Download Page # 1 SECTION – A (Total Marks : 21)

PAPER-I
SECTION – A (Total Marks : 21)
(Single Correct Answer Type)
This section contains 7 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY
ONE is correct.
1.
Consider the situation shown in figure. Wire PO has mass m, resistance R and slide on smooth, horizontal
conducting parallel rails separated by a distance . Rails are connected with a conducting strip at the left end
a uniform magnetic field B directed vertically downward. A light string, carrying a mass 2m at its one end, is
tied to the wire through a pulley. At t = 0, the set up is released from rest. Find the tension in the string at
9mR
t 2 2
Bl
A)
2.
B)
C)
D) none of these
A conducting disc of radius R is placed in a uniform and constant magnetic field B parallel to the axis of the
disc. With what angular speed should the disc be rotated about its axis such that no electric field develops in
the disc. (the electronic charge and mass are e and m)
B

 R
A)
Sol.
eB
2m
B)
eB
m
C)
2m
eB
D)
m
eB
(b)
Consider a free electron in the disc at point P distant x from centre of disc.
The magnetic force on free electron is
(towards left)
Centrifugal force
(towards right)
For net force on the electron at P to be zero
i.e., ex B  m2 x
eB
. There shall be no flow of free electrons radially outwards and hence no electric field shall develop
m
within the disc
or  
Page # 1
3.
Loop A of radius  r  R  moves towards loop B with a constant velocity V in such a way that their planes
are always parallel. What is the distance between the two loops (x) when the induced emf in loop A is
maximum
B
r
R
V
A
(a) R
Sol.
X
R
2
(b)

R
2
(c)
(d) R 1 

1 

2
(c)
is maximum when
4.
There exists a uniform magnetic and electric field of magnitude 1 T and 1 V/m respectively along positive Yaxis. A charged particle of mass 1 kg and of charge 1 C is having velocity 1 m/sec along X-axis and is at
origin at t  0 . Then the co-ordinates of particle at time  seconds will be:
(a)  0, 1, 2
Sol.

(b) 0,  2 / 2,  2


(c) 2, 2 / 2, 2


(d) 0, 2 / 2, 2

(d)
The particle will move in a non uniform helical path with increasing pitch
Its time period will be :
Changing the view, the particle is seemed to move in a circular path in
seconds the particle will be at point P, hence x coordinate will be 0
For linear motion along y-direction.
plane as below After
and OP = 2 Hence the coordinate
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5.
A resistor and an inductor in series are connected to a battery through a switch. After the switch has been
closed, what is the magnitude of current flowing when the rate of the increase of magnetic energy stored in
the coil is at a maximum?
A)
Sol.
V
4R
B)
V
3R
C)
V
2R
D)
V
R
(c)

LI 2 
The rate of increase of magnetic energy  E 
 is the difference between the power output of the battery
2 

and the power dissipated in the resistor.
6.
Sol.
The current through an inductor of 1H is given by i = 3t sin t. The voltage across the inductor of 1H is
(A) 3 sin t + 3 cos t
(B) 3 cos t + t sin t
(C) 3 sin t + 3t cos t
(D) 3t cos t + sin t.
(c)
| VL | L

7.
di
dt
d
(3t sin t) = 3 SIN T + 3T COS T.
dt
A V shaped rod kept inside a magnetic field of strength B0 is carrying A current i0. If AB = BC = L, then the net
magnetic force on the rod is
B

