) 100
2. The electric potential at a point situated at a distance r on the axis of a short electric dipole of
1
moment P is times _________
4 0
p p p
(A) (B) (C) (D) None of these
r3 r2 r
3. An electric dipole of moment P is kept along an electric field E. The work done in rotating it from an
equilibrium position by an angle q is
(A) PE 1  cos q  (B) PE 1  sin q  (C) PE cos q (D) PE sin q
4. The figure shows a Quadrapole. Assuming x  a , the

x
electric field at point A is ________ here, (P = qa)
(A)
6 Pa 2
(B)
6 Pa
(C)
2 Pa
(D)
3Pa 2 . a . a . .
A
+q 2q +q
4peo x 5 4peo x 4 4peo x 4 4peo x 5
5. An electric dipole is placed in a uniform field, the net force and net torque on the dipole is
(A) force = 0, torque may not be zero (B) force may not be zero
(C) force and torque both may not be zero (D) force = 0, torque = 0
6. An electric dipole is placed in a non–uniform electric field. Then net

(A) force experienced is zero while torque is not zero
(B) force experienced is zero and torque is also zero
(C) both force and torque are not zero
(D) force experienced is not zero while torque is zero
7. A molecule of HCl is placed in a electric field of 2.5  10 4 N/C . The dipole moment of molecule is
3.4  1030 . The maximum torque that can act on molecule is
(A) 6.5  1026 N-m (B) 7.5 1026 N-m (C) 8.5  1026 N-m (D) 1.5  1026 N-m
8. For short dipole, electric field magnitude at a point which is at a distance r from it and making an
angle ' q ' with its axis, is
p sin q p cos q p 1  3 cos2 q
(A) (B) (C) (D) None of these
4peo r 3 4peo r 3 4peo r3
 
9. The dipole moment of a dipole is 10 j . This is kept in a uniform electric field E  3i  4j , then the
torque acting on it is ______

(A) 30k 
(B) 30k 
(C) 40k 
(D) 40k
10. A dipole consists of two particles one with charge +1mC and mass 1 kg and the other with charge
1mC and mass 2 kg, separated by a distance of 3 m. For small oscillations about equilibrium
position, angular frequency, when placed in uniform field of 20 kv/m is
(A) 0.1 rad/s (B) 1.1 rad/s (C) 10 rad/s (D) 2.5 rad/s
CPP- PH(I)- PHY- 27
FIITJEE GAUSS’S LAW CPP

Name: …………………………………… Batch:…………………Date of submission:……………
1. An electric dipole of dipole moment is placed at the centre of a sphere of radius ' R ' , then the flux
passing through sphere is
P P P
(A) (B) (C) (D) zero
2
R eo Reo eo
2. A point charge ' q ' is placed at centre of a cube with side a. The flux linked with each face of cube is
q q q qa
(A) (B) (C) (D)
aeo 6eo eo eo

3. The electric field in a region is given by E   yiˆ . Here  is a constant of proper dimensions. Find
the total flux passing through a cube bounded by the surfaces, x =  , x = 2  , y = 0, y =  , z = 0,
z =.
(A) 6l2 (B) l3 (C) 3l3 (D) zero
4. A hemisphere body of radius R is placed in a uniform electric field E. What is the flux linked with the
curved surface, if the field is parallel to the base
(A) R2E (B) 4R2E (C) 2R2E (D) Zero
5. A charge q 0 is distributed uniformly on a ring of radius R. A sphere of equal radius R is constructed

with its centre on the circumference of the ring. The electric flux through the surface of the sphere is
q q 2qo
(A) o (B) o (C) (D) None of these
o 2o o
6. An elliptical cavity is carved out in a perfect conductor. A positive
charge q is placed at the centre of the cavity. The points A and B are
shown in figure, then A
(A) electric field near A in the cavity = electric field near B in the cavity. q B
(B) charge density at A = charge density at B

(C) potential at A = potential at B
q
(D) total electric field flux through the surface of the cavity = .
eo
7. An electron of 100 eV if fired directly towards a metal plate having surface charge density
2 106 cm2 . Find distance from where the electron be projected so that it just fails to strike the
plate.
(A) 0.22 mm (B) 0.44 mm (C) 0.66 mm (D) 0.33 mm
8. A large sheet carries uniform surface charge density  . A rod of length 2l has +
a linear charge density  on one half and  on the other half. The rod is
hinged at mid-point O and makes an angle  with the normal to the sheet. The 
O
torque experienced by the rod is:
l2 l l2 l 2
(A) cos  (B) cos2  (C) sin  (D) sin 
2o o 2o o +σ 
9. The electron is projected from a distance d and with initial velocity u parallel to a
uniformly charged flat conducting plate as shown. It strikes the plate after P u
traveling a distance l along the direction. The surface charge density of the d
conducting plate is equal to x
2domu2 2domu domu2 d mu l
(A) (B) (C) (D) o
el2 el el el
10. A long, hollow conducting cylinder is kept coaxially inside another long, hollow conducting cylinder of
larger radius, both the cylinders are initially electrically neutral.
(A) a potential difference appears between the two cylinders when a charge density is given to the
inner cylinder.
(B) a potential difference appears between the two cylinders when a charge density is given to the
outer cylinder.
(C) no potential difference appears between the two cylinders when a uniform line charge is kept
along the axis of the cylinders.
(D) no potential difference appears between the two cylinders when same density is given to both
the cylinders.
11. Electric charge is uniformly distributed along a long straight wire of radius 1 mm.
The charge per cm length of the wire is Q coulomb. Another cylindrical surface of
radius 50 cm and length 1 m symmetrically encloses the wire as shown in the
figure. The flux through the cylindrical surface is
Q 100Q 10 Q 100Q
(A) (B) (C) (D)
0 0 ( 0 ) (0 )

12. Given: E  (10 ˆi  7 ˆj) Vm1 . The electric flux through 1 m2 area in XZ plane is
(A) 10 Vm (B) 7 Vm (C) 100 Vm (D) 49 Vm
13. Q1 and Q2 are the charges inside and outside respectively of a closed surface S. Let E be the
electric field at any point on S and  be the flux of electric field over the closed surface. Which of the
following is correct?
(A) if Q1 changes, both E and  will change (B) if Q1 changes, E will change but  will not
change
(C) if Q1 = 0 and Q2  0 then may be E  0 but  = 0 (D) if Q1  0 and Q2 = 0 then may be E = 0 but  
0
14. Due to a charge inside the cube, the electric field is (see figure) Ex =
600x1/2 x 106, Ey = 0, Ez = 0. The charge inside the cube is nearly
(A) 600 C (B) 60 C
(C) 7 C (D) 6 C

15. In a region of space, the electric field is in the x-direction and proportional to x, i.e., E  E0 xiˆ .
Consider an imaginary cubical volume of edge a, with its edges parallel to the axes of coordinates.
The charge inside this volume is
1 1
(A) zero (B) 0E0a3 (C) E0 a 3 (D) 0E0 a2
0 6
FIITJEE CAPACITANCE CPP

Name: …………………………………… Batch:………………… Date of submission:……………
CPP- PH(I)- PHY- 29
1. CAPACITANCE & DIFFERENT KINDS OF ARRANGEMNT
1. An air capacitor of capacitance 6 F is immersed in oil whose dielectric constant is 2. The

capacitance of capacitor will be
(A) 2.5 F (B) 8.5 F (C) 22 F (D) 12 F
2. A metallic sheet is inserted between plates parallel to the plates of a parallel plate capacitor. The
capacitance of capacitor.
(A) Increases
(B) is independent of the position of the sheet which can be placed anywhere between the plates.
(C) is maximum when the metal sheet is in middle (D) both (a) and (b) are correct
3. In the given figure, a capacitor of non-parallel plates is shown. The plates B
of capacitor are connected by a cell of e.m.f V0 of σ denotes surface A

