Chapter 21
Electromagnetic Induction Solutions
SECTION - A
Objective Type Questions 1.
Dime Di mens nsio iona nall for formu mula la of ma magn gnet etic ic flu flux x is is (1) [M L2 T–2 A–1]
(3)
[M L2 T–3 A–1]
(1) Stationary uniform magnetic field
(2)
Stationary nonuniform magnetic field
(3) Time varying magnetic field
(4)
Not possible
(1) The number of turns in the coil
(2)
The rate of change of magnetic flux
(3) Time of rotation
(4)
The resistance of the circuit
(2)
[M L1 T–1 A–2]
(4)
[M L–2 T–2 A–2]
Sol. Answer (1) = BA
and F F = = ilB
B
F il
So dimensional formula will be ML 2T–2A–1 2.
An emf emf can can be be induc induced ed in in stat station ionary ary co coilil if itit is kep keptt in
Sol. Answer (3) Time varying –
3.
B
will induce emf as
d dt
The Th e indu induce ced d e.m e.m.f .f.. in a coil coil do does es not not de depe pend nd on
Sol. Answer (4) does not depend on resistance.
4.
Flux (in weber) in a closed circuit of resistance 10 ohm varies with time t (in second) according to the equation = 6 t 2 – 5 t + + 1. What is the magnitude of the induced current at t = = 0.25 s? (1) 1.2A
(2)
0.2A 0.
(3)
0.6A
(4)
0.8A
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Electromagnetic Induction
Solution of Assignment
Sol. Answer (2) 2
6t – 5t 1
–
l
5.
R
d dt
–12t 5
1 5 4
–12
10
0.2 A
A cylindric cylindrical al magnet magnet is kept kept along along the the axis of of a circular circular coil. coil. On rotati rotating ng the magn magnet et about about its axis, axis, the the coil will have induced in it (1) No current
(2)
A current
(3) Only an e.m.f.
(4)
Both an e.m.f. and a current
Sol. Answer (1) No change in flux, so no current will be induced. 6.
A magne magnett is brought brought near near a coil coil in two two ways ways (i) rapidl rapidly y (ii) slowly slowly.. The indu induced ced charg charge e will be (1) More in case (i)
(2)
More in case (ii)
(3) Equal in both the cases
(4)
More or less according to the radius of the coil
Sol. Answer (3) Induced charged is independent of speed of magnet. 7.
A circular circular loop of of flexible flexible conducti conducting ng material material is kept kept in a magnet magnetic ic field direct directed ed perpendic perpendicularly ularly into into its plane. plane. By holding the loop at diametrically opposite points its is suddenly stretched outwards, then (1) No current is induced in the loop
(2)
Anti-clockwise current is induced
(3) Clockwise current is induced
(4)
Only e.m.f. is induced
Sol. Answer (3) Flux will increase by stretching outwards so by Lenz's law clockwise current will be induced to oppose the change. 8.
An aeropla aeroplane ne is flying flying horizo horizontal ntally ly with a veloc velocity ity of 360 360 km/h. km/h. The distan distance ce between between the the tips tips of the wings wings of of aeroplane is 25 m. The vertical component of earth's magnetic field is 4 × 10 –4 Wb/m2. The induced e.m.f. is (1) 1 V
(2)
100 V
(3)
1 kV
(4)
Zero
Sol. Answer (1) = Bvl 4 10 –4 360
5 18
25
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Solution of Assignment
9.
57
Electromagnetic Induction
The magnetic flux through a coil varies with time t as shown in the diagram. Which graph best represents the variation of the e.m.f. E induced in the coil with time t ? t
E
E t
(1)
E t
(2)
E t
(3)
t
(4)
Sol. Answer (3) = Asint
–
d dt
– A cos t
E t
10. A coil having 500 square loops each of side 10 cm is placed with its plane perpendicular to a magnetic field which increases at a rate of 1.0 tesla/s. The induced e.m.f. (in volts) is (1) 0.5
(2)
0.1
(3)
1.0
(4)
5.0
(4)
Energy
Sol. Answer (4) NA
dB dt 2
5000.1 1 5 V
11.