 B
  60º   
  
  i 
  
0
0
A
Sol.
(A) B0i0 2L
(b)
(B) B0i0L
C
(C) zero
(D) B0i0 L 3
SECTION – B (Total Marks : 16)
(Multiple Correct Answers Type)
This section contains 4 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE OR
MORE may be correct.
1.
Uniform magnetic field
is acting in a region of length
enters in it at t = 0 with constant acceleration
. At,
as shown. A square loop of side
. Resistance per unit length of the square frame is
s:
Page # 3
(a) Induced current in the square frame is clockwise
(b) Induced current in the frame is 2.5 A
(c) Magnetic force on the frame is 25 N
(d) Magnetic torque on the frame is zero
Sol.
B,C
After 1 second,
Distance moved by the wire frame is
Speed,
2.
A proton is fired from origin with velocity
in a uniform magnetic field
. In the
subsequent motion of the proton :
(a) Its z co-ordinate can never be negative
(b) Its x co-ordinate can never be positive
(c) Its x and z co-ordinates cannot be zero at the same time
(d) Its y co-ordinate will be proportional to its time of flight
Sol.
B,D
Velocity of proton makes an angle of
with the direction of magnetic field.Therefore, path of the proton is
a helix. The plane of the circle of this helix is the plane formed by negative x and positive z-axis. Therefore,
x-coordinate can never be positive. Further, x and z co-ordinates will become zero simultaneously after every
pitch and y-coordinate of proton at any time t is
3.
In magnetic field
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(a) Acceleration of charge particle may be zero.
(b) Velocity of charge particle may be constant.
(c) Speed of charge particle is constant.
(d) Kinetic energy of charge particle is constant.
Sol.
A,B,C,D
In magnetic field speed remains constant
4.
A particle of mass m and charge q enters a magnetic field B with a velocity  at an angle  with the
direction of B
(a) The kinetic energy of the particle will remain constant for any value of 
m
2qB
m
(c) If   90 , the trajectory of the particle is a circle of radius r =
qB
(d) If   90 , the frequency of revolution of the particle is independent of the speed and the radius of the
(b) If   30 , the trajectory of the particle is a helix of radius r =
Sol.
circular path.
A,B,C,D
The force experienced by the particle is
Since F is perpendicular to , no work is done on the particle. Hence its speed (and therefore K.E.) will not
change. If  lies between 0o and 90o, the trajectory of the particle is a helix.
The x and y components of the velocity are
As x is parallel to B, the magnetic force due to x is zero. Thus the motion alon x-axis is at a uniform speed
x . As  y is perpendicular to B, the path of the particle is along a circle. The linear and circular motions
together give rise to a helical trajectory as shown in the figure. The radius of helix is given by
Page # 5
For   90o , the trajectory of the particle is a circle
Of radius =
and the frequency of revolution is
Given by
Thus, all the four choices are correct.
SECTION-C (Total Marls : 15)
(Paragraph Type)
This section contains 2 paragraphs. Based upon one of paragraphs 2 multiple choice questions and based on the other
paragraph 3 multiple choice questions have to be answered. Each of these questions has four choices (A), (B), (C) and (D) out of
which ONLY ONE is correct.
Paragraph for Questions 1 and 2
The circuit shown in the adjacent figure is set up and the switch S is, initially, kept closed for a long time.
1.
The switch S is now opened. The value of the current, when it attains the same value in both the inductors for
the first time, is
(A)
0.8A
(B) 0.4A
(a)
When the switch is opened, the total flux remains conserved :
L1 ii = (L1 + L2) If.
2.
The current in the circuit, after a very long time, is (with the switch open)
(A)
0.8A
(B) 0.4A
Sol.
(c)
(C) 1.5A
(D)
9
A.
7
(C) 1A
(D)
1.25A.
Sol.
Paragraph for Questions 3 and 5
3.
Sol.
4.
Sol.
5.
A coil having a resistance of 50.0 and an inductance of 0.5 H is connected to an AC source of 110 V, 50 Hz.
The impedance of the coil is (approximately)
(A)
165
(B) 55
(C) 330 (D)
none
of
these
(a)
The rms current in the circuit is
(A)
1.5 A
(B) 0.67 A
(C) 1 A
(D)
3A
(b)
If the frequency of the AC is decreased by a factor of 2, then the rms current
(A)
increases
(B)
decreases
(C)
remains uncharged
(D)
may increase or decrease depending on the actual phase of the applied voltage
Page # 6
Sol.
(a) The impedance is
Z  R 2  2 L2 and the rms
V
current is i rms  rms .
Z
SECTION-E (Total Marks : 28)
(Integer Answer Type)
This section contains 7 questions. The answer to each of the questions is a single digit integer, ranging from 0 to 9. The bubble
corresponding to the correct is to be darkened in the ORS.
1.
The figure shows part of a bigger circuit. At the moment, the capacity of the capacitor is 6 F and
decreasing at the constant rate 0.5 Fs 1 . The potential difference across the capacitor at this moment is
2
dV
1
1 d V
changing as under
 2Vs , 2  Vs  2 .
dt
2
dt
The current in the 4  resistor is decreasing at the rate of 1  As 1 .
Sol.
What is the potential difference (in micro volts) across the inductor at this moment ?
(4)
= 4 volts
2.
Sol.
3.
An LCR series circuit with 100 resistance is connected to an ac source of 200V and angular frequency
300rad/sec. When only the capacitance is removed, the current lags behind the voltage by 60 , when only the
inductance is removed the current leads the voltage by 60 . Calculate the current in LCR circuit in ampere.
(2)
LCR circuit is in resonance
An inductor of inductance 2.0 mH is connected across a charged capacitor of Capacitance 5.0 F and the
resulting LC circuit is set oscillating at its natural frequency. Let Q denote the instantaneous charge on the
capacitor and I the current in the circuit. It is found that the maximum value of charge Q is 200 C . When
Q  100 C the value of
Sol.
dI
is 10n As 1 find the value of n.
dt
(4)
Figure shows the LC circuit. The charge Q on the capacitor plates (and hence the current I in the circuit)
Page # 7
Since at t = 0, Q = Q0, the maximum charge,
we have Q = Q0 cos t (i)
Current
(ii)
(iii)
Given Q0
or
or
from (iii) we have
This result can also be obtained by applying Kirchhoff's loop rule to the LC circuit shown in figure.
or
6
4.
C. we have
A long solenoid of radius 2 cm is surrounded by a 100–turn coil of radius 4 cm having a total resistance 20,
connected to a galvanometer. It is observed that a charge of 800 C flows through the galvanometer when the
5A current through the solenoid is reversed. If the mutual inductance between the two is
5A
n
millihenry find n.
5
Solenoid
G
Sol.
(8)
 d 
 di  dq 1  d  M di
  
   M  ;
 dt 
 dt  dt R  dt  R dt
Page # 8
q 
5.
Sol.
M
i
R
An inductor coil joined to a 6V battery draws a steady current of 1.5A, but when this coil is connected to a
20V, 50Hz AC source it draws a current of 4A. Find the reactance of this coil (in ) when it is connected to a
30 V, 100 Hz AC source.
(6)
6
 4, Z  5
1.5
 XL (at 50 Hz)  3
 XL (at 100Hz)=2  3=6
R(coil) 
6.
Sol.
A series L–R circuit is fed by an AC source whose time period T = n, where  is the time constant of the
circuit (with a DC source). Find the value of n (to the closest integer) so that the applied voltage and the
current differ in phase by /4.
(6)
L
2 2R
or  

R
T
nL
2R
L 
n
2
 1 , n  6 (Rounded to the nearest integer)
n
Tn
7.
The current in the given circuit is increasing with a rate a = 4 amp/s. The charge on the capacitor at an instant
when the current in the circuit is 2 amp will be( IN MICRO COULOMBS) :
Sol.
(6) Using KVL,
Page # 9