F
charge density and E denotes electric field, then V0
 D
(A)  A  B (B) E F  E D (C) E F  E D (D)  A  B
4. An air capacitor consists of two parallel plates A and B as shown in figure. Plate A
is given a charge Q and plate B is given a charge 3Q. P is the median plane of the
capacitor. If C 0 is the capacitance of the capacitor, then
Q Q Q Q
(A) VP  VA  (B) VP  VA  (C) VP  VA  (D) VP  VB  
4C 0 2C 0 C0 4C 0 A P B
5. Three conducting spheres A, B and C are as shown in figure. The radii of three C
spheres are a,b,c respectively. A and B are connected by a conducting wire. B
A
The capacity of the system is a
 bc  1 1 1  abc 
(A) 4 0 a  b  c  (B) 4 0   (C) 4 0     (D) 4 0   b
 cb a b c  ab  bc  ca 
c
6. Two plates (area – S) charged to q 1 and q 2 q 2  q 1  are brought closer to form a capacitor of
capacitance C. The potential difference across the plates is:
q q2 q q2 q q2 2q 1  q 2 
(A) 1 (B) 1 (C) 1 (D)
2C C 4C C
7. A parallel plate capacitor having area A is given a charge q and q on its plates. Two plates exert
force of attraction given by:
1 q2  q2 q2 q2
(A) (B) 0 (C) (D)
4 0 A 2A 2 0 A 0A
8. One plate of a capacitor is connected to a spring a shown. Area of both
plates is A. In the steady state separation between the plates is 8d
(spring was unstretched and the distance between the plates was d ,
when the capacitance was uncharged). The force constant of spring is
approximately.
4 0 AE 2 2 0 AE 6 0 E 2  0 AE 3
(A) (B) (C) (D) E
d3 d2 Ad 3 2 d3
9. In the given figure a capacitance of plate area A is charged upto charge q.
The mass of each plate is m 2 . The lower plate is rigidly fixed. Find the value
of m 1 , so that the system remains in equilibrium.
q2 q2 m1
(A) m 2  (B) m2 (C)  m2 (D) None of the above
 0 Ag 2 0 Ag
10. There is an air-filled 1-pF parallel-plate capacitor. When the plate separation is doubled and the
space is filled with wax, the capacitance increases to 2 pF. The dielectric constant of wax is
(A) 2 (B) 4 (C) 6 (D) 8
2. COMBINATION OF CAPACITORS
1. Three capacitors 4 F, 6 F and 12 F are connected in series to a 10 V. the charge on the middle
capacitor is
(A) 10 C (B) 20 C (C) 60 C (D) 5 C
3F 3F 3F 3F
2. The resultant capacitance between A and B in A
the figure is
(A) 1F (B) 10 F 2F 2F 2F 3F
(C) 50 F (D) 1.5 F

B
3F 3F 3F 3F
C0 C0
M N
3. The equivalent capacitors between points M and N is
10 C0
(A) C0 (B) 2 C 0 C0
11
C0
(C) C 0 (D) None of these
C0
4. In the given figure the equivalent capacitance between

A and B is
(A) 3C / 4 (B) 4 C A B
C C C C C C
(C) 3 C / 2 (D) 6 C / 2
A 0
C
C
5. The equivalent capacitance between points A and B is C
(A) C / 4 (B) C / 2
(C) C (D) 2 C C C C
B0
6. Five identical capacitor plates are arranged as shown figure. Each plate
has an area A and distance between adjacent plates is d. The charge on 1 2 3 4 5
V

plate 1 is: 
E AV E AV 2 E AV E AV
(A) 0 (B) 0 (C) 0 (D) 0
d d 2d 3d
CPP- PH(I)- PHY- 31
7. A capacitor has square plates each of side ‘a’ making an angle 
between them as shown in figure. The capacitance for small  .

 a 0 a 2 a 
(A) 0 (B) 1  2d 
d
d d
0 a 2  a  0 a3   
(C) log d  (D)  a 
d d  2d  a
C C C C
P
8. In the network shown in figure, C1  6 F and C  9 F . 
The equivalent capacitance between points P and Q is

(A) 3F (B) 6 F C1 C1 C1
C
(C) 9 F (D) 12 F
Q
C C C C
9. A parallel plate capacitor is made by stacking 10 identical metallic plates equally spaced from one
another and having the same dielectric between the plates. The alternate plates are then connected.
If the capacitor formed by two neighbouring plates has a capacitance ‘C’, the total capacitance of the
combination will be
C C
(A) (B) (C) 9C (D) 10C
10 9
P
10. In the arrangement shown in figure, each capacitor has capacitance
C  1F , then the equivalent capacitance across PQ is
(A) 0.5 F (B) 1 F
(C) 2 F (D) infinity Q
11. Each of the three plates shown in figure has an area of 200 cm2 on one side
and the gap between the plates is 0.2 mm. The charge on each surface of plate E  10 V
and the equivalent capacitance of the system is

(A) 8.85 nC , 0.885 nF (B) 17.7 nC , 1.77 nF
A B C
(C) 4.42 nC , 0.442 nF (D) 2.95 nC , 0.295 nF

B
3F 1F
12. In steady state the potential difference between points A and
3F 1F
B and between points B and C is
(A) 50 V, 50 V (B) 40 V, 60 V
(C) 25 V, 75 V (D) 80 V, 20 V
1F 20 
A 20  100 V C
13. Two square metallic plates of side 1m are kept 0.01 m apart, like a parallel plate capacitor in air in
such a way that one of their edges is perpendicular to an oil surface in a tank filled with an insulating
oil. The plates are connected to battery of e.m.f 500 V. The plates are then lowered vertically into oil
-1
at speed of 0.001 ms .Then the current drawn from battery during the process is
(Dielectric constant of oil = 11 and  0  8.85 10 12 N 1 C 2 m 2 )
(A) 1.106 10 9 A (B) 8.85  10 9 A (C) 4.425 10 9 A (D) 4.425  10 10 A
C1
N
14. The equivalent capacitance between points M and N is:
(A) infinity (B) C1 + C2
C1C 2
(C) (D) zero M C2
C1  C 2
15. The region between the plates of a parallel plate capacitor is filled with
dielectric slabs of different dielectric constants as shown in the figure.
Find the capacity if the capacity of the capacitor with air between the K1  2 K2  3
plates is 20 mF
(A) 40 mF (B) 48 mF (C) 20 mF (D) 10 mF
16. In the given figure, the equivalent capacitance between A and B is: B DE
(A) 3C (B) C/3   
A C
(C) 3/2 C (D) Infinity C C
17. For the given circuit, the equivalent capacitance

between P and Q P Q
(A) 6C (B) 4C
(C) 3C/2 (D) 2C C C C C C
18. The equivalent capacitance between points A and B is: C2 C2 C2

A
(A) n 2 C1 (B) infinity
 2C  n 2 C  1  C
 1  C1 nC1 n 2 C1 to 
(C)   (D) zero
 2 
 
B
19. The equivalent capacitance of the circuit across the terminals A and B 2 F 6 F
is equal to: B A
36
(A) 13 F (B) F (C) 3F (D) 3 / 4 F 2 F 3 F
13
20. Four equal capacitors, each with a capacitance (C) are connected to a 10 V
battery of emf 10 V as shown in the adjoining figure. The mid-point of the A C

capacitor system is connected to earth. Then the potentials of B and D are
respectively:
B E D
(A) +10 V, 0 V (B) +5 V, -5 V
C C C C
(C) -5 V, +5 V (D) 0 V, - 5 V
Earth
21. Three identical capacitors are first connected in series and then first and last Q
conductors of combination are connected to the earth. A charge Q is given to
second conductor of first capacitor. Then potential of this conductor is:
Q Q 2Q 3Q
(A) (B) (C) (D)
3C C 3C 2C
CPP- PH(I)- PHY- 33
22. In the given circuit, potential of point A is: C0
A C0
E
(A) zero (B) 0 E 0 C0
E0
2
C0
(C) 2E 0 (D) None of these E0
C0
A
C1
23. The potential difference between points A and B of the circuit is: C2
(A) C 2  C1 E (B) C 4  C 3 E
C 2 C 3  C1C 4 E C 2 C3  C1C 4 E C3
B
C4
(C) (D)
C1  C 2  C 3  C 4  C1  C 2 C 3  C 4 
E
24. The equivalent capacitance of a combination shown in the figure is

