SAMPLE PAPER- (2023-24)

Subject: Physics Max. Marks:70

Grade:12 Time: 3hours
Section – A
1. A proton and an alpha particle having the same initial speed enter a region of uniform 1
magnetic field and describe circular paths. If the radii of the circles are R 1 and R2 respectiely,
the ratio R1 :R2 is
a) 1:1
b) 1:2
c)1:4
d)2:1
2. 1
A shunt resistance required to allow 4% of the main current through the galvanometer of

resistance 48Ω is

a)1 Ω

b)2 Ω

c)3 Ω
d)4 Ω
3. 1
A proton, a deuteron and an α−particle with the same kinetic energy enter a region of uniform
magnetic field moving at right angles to B. What is the ratio of the radii of their circular paths?

a)1: √2: 1
b)1: 1: 1
c)2: 1: 1
d)√2: √2: 1

4. Biot _Savart law can be expressed alternatively as: 1

a) Coulomb’s law
b) Ampere’s circuital law
c)Ohm’s law
d)Gauss’ law

Page 1 of 10
5. If the number of turns in a moving coil galvanometer of current sensitivity C and voltage 1
sensitivity V is doubled, then
a) C remains unchanged, but V is doubled
b) Both C and V are halved
c)Both C and V are doubled
d)C is doubled and V remains unchanged
6 Biot -savart law indicates that the moving electrons (velocity v) produce a magnetic 1
field B such that
a) it obeys inverse cube law
b) it is along the line joining the electron and point of observation

c)
d)
7 A galvanometer of resistance G is converted into an ammeter using a Shunt of resistance R. 1
If the ratio of the heat dissipated through the galvanometer and shunt is 3:4, then R equals:
a)4/3G
b)3/4G
c)16/9G
d)9/16 G
8 To protect galvanometer from possible damages due to large current, which of the following 1
is connected to its coil:
a) low resistance wire in series
b) low resistance wire in parallel
c)high resistance wire is series
d)high resistance wire in parallel
9 The suspension wire in a moving coli galvanometer has ……. torsional constant 1
a)low
b)high
c)medium
d)zero
10. Ampere’s law is applicable for …………. current distribution whereas the Biot Savart’s law 1
is applicable for ………. current distribution

a) symmetrical ; asymmetrical.
b) asymmetrical ; symmetrical.
c) Both symmetrical
d) Both asymmetrical.

11 A rectangular loop of sides 10 cm and 5 cm carrying a current I of 12 A is placed in different 1

orientations as shown in the figures below :

Page 2 of 10
 Ans:B) and (D), respectively

12 An electron is projected with uniform velocity along the axis of a current carrying long 1
solenoid. Which of the following is true?
a) The electron will be accelerated along the axis.
b) The electron will be accelerated along the axis.
c) The electron will experience a force at 45° to the axis and hence execute a helical
path.
d) The electron will continue to move with uniform velocity along the axis of the
solenoid.
13 The maximum current that can be measured by a galvanometer of resistance 40 Ω is 10 mA. 1
It is converted into voltmeter that can read up to 50 V. The resistance to be connected in the
series with the galvanometer is:
a) 2010 Ω
b)5040 Ω
c) 4960 Ω
d) 4050 Ω
14 1
A circular coil of radius R carries a current I. The magnetic field at its centre is B. The distance from the centre on the
of the coil where the magnetic field will be B/8 is

a)3R
b)2R
c) R√2
d) R√3
15 A voltmeter essentially consists of 1
a) a high resistance, in series with a galvanometer
b) a high resistance, in parallel with a galvanometer
c)a low resistance, in series with a galvanometer
d) a low resistance, in parallel with a galvanometer