(A) C (B) 2C C
C
(C) C/2 (D) None of these
C
2 F
3 F
25. Find out the charge on the condenser of capacity 5 F as shown in C D
the figure. 4 F
(A) 4.5 C (B) 9 C 5 F
B E
(C) 7 C (D) 30 C
A F
26. The effective capacitance between A and B in figure shown

2C C
2
(A) 2C (B) C
3 5C
A B
4
(C) C (D) None of these 4C 2C
3
E
27. If E = 90V, C2=3C1, then potential difference
between P and Q will be
(A) 30 V (B) 10 V C1 C2
(C) 19 V (D) 8 V
 Q
C1 P C
1
28. The charge on the capacitor of capacitance 4 F in the circuit is 4 F

(A) 350 C (B) 150 C 70 V 5F
(C) 200 C (D) 550 C 10 F

8F 8F
29. Find the effective capacity between A and B is
(A) 1F (B) 5 F
8F
(C) 3 F (D) 7 F 8F 8F
A B
30. In the circuit if the potential difference across 4 F condenser is 6V the p.d
3F 4 F
between 5F condenser is
(A) 7.5 V (B) 14 V
(C) 10.5 V (D) 4.5 V
5F
3. COMBINING CAPACITORS AFTER CHARGING
1. Two identical capacitors 1 and 2 are connected in series to a battery as

shown in figure. Capacitor 2 contains a dielectric slab of dielectric
constant K as shown. Q1 and Q2 are the charges stored in the capacitors. 1 2
Now the dielectric slab is removed and the corresponding charges are
Q11 and Q21. Then
Q1 K  1 Q1 K  1 Q1 K  1 Q1 K
(A) 2  (B) 2  (C) 2  (D) 1  E
Q1 K Qc 2 Q2 2K Q1 2
2. Two charged metal spheres A and B have radii in the ratio 2 : 3 with charge 5 x 10-6C and 10 x 10-6C
respectively. If they are connected by a wire, then
(A) 5 μC of charge flows from B to A till their charges are equal
(B) 1 μC of charge flows from A to B till common potential is reached.
(C) 1 μC of charge flows from B to A till common potential is reached
(D) No charge flows between A and B
3. Two parallel plate capacitors of capacitances C and 2C are connected in parallel and charged to
potential difference V by a battery. The battery is then disconnected and the space between the
plates of capacitor ‘C’ is completely filled with a material of dielectric constant ‘K’. The potential
difference across the capacitors now becomes.
V 2V 3V 3V
(A) (B) (C) (D)
K 1 K2 K2 K 3
4. A parallel plate condenser with a dielectric of dielectric constant ‘K’ between the plates has a
capacity ‘C’ and is charged to potential ‘V’. The dielectric slab is slowly removed from between the
plates and then reinserted. The net work done by system in this process is
1 CV 2 K  1
(A) zero (B) K  1CV 2 (C) (D) K  1 CV 2
2 K
5. A capacitor C is charged to a potential V by a battery. The emf of the battery is V . It is

disconnected from the battery and again connected with it, with its polarity reversed to the battery:
(A) The work done by the battery is 2CV 2
(B) The total charge passing through the battery is 2CV
(C) The initial and final energy of a capacitor is same (D) All of these
S
6. In the given figure, find the charge flowing through section AB when
switch S is closed:
(A) C 0 E / 12 (B) C 0 E / 4 A
C0 C0 C0 C0
(C) C 0 E / 3 (D) None of these
E
B
CPP- PH(I)- PHY- 35
7. In the given figure the capacitor of plate area A is charged upto
charge q . The ratio of elongation (neglect force of gravity) in k2 k1
springs C and D at equilibrium position is:
k k D C
(A) 1 (B) 2 (C) k 1 k 2 (D) None of these
k2 k1
8. Two capacitors A and B with capacitance 3 F and 2F are charged to

2 F
potential of 100 V and 180 V respectively. The plates of the capacitor are
connected as shown in figure with one wire from each capacitor free. The
C
upper plate of A is positive and that of B is negative. An unchanged 2 F
 3F 2 F 
capacitor C with lead wire falls on the free ends to complete the circuit. A B
Then the final charge on three capacitors are 100 V 180 V
(A) 90 C ,150 C , 210 C (B) 80 C ,150 C , 210 C
(C) 90 C ,180 C , 210 C (D) 90 C ,150 C , 240 C
9. A capacitor of capacitance ‘C’ is fully charged by a 200 V supply. It is then discharged through a
small coil of resistance wire embedded in a thermally insulated block of specific heat
2.5  10 2 Jkg 1 k 1 and of mass 0.1 kg. If the temperature of block rises by 0.4 K, the value of ‘C’ is
(A) 500 F (B) 400F (C) 300 F (D) 200F
10. Two condensers of capacities C1 and C 2 are charged to potentials V1 and V2 .

What is the common potential when they are connected in parallel? Find the loss of energy?
C V  C 2 V2 1 C1 C 2 C V  C 2 V2 1 C1C 2
(A) 1 1 ; V1  V2 2 (B) 1 1 ; V1  V2 2
C1  C 2 2 C1  C 2  C1  C 2 2 C1  C 2 
C1V2  C 2 V1 1 C1  C 2  C1V2  C 2 V1 1 C1  C 2 
(C) ; V1  V2 2 (D) ; V1  V2 2
C1  C 2 2 C1C 2 C1  C 2 2 C1C 2
4. DIELECTRIC FORCE & DIELECTRIC CHARGE
1. Find the capacitance of the capacitor shown in figure. The plate area is A
and the separation between the plates is d. Different dielectric slabs in a
particular part of the figure are of the same thickness and the entire gap
between the plates is filled with the dielectric slabs.
2K1K 2  0 A  A  A
(A) (B) 0 (K1  K 2 ) (C) 0 (K1  K 2 ) (D) none of these
d(K1  K 2 ) d 2d
2. Find the capacitance of the capacitor shown in figure. The plate area is A and the
separation between the plates is d. Different dielectric slabs in a particular part of
the figure are of the same thickness and the entire gap between the plates is filled
with the dielectric slabs.
30 A(K1K 2  K 2K 3  K 3K1 ) 30 AK1K 2K 3  A
(A) (B) (C) 0 (K1  K 2  K 3 ) (D) none of these
d(K1  K 2  K 3 ) d(K1K 2  K 2K 3  K 3K1 ) 2d
3. Find the capacitance of the capacitor shown in figure. The plate area is
A and the separation between the plates is d. Different dielectric slabs
in a particular part of the figure are of the same thickness and the entire
gap between the plates is filled with the dielectric slabs.
2K1K 2  0 A 30 AK1K 2K 3 0 A

(A) (B) (C) (K1  K 2 ) (D) none of these
d(K1  K 2 ) d(K1K 2  K 2K 3  K 3K1 ) 2d
4. The capacitance of a parallel plate capacitor with plate area A and
separation ‘d’ is C. The space between the plates is filled with two
wedges of dielectric constants K 1 and K 2 as shown in figure.
The capacitance of resulting capacitor is K2
K  K 1 d log  K 2  K K A K  d
(A) C  2 e  (B) C  2 1 0 log e  1 
K 1 K 2 A 0  K1  K1  K 2 d  K 2  K1
K1  K 2 d log  K2  K1K 2 A 0 K 

log e  2 
(C) C  e


 (D) C 
A 0 K1K 2  K1  K 2  K1 d  K1 
a
5. Figure shows a parallel plate capacitor having square plate of edge ‘a’ and plate
separation d. The gap between the plates is filled with a dielectric of dielectric d K
constant K which varies parallel to an edge as K  K 0   x , where K and  are

constants and x is the distance from the left end. Then the capacitance is
 d a   a a   a2  a   a2  ax 
(A) 02 K 0   (B) 02 K 0   (C) 0 K 0   (D) 0 2 K 0  
a  2 d  2  d  2  d  2
6. Figure shows a parallel plate capacitor with plates of width ‘b’ and
length l . Separation between the plates is ‘d’. The plates are rigidly
clamped and connected to battery of e.m.f V. A dielectric slab of d
K
thickness ‘d’ and dielectric constant ‘K’ is slowly inserted between

the plates. Then the energy of system when length ‘x’ of the slab is
x
introduced into capacitor is l
 bv  0 bv 2  bv 2 2 2
(A) 0 l  xk  1 (B) l  xk  1 (C) 0 l  xk  1 (D)  0bv2 l  xk  1
2d 2d 2 2d 2d
7. A parallel plate condenser is charged by a battery. The battery is removed and a thick glass slab is
placed between the plates. Now:
(A) the capacity of the condenser is increased
(B) the potential across the plates is decreased
(C) the electric field between the plates is decreased (D) all of the above
8. An air filled parallel plate capacitor has a capacitance of 10 12 F . The separation of the plates is
doubled and wax is inserted between them, which increases the capacitance to 2 10 12 F. The
dielectric constant of wax is:
(A) 2 (B) 3 (C) 4 (D) 8
9. Between the plates of parallel plate capacitor, a dielectric slab of dielectric L
constant K is inserted. Plates have area A and distance between the plate Slab
is d and charge on the plate is Q . If the inserted length is x and the edge K d
effect is ignored then the force on the slab is: (Give C 0   0 A / d )
x Area  A
Q Q
(A) attractive and equal to K  1 (B) repulsive and equal to K  1
2C 0 L 2C 0 L
(C) attractive and equal to

Q2

K  1 (D) repulsive and equal to
2
2C 0 L  x 
1
 L K  1
 
Q2

K  1
2
2C 0 L  x 
1
 L K  1
 
CPP- PH(I)- PHY- 37
10. Inside two identical capacitors, two identical dielectric slabs are
introduced as shown in figure. What will happen, if slab of capacitor B A B
is pulled out, with the battery remain connected? F
(A) During the process charge flows from a to b
(B) Finally charge on B will be less than charge on A
 
(C) During the process work done by external force F appear as heat in  
the circuit (D) None of the above a b
FIITJEE CURRENT ELECTRICITY CPP

Name: …………………………………… Batch:………………… Date of submission:……………
1. OHM’S LAW & DRIFT VELOCITY

20
1. 10 electrons are flowing through a cross section of a wire every second. The current in the wire is
–19 6
(A) 1.6  10 A (B) 1 A (C) 16 A (D) 10 A
2. A current of 40 A exists in a wire of 1 mm2 area of cross-section. If the number of free electrons per
cubic centimeter is 1025, the drift velocity is
–3 –1 –3 –1 –3 –1 -3 –1
(A) 250  10 cm s (B) 25.0  10 cm s (C) 2.50  10 cm s (D) 1.25  10 cm s
3. An aluminum wire of diameter 4 mm carries a current of 4.4 A. The current density is

(A) 3.5  102 A m–2 (B) 1.75  105 A m–2 (C) 1.75  104 A m–2 (D) 3.5  105 A m–2
4. A conducting wire of cross-section 0.1 mm2 carries a current of 5 A produced by an electric field at
100 V/m. The resistivity of the material is
(A) 2.0  10–3 Ω m (B) 2.0  10–3 Ω mm (C) 2.0  10–3 Ω cm (D) 2.0  10–3 Ω μm
5. Given a current carrying wire of non-uniform cross-section, which of the following quantity or
quantities is constant throughout the length of the wire?
(A) Current, electric field and drift speed (B) Drift speed only
(C) Current and drift speed (D) Current only
2. COMBINATION OF RESISTORS
1. A metal block has length 50 cm, breadth 30 cm and thickness 20 cm. When a current passes
through it parallel to its length, its resistance is R. If the current is passed through it parallel to its
breadth, then its resistance is
(A) 9R 25 (B) 4R 25 (C) 25R 4 (D) 25R 9
2. A wire of length 4 m and radius 0.25 mm has a resistance of 24 Ω. The resistivity of the wire is
(A) 17.75  10-4 Ω m (B) 17.75  10-6 Ω m (C) 17.75  10-4 Ω cm (D) 17.75  10-8 Ω m
3. A wire of resistance R is stretched to thrice its length. The new resistance is

(A) 3R (B) 9R (C) R / 3 (D) R / 9
4. At 30°C the resistance of a conductor is 5 Ω. The temperature at which the resistance of the same
conductor is 5.2 Ω is (given that the temperature coefficient of resistance for this conductor is 0.001
°C–1)
(A) 41°C (B) 71°C (C) 100°C (D) 170°C
5. The resistances of a wire made of iron and another made of copper are 4.8 Ω and 5 Ω respectively
at 20°C. Their temperature coefficient of resistances are 5  10-3 K-1 and 4  10-3 K-1 respectively..
The temperature at which their resistances are equal is
(A) 70°C (B) 82°C (C) 110°C (D) 132°C
6. Four identical wires, each of resistance R, are connected to form a square. The equivalent
resistance between the ends of any side is
(A) 4R (B) 2R (C) 3R/4 (D) R/4
7. Resistances R, 2R, 4R, 8R ………..∞ are connected in parallel. The effective resistance of the
combination is
(A) R/2 (B) R (C) 2R (D) 4R
8. Two wires made of same material and of same length have their resistances in the ratio 2:3. The
ratio of masses of the wires is
(A) 2:3 (B) 3:2 (C) 1:1 (D) 5:6
9. The equivalent resistance of the circuit 1Ω 1Ω 1Ω 1Ω

shown is 1Ω 1Ω 1Ω 1Ω
(A) 13/3 Ω (B) 3/13 Ω 2Ω 2Ω
2Ω 2Ω
(C) 16/3 Ω (D) 3/16 Ω
2Ω 2Ω 2Ω 2Ω
10. Six equal resistances, each 4 Ω are connected together making the arms of a tetrahedron. The
equivalent resistance across any two adjacent vertices is.
(A) 10 Ω (B) 2/3 Ω (C) 4 Ω (D) 2 Ω
11. A wire of resistance 24 Ω is bent in the form a regular polygon of 6 sides. The effective resistance
between the ends of any one side is
(A) 50/18 Ω (B) 10/3 Ω (C) 4 Ω (D) 20/3 Ω
12. The ring shown in the figure has zero resistance. The equivalent 6R
6R
resistance between the points A and B will be B
2R
A
(A) R (B) 2R (C) 3R (D) 4R 6R
A
13. Five identical resistances are connected in a network as
shown in the figure. If the resistance between A and B is 4 Ω,
find the resistance of each wire
(A) 9 Ω (B) 7 Ω
(C) 5 Ω (D) 3 Ω B
B
30  4
14. Find the effective resistance between A and B in the figure
shown here. 6
10 
(A) 2 Ω (B) 4 Ω A 8
(C) 6 Ω (D) 8 Ω 5
10 
B
15. A uniform wire of resistance 36 Ω is bent in the form of a
circle. The effective resistance across the points A and B is 600 A

(A) 5 Ω (B) 6.0 Ω 0
(C) 7.2 Ω (D) 30 Ω
16. Three resistors of resistance 5 Ω, 10 Ω and 12 Ω are in parallel. The current through 10-Ω resistor is
2 A. The currents through other resistors are
(A) 2 A, 6 A (B) 4/3 A, 2 A (C) 3 A, 4 A (D) 4 A, 5/3 A
17. Three conductors draw currents 1 A, 2 A and 4 A respectively when connected across a battery in
parallel. If all those resistances are connected in series to the same battery, the current drawn is
(A) 4 A (B) 7 A (C) 1 A (D) 2 A
7 7 7
CPP- PH(I)- PHY- 39
18. Two wires of same material having lengths l , 2l and radius 2R, 3R are connected in parallel across
a source. If the current in shorter wire is I, the current in the longer wire is
(A) I (B) I/2 (C) 9I/8 (D) 8I/9
19. Two resistors made of same material having lengths 3 cm, 5 cm and radii 1 mm, 3 mm are
connected in series to a cell of e.m.f. 16 V and negligible resistance. Potential difference across
shorter wire is
(A) 2.5 V (B) 8 V (C) 13.5 V (D) 16 V
20. Two resistors of 3 Ω and 7 Ω are connected in parallel. If the total current through the resistors is 15
A, then the currents through the resistors are
(A) 10.5 A, 4.5 A (B) 9.5 A, 3.5 A (C) 8.5 A, 2.5 A (D) 7.5 A, 1.5 A
4
4 4
21. The current in the circuit given below 4 4