SECTION B

Page 3 of 10
 Two statements are given-one labelled Assertion (A) and the other labelled Reason (R). Select
the correct answer to these questions from the codes (a), (b), (c) and (d) as given below.
a) Both A and R are true, and R is the correct explanation for A.
b) Both A and R are true, and R is NOT the correct explanation for A.
c) A is true but R is false.
d) A is false and R is also false
16 Assertion: Free electrons always keep on moving in a conductor even then no magnetic 1
force act on them in magnetic field unless a current is passed through it.
Reason: The average velocity of free electron is zero.
17. Assertion: A proton and an alpha particle having the same kinetic energy are moving in 1
circular paths in a uniform magnetic field. The radii of their circular paths will be equal.
Reason: Any two charged particles having equal kinetic energies and entering a region of
uniform magnetic field B in a direction perpendicular to B, will describe circular trajectories
of equal radii
18 Assertion: A charge, whether stationary or in motion produces a magnetic field around it. 1
Reason : Moving charges produce only electric field in the surrounding space.
SECTION C

19 2
Two wires of equal lengths are bent in the form of two loops. One of the loop is square
shaped whereas the other loop is circular .These are suspended in a uniform magnetic field
and the same current is passed through them. Which loop will experience greater torque?
.

20 A charged particle, having a charge q, is moving with a speed v along the x-axis. It enters a 2
region of space where an electric field E(= Ej) and a magnetic field B are both present. The
particle, on emerging from this region, is observed to be moving along the x-axis only.
Obtain an expression for the magnitude of B in terms of v and E. Give the direction of B.

21 An electron and a proton, moving parallel to each other in the same direction with equal 2
momenta, enter into a uniform magnetic field which is at right angles to their velocities. Trace
their trajectories in the magnetic field.

22 In the figure, the straight wire AB is fixed while the loop is free to move under the influence
of the electric currents flowing in them. In which direction does the loop begin to move?
Give reason for your answer.

Page 4 of 10
23 A neutron, an electron and an alpha particle moving with equal velocities enter a uniform 2
magnetic field directed into the plane of the paper as shown. Trace their paths in the field
and justify your answer

OR
Two identical circular coils, p and q each of radius r, carrying current 1 a and √3 a
respectively, are placed concentrically and perpendicular to each other lying in the xy and yz
planes. find the magnitude and direction of the net magnetic field at the centre of the coils

24 2
A coil of 200 turns has a cross sectional area 900mm2 . It carries a current of 2 ampere. The
plane of the coil is perpendicular to a uniform magnetic field 0.5 T. Calculate (i) the
magnetic moment of the coil and (ii) the torque acting on the coil.

25 2
A rectangular loop of sides 25 cm and 10 cm carrying current of 15A is placed with its
longer side parallel to a long straight conductor 2.0 cm apart carrying a current of 25A. What
is the torque acting on the loop and the new force on the loop?

SECTION D
26 3
Find the magnitude and direction of the net magnetic field at the common centre of the two
coils.

Page 5 of 10
27 . The figure shows three infinitely long straight parallel current carrying conductors. Find the 3
(i) magnitude and direction of the net magnetic field at point A lying on conductor 1,
(ii) magnetic force on conductor 2

28
Two very small identical circular loops, (1) and (2), carrying equal currents I are placed
vertically (with respect to the plane of the paper) with their geometrical axes perpendicular
to each other as shown in the figure. Find the magnitude and direction of the net magnetic
3
field produced at the point O.

29. Derive the expression for the force acting on a current carrying conductor of length L in a 3
uniform magnetic field ‘B’.
OR
A square loop of side 20 cm carrying current of 1A is kept near an infinite long straight wire
carrying a current of 2A in the same plane as shown in the figure. Calculate the magnitude
and direction of the net force exerted on the loop due to the current carrying conductor

Page 6 of 10
30 A long straight wire AB carries a current of 4A. A proton A travels at 4x106 m/s parallel to 3
the wire,0.2 m from it and in a direction opposite to the current as shown in the figure
.Calculate the force which the magnetic field of current exerts on the proton also specify the

direction of the force

SECTION E
31 a) Derive the expression for the torque acting on a rectangular current carrying coil placed in 5
uniform magnetic field
b) An -particle is accelerated through a potential difference of 10 kV and moves along x-
axis. It enters in a region of uniform magnetic field B = 2  10–3 T acting along y-axis.
Find the radius of its path. (Take mass of -particle = 6·4  10–27 kg )
OR
a) A straight thick long wire of uniform cross section of radius ‘a’ is carrying a steady
current I. Use Ampere’s circuital to obtain a relation showing the variation of the
magnetic field inside and outside the wire with distance r, (r<a) and (r>a) of the field
point from the centre of its cross section.
b) A current carrying conductor PQ of length 1m,mass 4.4 x 10−3 kg and resistance 50 mili-
ohm is kept in a uniform magnetic field of 1.8mT as shown. Calculate the potential V
that must be applied to the conductor PQ so that it remains in equilibrium in the
magnetic field.