(A) 0.5 A (B) 0.7 A
(C) 0.9 A (D) 1.0 A 4
1.8 V 2 / 3
2
22. In the circuit shown in the figure, if the current in the 5 Ω resistor is 14 5
A, the constant voltage V of the cell is 10 
V 10 
(A) 63 V (B) 126 V
(C) 6.3 V (D) 12.6 V
12 V 1
6
23. The current from the battery in the network shown below is 4
(A) 1 A (B) 1.5 A 12 
1
(C) 2 A (D) 2.5 A
8
24. Resistances of 2 Ω and 3 Ω are connected in series. If the P.D. across the 2 Ω resistor is 3 V, the
P.D. across 3 Ω resistor is
(A) 2 V (B) 9 V (C) 3 V (D) 4.5 V
12  8 0.3 
25. In circuit shown in the figure the emf of the cell is 3.6
V. The current flowing through the 6-Ω resistor is 4
(A) 0.1 A 8
(B) 0.2 A 6
(C) 0.3 A
(D) 1.2 A
3
4
26. A 5-Ω resistor is connected to a 15-V cell. The power drawn by the resistor is
(A) 75 W (B) 3 W (C) 35 W (D) 45 W
27. A bulb is rated 110-W, 220-V. The current drawn by this bulb when it is connected to a 110 V
source is
(A) 1 A (B) 0.5 A (C) 0.25 A (D) 0.05 A
28. Two bulbs A and B are rated 100-W, 220-V and 50-W, 110-V. The true statement among the
following is
(A) The resistance of A is more than the resistance of B
(B) The current drawn by A is less than the current drawn by B
(C)When the two bulbs are connected in series to a 220-V source, bulb B glows brighter than bulb A
(D) All the above
29. Four 5-Ω resistors are connected together along the edges of a square. A 20-V battery of negligible
internal resistance is connected across a pair of diagonally opposite corners of the square. The
power dissipated in the circuit is
(A) 100 W (B) 75 W (C) 80 W (D) 50 W
30. Two 100-W, 220-V bulbs are connected in series across a 110-V source. The net power delivered
by the source is
(A) 200 W (B) 100 W (C) 25 W (D) 12.5 W
3. CIRCUITS
1. A battery of emf 2 V is connected to an external resistance which is equal to its internal resistance,
the p.d. across the external resistance is
(A) 2 V (B) 1 V (C) 4 V (D) zero
2. The emf of a Daniel cell is 1.08 V. When the terminals of the cells are connected to a resistance of 3
Ω, the p.d. across the terminals was found to be 0.6 V. The internal resistance of the cell is
(A) 0.2 Ω (B) 3.24 Ω (C) 1.8 Ω (D) 2.4 Ω
3. When two cells each of emf 2 V are connected in series with a combination of two resistors of 3 Ω
and 6 Ω in parallel, the terminal voltage of the battery is 2 V. The internal resistance of each cell is
(A) 1 Ω (B) 2 Ω (C) 3 Ω (D) 4 Ω
4. A car has a fresh, storage battery of emf 12 V and internal resistance 2  10-2 Ω. If the starter motor
draws a current of 80 A, then the terminal voltage when the starter is on, is
(A) 12 V (B) 8.4 V (C) 10.4 V (D) 9.3 V
12 A
3A
5. The figure shows a net work of currents. The magnitude of
currents is shown here. The current I will be
(A) –3 A (B) 3 A 8A
(C) 13 A (D) 20 A
I
5A
A
6. Find the E in the given loop
E 3
(A) –24 V (B) 24 V
(C) 4 V (D) zero 1A 1A
4
10 V
6
B 2 A 5V C
E1  4 V R1  2 
7. In the circuit shown, E1 = 4.0 V, E2 = 6.0 V, R1 = 2 Ω, R2 = 4 Ω

and R3 = 2 Ω. The current I1 is, I1
R3  2 
(A) 1.6 A (B) 1.8 A
(C) 1.25 A (D) 1.0 A I2
E 2  6V
R2  4 
CPP- PH(I)- PHY- 41
10 
8. In the circuit shown below, the galvanometer deflection is

zero. The resistance ‘X’ is then 4 7
(A) 1.4 Ω (B) 7.0 Ω
(C) 2.8 Ω (D) 2.1Ω
x
X 
R
5
9. To balance the bridge circuit shown in the figure, the value of R is 12 
(A) 4 Ω (B) 8 Ω G
(C) 12 Ω (D) 20 Ω 60 
15 
8V 50 
10. In the circuit shown in the figure, the reading of the voltmeter V2 is V1
(A) zero (B) 2 V 20  30 

(C) 4 V (D) 6 V
10  V2 15 
11. A 6 Ω resistor is connected in the left gap of a metre bridge. In the second gap a 3 Ω resistor and a
6 Ω resistor are connected in parallel. The balancing point of the bridge is at
(A) 25 cm (B) 30 cm (C) 60 cm (D) 75 cm
12. In a metre bridge experiment the null deflection is obtained at a length of 30 cm when a standard
resistance 4.2 Ω is used. The value of the resistance in the left gap is
(A) 1.5 Ω (B) 1.8 Ω (C) 4.2 Ω (D) 9.8 Ω
13. When an unknown resistance and a resistance of 6 Ω are connected in the left and right gaps of a
meter bridge, the balancing point is obtained at 50 cm. If a 3 Ω resistor is connected in parallel to
resistance in the right gap, the balance point
(A) decreases by 25 cm (B) increases by 25 cm (C) decreases by 16.7 cm (D) increases by16.7 cm
14. When two unknown resistances x and y are connected in the left and right gaps of a metre bridge,
the balancing length is 70 cm. When a 5 Ω resistor is connected in parallel to x, the balancing length
becomes 35 cm. The values of x and y are respectively
50 50 50 50
(A) 7 Ω, 3 Ω (B) Ω, Ω (C) Ω, Ω (D) 3 Ω, 7Ω
7 3 3 7
15. When a known resistance 10 Ω and a conductor are connected in the right and left gaps respectively
and the conductor is kept at 0°C, the balancing length is 50 cm. If the temperature of the conductor
in the left gap is increased to 100°C, the balancing length shifts to 60 cm. The temperature
coefficient of resistance of the material of the conductor is
(A) 0.005 /°C (B) 0.0025 /°C (C) 0.05 /°C (D) 0.025 /°C
16. A potentiometer wire of 10 m length and 20-Ω resistance is connected in series with a resistance 80
Ω and a battery of emf 4 V. Potential gradient on the wire will be (in mV/cm)
(A) 0.8 (B) 0.16 (C) 0.2 (D) 0.4
17. Two cells of emf’s E1 and E2 when placed in series produce null deflection at a distance of 204 cm in
a potentiometer. When placed in opposition they produce null deflection at 36 cm. If E1 = 1.4 V, E2
is
(A) 20 V (B) 9.8 V (C) 0.98 V (D) 0.2 V
18. When 6 identical cells of no internal resistance are connected in series in the secondary circuit of a
potentiometer, the balancing length is l. If two of them are wrongly connected, the balancing length
becomes
(A) l /4 (B) l /3 (C) l (D) 2 l /3
19. A potentiometer wire of length 100 cm has a resistance of 10 Ω. It is connected in series with a
resistance and a cell of emf 2 V and of negligible resistance. A source of emf 10 mV is balanced
against a length of 40 cm of the potentiometer wire. What is the value of external resistance?
(A) 790 Ω (B) 800 Ω (C) 780 Ω (D) 810 Ω
E r
20. The potentiometer wire AB is 600 cm long. The distance from A

where the jockey J should touch the wire to get zero deflection in A
R  15r
B
J
the galvanometer is
r
(A) 230 cm (B) 200 cm G
E
(C) 300 cm (D) 320 cm 2
V
21. Two batteries, one of emf 18 V and internal resistance 2 Ω and the 18 V
2
other of emf 12 V and internal resistance 1 Ω are connected as
shown in the figure. The voltmeter V will record a reading of
1
(A) 30 V (B) 18 V
12 V
(C) 15 V (D) 14 V
10 V
2
22. Find the emf and internal resistance of a single battery which
6V
is equivalent to a combination of three batteries as shown in 1
figure.
(A) 20 V, 5 Ω (B) 13 V, 2 Ω 2
4V
(C) 9 V, 2 Ω (D) 2 V, 3 Ω
23. 100 cells each of emf 5 V and internal resistance 1 Ω are to be arranged so as to produce maximum
current in a 25 Ω resistance. Each row is to contain equal number of cells. The number of rows
should be
(A) 2 (B) 4 (C) 5 (D) 10
10 V
1
24. Find the equivalent emf and internal resistance of the arrangement
4V 2
shown in the figure
(A) 20/3 V, 5 Ω (B) 7 V, 0.5 Ω
(C) 7.5 V, 0.5 Ω (D) 10/3 V, 5 Ω 6V
2
25. Two cells A and B of emf 1.3 V and 1.5 V respectively are arranged as E1 r1
shown in the figure. The voltmeter reads 1.45 V. If the voltmeter is A

assumed to be ideal, which cell has the higher internal resistance and how V
many times?
B
(A) r1 = 2r2 (B) r1 = 3r2 (C) 2r1 = r2 (D) 3Sr1 = r2 r2
E2
4. R.C.CIRCUITS
CPP- PH(I)- PHY- 43
1. An uncharged capacitor (C = 5.00 μF) and a resistor (R = 8.00  105 Ω) are connected in series to an
ideal battery (ε = 12.0 V). Find the time constant of the circuit.
(A) 40 s (B) 40 ms (C) 4.0 s (D) 4.0 ms
2. A 20-nF capacitor is connected in series with a 2-MΩ resistor to a battery. If the emf of the battery is
12 V, find the maximum charge on the capacitor.
(A) 240 μC (B) 0.240 μC (C) 24.0  10-9 C (D) 24 nC
3. A 6.0-μF capacitor is charged to 12.0 V and is then connected to a resistor through a switch which is
open at t = 0 s. If the resistance offered by the resistor is 600 kΩ, what is the maximum current in
the circuit?
(A) 200 μA (B) 20 mA (C) 2.0 μA (D) 20 Μa
C R1
4. Two resistors R1 = R2 = 10.0 Ω are connected to a 10-μF
capacitor through a 10.0 V battery and a switch S. The switch R2
is closed at t = 0. Find the steady-state current in the cell.
(A) 1.0 A (B) 2.0 A
(C) 0.5 A (D) zero S
ε
R1 C
Answer the questions 5 to 9 based on the information given in the
figure shown here S
R1 = 2.0 Ω; R2 = 2.0 Ω
ε
C = 10.0 F; ε = 6.0 V R2
5. If initially the switch S is open, the capacitor is uncharged. At t = 0 the switch is closed, determine
the time constant for charging
(A) 40 μs (B) 10 μs (C) 30 μs (D) 20 μs
6. Determine the maximum charge on the capacitor.

(A) 30 μC (B) 40 μC (C) 50 μC (D) 60 μC
7. Find the current in the cell while charging as a function of time.

(A) i t   3e 5.010
4
t

(B) i t   3 1 - e 5.010
4
t
 
(C) i t   3 1  e -5.010
4
t
 (D) i t   3  e 5.010
4
t
8. If after a long time the switch S is opened what would be the time constant for discharging?
(A) 10 μs (B) 20 μs (C) 30 μs (D) 40 μs
9. Determine the potential difference across the capacitor as a function of time while discharging when
the switch is opened.
4 4 4 4
(A) vt   6 V e 2.5 10 t
(B) vt   6 V e 5.0 10 t
(C) vt   3 V e 2.5 10 t
(D) vt   3 V e 5.0 10 t
10 V
10. In the RC-circuit shown in the adjoining figure determine the 2Ω
ratio of the steady-state currents in the 10-V battery and the 8Ω
20-V battery. 3 μf 6 μf
4Ω
(A) 2:1 (B) 1:4
1Ω
(C) 1:2 (D) 4:1
20 V
11. A 60-kΩ resistor is connected in series with a 5-μF capacitor through a battery (ε = 12.0 V) and a
switch which is initially open. If at t = 0 the switch is closed find the ratio of charge on the capacitor to
the current in the battery at t = 300 ms.
(A) 0.3e - 1 (B) 0.3 e (C) 1/e (D) 0.3e  1
12. A capacitor C initially charged to a potential V was allowed to discharge through a resistor R. If the
initial potential of the capacitor is doubled what change (s) should be carried out to maintain the
same q-t graph?
(A) R and C should be halved (B) Only C should be halved
(C) C should be doubled and R halved (D) C should be halved and R doubled
5
13. A capacitor C = 5.0 μF and a resistor, R = 8  10 Ω are connected in series to a battery, ε = 6.0 V
and the capacitor is charged to 6.0 V. What is the work done by the battery?
(A) 90 μJ (B) 45 μJ (C) 30 μJ (D) 180 μJ
PHASE – 5(LEVEL-II(JEEA)
ELECTROSTATICS (ANSWERS)
1. COULOMB’S LAW
1. A 2. C 3. A 4. A
5. C 6. B 7. C 8. A
9. B 10. C
2. ELECTRIC FIELD
1. B 2. D 3. C 4. B
5. B 6. B 7. D 8. C
9. B 10. B 11. A 12. D
13. A 14. D 15. B 16. D
17. A,B,C,D 18. C 19. B 20. D
3. ELECTRIC POTENTIAL ENERGY
1. A 2. D 3. A 4. D
5. C 6. C 7. B 8. B
9. B 10. A 11. A 12. D
13. C 14. B 15. B 16. D
17. D 18. A
4. ELECTRIC POTENTIAL
1. C 2. A 3. D 4. B
5. A 6. C 7. B 8. C
9. C 10. A 11. C 12. B
13. D 14. A 15. D 16. A
17. B 18. C
5. DIPOLE
CPP- PH(I)- PHY- 45
1. B 2. B 3. A 4. B
5. A 6. C 7. C 8. B
9. B 10. A
GAUSS’S LAW
1. D 2. B 3. D 4. D
5. D 6. C,D 7. B 8. C
9. A 10. A 11. B 12. B
13. A,C 14. C 15. B
CAPACITANCE
1. CAPACITANCE & DIFFERENT KINDS OF ARRANGEMNT
1. D 2. D 3. D 4. B
5. B 6. A 7. C 8. A
9. C 10. B
2. COMBINATION OF CAPACITORS
1. B 2. A 3. A 4. A
5. D 6. A 7. B 8. A
9. C 10. C 11. B 12. C
13. C 14. A 15. B 16. D
17. D 18. B 19. B 20. B
21. C 22. A 23. D 24. B
25. B 26. A 27. B 28. C
29. C 30. B
3. COMBINING CAPACITORS AFTER CHARGING
1. C 2. C 3. C 4. A
5. D 6. A 7. B 8. A
9. A 10. A
4. DIELECTRIC FORCE & DIELECTRIC CHARGE
1. A 2. B 3. C 4. D
5. C 6. C 7. D 8. C
9. C 10. A
CURRENT ELECTRICITY
1. OHM’S LAW & DRIFT VELOCITY