32 (a)State Biot-savart law. Give its vector form 5

(b)Two parallel coaxial circular coils of equal coils of equal radius R and equal number of
turns N carry equal currents I in the same direction and are separated by a distance 2R.Find
the magnitude and direction of the net magnetic field produced at the mid -point of the line
joining their centers.

OR
a)With the help of a neat labeled diagram, state the principle of moving coil galvanometer?
Show that the current in the coil is directly proportional to the deflection of the coil?
A galvanometer with a coil of resistance 120 ohms shows a full scale deflection for a current
of 2.5mA. How will you convert the galvanometer int an ammeter of range 0 to 7.5A? [s=
0.004 Ω connected in parallel to the galvanometer]
Page 7 of 10
 Ans:a) Diagram ,working(3marks)

33. (a) Write the expression for the equivalent magnetic moment of a planer current loop of area 5
A, having N turns and carrying a current i. Use the expression to find the magnetic dipole
moment of a revolving electron.
A galvanometer of resistance ‘G’ can be converted into a voltmeter of range
b) A galvanometer of resistance G is converted into a voltmeter to measure upto V volts by
connecting a resistance R1. In series with the coil. If a resistance R2 is connected in series with it,
then it can measure upto V/2 volts. Find the resistance, in terms of R1 and R2, required to be
connected to convert it into a voltmeter that can read upto 2 V. Also find the resistance G of the
galvanometer in terms of R1 and R2.

OR

a)State the Lorenz’s force and express it in vector form. Which pair of vectors are always

perpendicular to each other? Derive the expression for the force acting on a current carrying

conductor of length L in a uniform magnetic field ‘B’.

b)A rectangular loop of wire of size 2.5 cm × 4 cm carries a steady current of 1 A. A straight
wire Carrying 2 A current is kept near the loop as shown. If the loop and the wire are
coplanar, evaluate the magnitude and direction of the force on the loop due to the current
carrying wire.

CASE STUDY 1
34 A galvanometer can be converted into voltmeter of given range by connecting a suitable 4
resistance Rs in series with the galvanometer, whose value is given by
Rs=v/ig-Gwhere V is the voltage to be measured, I g is the current for full scale deflection of
galvanometer and G is the resistance of galvanometer

Series resistort (R s ) increases range of voltmeter and the effective resistance of

Page 8 of 10
 galvanometer. It also protects the galvanometer from damage due to large current.
Voltmeter is a high resistance instrument and it is always connected in parallel with the
circuit element across which potential difference is to be measured. An ideal voltmeter has
infinite resistance
a) How we can convert a moving coil galvanometer (MCG) into a voltmeter ?
b) The resistance of an ideal voltmeter is

c)10 mA current can pass through a galvanometer of resistance 25Ω .What resistance in
series should be connected through it, so that it is converted into a voltmeter of 100 V?
OR

A milliammeter of range 0 to 25 mA and resistance of 110Ω is to be converted into a

voltmeter with a range of 0 to 25 V. The resistance that should be connected in series will be

35 4
CASE STUDY 2

An electron with speed V o << c moves in a circle ofradius ro in a uniform magnetic field. This
electron is able to traverse a circular path as magnetic field is perpendicular to the velocity of
the electron. A force acts on the particle perpendicular to both v⃗ 0 and B⃗. This force
continuously deflects the particle sideways without changing its speed and the particle will
move along a circle perpendicular to the field. The time required for one revolution of the
electron is To .

a) If the given electron has a velocity not perpendicular to B, then what is the trajectory
of the electron?
b) If this electron of charge (e) is moving parallel to uniform magnetic field with
constant velocity v, the force acting on the electron is?
c) If the speed of the electron is now doubled to 2v o .The radius of the circle will change
to ?
OR

Page 9 of 10
………………………………………………………………………

***

Page 10 of 10