1. C 2. C 3. D 4. B 5. D
2. COMBINATION OF RESISTORS
1. A 2. A 3. B 4. B 5. A 6. C 7. A
8. B 9. C 10. D 11. B 12. D 13. B 14. C
15. A 16. D 17. B 18. C 19. C 20. A 21. C
22. B 23. B 24. D 25. A 26. D 27. C 28. A
29. C 30. D
3. CIRCUITS
1. B 2. D 3. A 4. C 5. A 6. B 7. B
8. C 9. B 10. A 11. D 12. B 13. B 14. C
15. A 16. A 17. C 18. B 19. A 20. D 21. D
22. B 23. A 24. C 25. B
4. R.C.CIRCUITS
1. C 2. B 3. D 4. A 5. D 6. D 7. C
8. D 9. A 10. B 11. A 12. D 13. D
CPP- PH(I)- PHY- 47
LEVEL-III (JEEA)
COULOMB’S LAW
Single Correct
1. A cube shaped Gaussian surface has one corner at the origin of coordinates and the diagonally
opposite corner at (d, d, d) such that the edges of the cube are aligned with the coordinate axis.
 d d d
Charged particles and their locations (x, y, z) are q1 = 33 nC at (d/2, 0, 2d), q2 = –5 nC at  , , 
3 4 3
 d d d
and q3 = –19 nC at  , ,  . What is the flux for the Gaussian surface?
 4 2 3
2
(A) –2900 N.m /C (B) 2900 N.m2/C (C) 1900 N.m2/C (D) –1900 N.m2/C
2. Two infinite and parallel sheets of charge have the same charge density  C/m2. What is the field (a)
in the region between the sheets, and (b) in the region not between the sheets
 
(A) zero, respectively (B) , zero respectively
0 0
2  2
(C) , zero respectively (D) , respectively
0 0 0

3. The potential field of an electric field E = (y î + x ˆj ) is:
(A) V = – xy + constant (B) V= – (x + y)+ constant
(C) V = – (x2 + y2) + constant (D) V = constant
Multi Correct
  
4. A point charge q is placed at origin. Let E A , E B and EC be the electric field at three points
A (1, 2, 3), B (1, 1, — 1) and C (2, 2, 2) due to charge q. Then:
       
(A) E A  E B (B) E A || EC (C) | E B | 4| EC | (D) | E B | 8| EC |
5. A particle of charge q and mass in moves rectilinearly under the action of an electric field E =  - x.
Here,  and  are positive constants and x is the distance from the point where the particle was
initially at rest. Then:
(A) the motion of the particle is oscillatory

(B) the amplitude of the particle is


(C) the mean position of the particle is at x =

q
(D) the maximum acceleration of the particle is
m
Comprehension
A conducting spherical shell having an inner radius a and outer radius b carries a net charge Q. If a
point charge q is placed at the centre of this shell
6. Determine the surface density on the inner surface
q q q q
(A) 2
(B) 2
(C) 2
(D)
4a 4a 2a 2a2
7. Determine the surface density on the outer surface

 (Q  q)   (Q  q)   (Q  q)   (Q  q) 
(A)  2 
(B)  2 
(C)   (D)  
 4b   4 a   4 b 2   4a2 
Integer Type
8. Two identical particles of charge q each are connected by a massless spring of force constant k.
They are placed over a smooth horizontal surface. They are released when the separation between
them is r and spring is unstretched. If maximum extension of the spring is r, the value of k is
q 1
, where x is: (neglect gravitational effect)
xr  0 r
9. A solid conducting sphere of radius 10 cm is enclosed by a thin metallic shell of radius 20 cm. A
charge q = 20C is given to the inner sphere. Find the heat generated in the process, the inner
sphere is connected to the shell by a conducting wireT
Matrix Match
10. Match the following Column–I with Column–II.
Column – I Column – I
(A) Charged conducting shell (p) 
E=
2 0
(B) Charged conducting sphere (q) at infinity; E = 0, V = 0
(C) Uniformly charged non–conducting (r) kq
at center; E=0, V =
sphere R
(D) Infinite sheet of charge (s) 3kq
at center; E = 0, V =
2R
GAUSS LAW
Single Correct
1. Mark the correct options
(A) Gauss’s law is valid only for symmetrical charge distribution
(B) Gauss’s law is valid only for charges placed is vacuum
(C) the electric field calculated by gauss’s law is the field due to the charges inside the Gaussian
surface
(D) the flux of the electric field through a closed surface due to all the charges is equal to the flux
due to the charges enclosed by the surface.
2. Electric charges are distributed in a small volume. The flux of the electric field through a spherical
surface of radius 10 cm surrounding the total charge is 25 V–m. The flux over concentric sphere of
radius 20 cm will be
(A) 25 Vm (B) 50 Vm (C) 100 Vm (D) 200 Vm
CPP- PH(I)- PHY- 49
3. A metallic plate having no net charge is placed near a finite metal plate carrying a positive charge.
The electric force on the plate will be
(A) towards the plate (B) away from the plate (C) parallel to the plate (D) zero
Multi Correct
4. If the flux of the electric field through a closed surface is zero.

(A) the electric field must be zero everywhere on the surface
(B) the electric field may be zero everywhere on the surface
(C) the charge inside the surface must be zero
(D) the charge in the vicinity of the surface must be zero
5. A large nonconducting sheet M is given a uniform charge M

density. Two uncharged small metal rods A and B are placed
near the sheet as shown in figure. A B
(A) M attracts A (B) M attracts B
(C) A attracts B (D) B attracts A
Comprehension
A long coaxial cable consists of an inner cylindrical conductor with radius a and outer coaxial cylinder with
radius b and outer radius c. The outer cylinder is mounted on insulting supports and has no net charge. The
inner cylinder has a uniform positive charge per unit length .
6. The electric field at any point between inner and outer cylinders is
 
(A) radially outward (B) radially inward
20r 20r

(C) co–axially (D) none of these
20r
7. The electric field at any point P(x > c) outside the outer cylinder is
 
(A) radially inward (B) radially outward
20r 20r

(C) co–axially (D) none of these
20r
8. Find the charge per unit length of inner surface and outer surface of the outer cylinder
(A) – on inner, + on outer surface (B) – on outer, + on inner surface
 
(C) on both inner and outer surfaces (D) on both inner and outer surfaces
2 2
Integer
9. The electric field in a region is radially outwards and has a magnitude E = Kr. The charge contained
in a sphere of radius a is K40an . Find n.
–6
10. A charged particle having a charge –2 x 10 C is placed close to the non–conducting plate having a
surface charge density 4 x 10–6 Cm–2. The force of attraction between the particle and the plate is
nearly 0.15X N. where X is
Matrix Match
11. A thin conducting shell of radius R is given a charge Q as shown in
figure. A
r
B
R Q
Column – I Column – II
(A) Magnitude of electric field at A (p) Q
40 r
(B) Magnitude of electric field at B (q) Q
40R
(C) Electric potential at A (r) Q
40 r 2
(D) Electric potential at B (s) zero
CAPACITORS
Single Correct
1. The distance between the plates of a parallel plate air condenser is d. If a copper plate of same area
but thickness d/2 is placed between the plates then the new capacitance will become
(A) doubled (B) half (C) one fourth (D) remain unchanged
2. The energy stored in a condenser is in the from of

(A) potential energy (B) magnetic energy (C) elastic energy (D) kinetic energy
3. A condenser of capacity 500 F is charged at the rate of 50 C/s. The time taken for charging the
condenser 10 V will be
(A) 10 s (B) 25 s (C) 50 s (D) 100 s
Multi Correct
4. X and Y are large, parallel conducting plates close to each X Y
other. Each face has an area A, X is given a charge Q, Y is
without any charge. Points A, B and C are as shown in the
figure. A B C
Q
(A) the field at B is
20 A
Q
(B) the field at B is
0 A
(C) the fields at A, B and C are of the same magnitude
(D) the fields at A and C are of the same magnitude, but in opposite directions
5. Three identical, parallel conducting plates A, B and C are placed as shown. Switches S1 and S2 are
open, and can connect A and C to earth when closed. +Q charge is given to B.
(A) if S1 is closed with S2 open, a charge of amount Q will pass A B C
through S1
(B) if S2 is closed with S1 open, a charge of amount Q will pass d
through S2
Q 2d
(C) if S1 and S2 are closed together, a charge of amount will C
3 +Q
2Q
pass through S1, and a charge of amount will pass
3
S1 S2
through S2
(D) all the above statements are incorrect
Comprehension
CPP- PH(I)- PHY- 51
On your first day as an electrical technician you are asked to determine the leakage current in a capacitor.
The capacitor consists of two parallel–plates. The plates have equal and opposite charge Q. The dielectric
has dielectric constant K and a resistivity . The plates have area A and separation between the two plates is
d.
6. The leakage resistances is

A d d  d2
(A) R  (B) R  (C) R  (D) R  K
d A KA A
7. The leakage current is

Q QK Q Q0
(A) (B) (C) (D)
K 0 0 0 K
Integer
8. A parallel plate condenser is connected to a battery of emf 4 volt. If a plate of dielectric constant 8 is
inserted into it, then the potential difference on the condenser will be
9. The minimum number of condensers each of capacitance of 2 F, in order to obtain resultant
capacitance of 5 F will be
Matrix Match
0 A
10. In a parallel plate capacitor C = , where all the terms have their usual meanings.
d
Column – I Column – II
(A) Disconnected from battery and increase in d of a (p) Capacitance increases and
charged capacitor potential energy decreases
(B) Disconnected from battery and increase in A of a (q) Capacitance increases and
charged capacitor potential energy increases
(C) Disconnected from battery and insert a dielectric (r) Capacitance decreases and
slab in a charged capacitor potential energy increases
(D) Insert a dielectric slab in a charged capacitor (s) Charge remain constant
without disconnecting from the battery
CURRENT ELECTRICITY
Single Correct
1. In the following circuit diagram(shown in figure) if E1 R1
the ammeter reading is zero, then the voltmeter
reading will be
(A) zero (B) E1 + E2 4
(C) E1 (D) E2
R2
E2
2. Which physical quantity cannot be determined with the help of potentiometer?

(A) I (B) V (C) L (D) R
3. If I current is flowing in a potentiometer wire of length L and resistance R, then potential gradient will
be
IR RL IL
(A) (B) I R L (C) (D)
L I R
Multi Correct
4. When some potential difference is maintained 20 C 5

between A and B, current I enters the network at A
and leaves at B.
A B
(A) the equivalent resistance between A and B is 8
(B) C and D are at the same potential
(C) no current flows between C and D
31 D
(D) current flows from D to C 5 20
5
5. In the circuit shown the cell has emf = 10 V and 3 2 2

internal resistance = 1 .
(A) the current through the 3– resistor is 1 A  =10V
(B) the current through the 3– resistor is 0.5 A 8 8 4
r =1 
(C) the current through the 4– resistor is 0.5 A
(D) the current through the 4– resistor is 0.25
A 2 2 2
Comprehension
The average bulk resistivity of the human body (apart from the surface resistance of the skin) is about 5–m.
The conducting path between the hands can be represented approximately as a cylinder 1.6m long and
0.1m diameter. The skin resistance may be made negligible by soaking the hands in salt water. A lethal
shock current needed is 100 mA. Note that a small amount of potential difference could be fatal if the skin is
damp.
6. What is the order of resistance between the hands

(A) 102  (B) 103  (C) 104  (D) none of these
7. What potential difference is needed between the hands for a lethal shock current ?
(A) 100 V (B) 10 V (C) 120 V (D) 150 V
8. The power dissipated in the body is

(A) 1 W (B) 0.1 W (C) 100 W (D) 10 W
Integer
7 7 A
A B
9. In the adjoining figure the potential difference
2
between the points A and B will be (3  )V . 7 5V 7
y
Find y D 7 7 C
S= 40
+ –
10. In the following circuit if key K is pressed then
the galvanometer reading becomes half. The
resistance of galvanometer is 10Z. where z is
R G
K
S= 40
CPP- PH(I)- PHY- 53
Matrix Match
i4
R1 R2
11. Match the following Column–I with Column–II.
i1
A R5 i B
i2 i5
R3 i3 R4
Column – I Column – I
(A) R1 R 3 (p) i1  i 2  i 4  i5

R 2 R4
(B) R1 = R2 = R3 = R4 = R5 (q) i3  0
(C) R1 = R4, R3 = R2 (r) i3  0
(D) R5 = 0 (s) i1R1  i 2 R 3 , i 4 R 2  i5 R 4
(t) R1R 3 R 2R 4
R AB  
R1  R 3 R 2  R 4
LEVEL-III (JEEA)
ANSWERS
COULOMB’S LAW
1. A 2. A 3. A 4. A,C
5. A,B,C,D 6. B 7. C 8. 2
9. 9 10. A–q,r; B–q,r; C–q,s; D–p
GAUSS LAW
1. D 2. A 3. A 4. B,C
5. A,B,C,D 6. A 7. B 8. A
10. 6 11. A – s, B – r, C – q, D – p
CAPACITORS
1. A 2. A 3. D 4. A,C,D
5. A,B,C 6. B 7. A 8. 4V
9. 4 10. A – r,s, B – p, s, C – p, s, D – q
CURRENT ELECTRICITY
1. D 2. C 3. A 4. A,B,D
5. A,D 6. B 7. A 8. D
9. 6 10. 4 11. A–p,q,s,t; B– p,q,s,t; C–p,t; D–r
* * *

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FIITJEE PHASE–V (PHYSICS) CPP

LEVEL-0 (INTERMEDIATE QUESTIONS)

Name: …………………………………… Batch:…………………Date of submission:……………….

ELECTRIC CHARGE & FIELDS

VERY SHORT ANSWER QUESTIONS

1. What is meant by the statement ‘charge is quantized’?

SHORT ANSWER QUESTIONS

VERY SHORT ANSWER QUESTIONS

SHORT ANSWER QUESTIONS

relation with electric potential of a charge.

dielectrics in an external field.

VERY SHORT ANSWER QUESTIONS

1. Define mean free path of electron in a conductor.

2. State Ohm’s law and write its mathematical form.

3. Define resistivity or specific resistivity.

4. Define temperature coefficient of resistance.

7. Why is manganin used for making standard resistors?

resistance and tolerance?

9. Write the color code of a carbon resistor of resistance 23 kilo ohms.

12. Why are household appliances connected in parallel?

LONG ANSWER QUESTIONS

1. The dielectric constant K of an insulator can be

3. With a rise in temperature, the dielectric constant K of a liquid

10. Which of the following is a sure test of electrification ?

11. A positive point charge Q is brought near an isolated metal cube

ELECTRIC FIELD & POTENTIAL

4. An electric dipole placed in a non–uniform electric field will experience

13. A spherical equipotential surface is not possible

8. A charge q is distributed uniformly on a ring of radius r. A A

(From Q.9 – 12)

9. Which of the surfaces have zero flux?

10. The flux passing through the surface S5 will be

11. Total flux passing through the cube

12. The total electric charge inside the cube

13. Total flux passing through the cube

17. The charge within the cube

18. Match the table

19. What is the field at a distance r outside the conductor ?

9. To obtain 3 F capacity from three capacitors of 2 F each, they will be arranged

11. A dielectric material of dielectric constant K introduces half the

17. In the connections shown in the figure, the equivalent capacity

1. V–I graphs for parallel and series combination of two metallic v B

2. The current in the arm CD of the network in the B

4. What is the ammeter reading in the circuit of the 10V

5. Five resistances are connected as shown in the 2.5 

6. The figure, represents a part of closed circuit.

7. A uniform wire of resistance 20  having resistance 1 /m resistance

9. Two resistors of resistance 200 k and 1 M 200k  x 1M

11. The value of current I in the circuit shown in the 60 

14. Five resistances are connected as shown in the

15. The equivalent resistance between points A and B in the

16. A cell of negligible emf of 2 V is connected to a series combination of 2 , 3  and 5 . The

19. The equivalent resistance between A and B in the network in 3

20. In the circuit shown here, E1 = E2 = E3 = 2 V and R1 = R2 = 4 . E1 R1

5. The vector form of coulomb’s law is

4. A point charge q  1C and mass 1 kg is projected with a speed

3. ELECTRIC POTENTIAL ENERGY

shown in figure. A third particle of mass 1g and charge q 3  4C is q3 y = 4m