The physical quantity, which is conserved on the basis of Lenz's Law is (1) Charge
(2)
Momentum
(3)
Mass
Sol. Answer (4) 12. A short bar magnet passes at a steady speed right through a long solenoid. A galvanometer is connected across the solenoid. Which graph best represents the variation of the galvanometer deflection with time t ? G
S
(1)
N
t
(2)
N
S
t
(3)
t
(4)
t
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Electromagnetic Induction
Solution of Assignment
13. A metallic ring with a cut is held horizontally and a magnet is allowed to fall vertically through the ring, then the acceleration of this magnet is (1) Equal to g
(2)
More than g
(3) Less than g
(4)
Sometimes less and sometimes more than g
Sol. Answer (1) 14. A bar magnet is made to fall through a long vertical copper tube. The speed (v ) of the magnet as a function of time (t ) is best represented by v d
a c
b t
(1) a
(2)
b
(3)
c
(4)
d
Sol. Answer (4) 15. A loop of irregular shape made of flexible conducting wire carrying clockwise current is placed in uniform inward magnetic field, such that its plane is perpendicular to the field. Then the loop (1) Experiences force
(2)
Develops induced current for a short time
(3) Changes to circular loop
(4)
All of these
Sol. Answer (4) 16. A loop of irregular shape of conducting wire PQRS (as shown in figure) placed in a uniform magnetic field perpendicular to the plane of the paper changes into a circular shape. The direction of induced current will be
(1) Clockwise
(2)
Anti-clockwise
(3)
No current
(4)
None of these
Sol. Answer (2) Using Lenz's law, inward flux is increasing. So to oppose this change current will be anticlockwise. 17. When a conducting wire XY is moved towards the right, a current flows in the anti-clockwise direction. Direction of magnetic field at point O is X O Y
(1) Parallel to motion of wire
(2)
Along XY
(3) Perpendicular outside the paper
(4)
Perpendicular inside the paper
Sol. Answer (3) Using Lenz's law Aakash Educational Services Pvt. Ltd. - Regd. Office : Aakash Tower, Plot No.-4, Sector-11, Dwarka, New Delhi-75 Ph.011-47623456
Solution of Assignment
Electromagnetic Induction
59
18. A copper rod of length l is rotated about one end perpendicular to the uniform magnetic field B with constant angular velocity . The induced e.m.f. between its two ends is (1) Bl 2
3
(2)
2
B l
2
(3)
1 2
B l
2
(4)
2 Bl 2
Sol. Answer (3)
=
1 2
B l
2
19. A coil having number of turns N and area A is rotated in a uniform magnetic field B with angular velocity about its diameter. Maximum e.m.f. induced in it is given by
(1) NAB
NAB
(2)
(3)
NA B
(4)
B NA
Sol. Answer (1) NBA cos NBA cos t
–
d dt
NBA sin t
max
NBA
20. A flat coil of 500 turns, each of area 50 cm 2, rotates in a uniform magnetic field of 0.14 Wb/m 2 about an axis normal to the field at an angular speed of 150 rad/s. The coil has a resistance of 5 . The induced e.m.f. is applied to an external resistance of 10 . The peak current through the resistance is (1) 1.5 A
(2)
2.5 A
(3)
3.5 A
(4)
4.5 A
Sol. Answer (3) N = 500, A = 50 cm2, B = 0.14 Wb/m 2 = 150 rad/s,
R = 5
max = NBA l max
max
R
3.5 A
21. Eddy currents are induced when (1) A metal block is kept in a changing magnetic field (2) A metal block is kept in a uniform magnetic field (3) A coil is kept in a uniform magnetic field (4) Current is passed in a coil Sol. Answer (1) Aakash Educational Services Pvt. Ltd. - Regd. Office : Aakash Tower, Plot No.-4, Sector-11, Dwarka, New Delhi-75 Ph.011-47623456
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Electromagnetic Induction
Solution of Assignment
22. A motor starter (1) Is a variable resistor
(2)
Offsets the back emf variations
(3) Helps start a DC motor
(4)
All of these
Sol. Answer (4) 23. A simple electric motor has an armature resistance of 1 and runs from a d.c. source of 12 V. It draws a current of 2 A when unloaded. When a certain load is connected to it, its speed reduces by 10% of its initial value. The current drawn by the loaded motor is (1) 3 A
(2)
6A
(3)
2A
(4)
1A
Sol. Answer (1) 24. Which of the following is possible application of an RC circuit? (1) Windshield wipers (2) Flashing red lights on roadway construction sites (3) Heart pacemakers (4) All of these Sol. Answer (4) 25. The current passing through a choke coil of self inductance 5 H is decreasing at the rate of 2 A /s. The e.m.f. developed across the coil is (1) 10 V
(2)
– 10 V
(3)
– 2.5 V
(4)
2.5 V
Sol. Answer (1)
L = 5 H,
Ldi dt
di dt
2 A/s
5 2 10 V
26. When the number of turns in a solenoid are doubled without any change in the length of the solenoid, its self inductance becomes (1) Half
(2)
Double
(3)
Four times
(4)
Eight times
Sol. Answer (3) L
n2
So if n' = 2n L' = 4L 27. A coil of resistance 20 ohms and inductance 5 H has been connected to a 100 volt battery. The energy stored in the coil is (1) 31.25 J
(2)
62.5 J
(3)
125 J
(4)
250 J
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Solution of Assignment
Electromagnetic Induction
61
Sol. Answer (2) l
100 20 1
Ll
2
5A 2
1 2
5 5
2
62.5 J
28. The magnetic energy stored in a long solenoid of area of cross-section A in a small region of length L is 2
(1)
B AL
AL
(2)
2
2 0
2 0
(3)
1 2
2
0 B 2 AL
B AL
(4)
2 0
Sol. Answer (4) 2 B Energy Volume 2 0
⇒
Energy
B
2
AL 2 0
29. An inductor is connected to a direct voltage source through a switch. Now (1) Very large emf is induced in inductor when switch is closed (2) Larger emf is induced when switch is opened (3) Large emf is induced whether switch is closed or opened (4) No emf is induced whether switch is closed or opened Sol. Answer (2) 30. A long solenoid has self inductance L. If its length is doubled keeping total number of turns constant then its new self inductance will be
(1)
L
(2)
2
2L
(3)
L
L
(4)
4
Sol. Answer (1) L
0 n 2 Al
N L 0 l L
0N
Al
2
l ⇒
2
L'
A
⇒
L
1 l
L 2
31. If L and R denote inductance and resistance respectively, then the dimension of L/R is (1) [M0L0T –1]
(2)
[M0L0T1]
(3)
[M0L0T2]
(4)
[MLT2]
Sol. Answer (2)
L R
represents time constant hence will have dimension of time.
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Electromagnetic Induction
Solution of Assignment
32. A solenoid has 2000 turns wound over a length of 0.3 m. The area of its cross section is 1.2 × 10 –3 m2. Around its central section a coil of 300 turns is wound. If an initial current of 2 A is reversed in 0.25 s, the e.m.f. induced in the coil is equal to (1) 6 × 10 –4 V
(2) 4.8 × 10 –2 V
(3)
2.4 × 10 –2 V
(4)
48 kV
Sol. Answer (2) NBA ⇒ i t
4
0.25
d dt
⇒ NA
, So 4.8 10
–2
dB dt
NA 0n
i
t
V
33. With the decrease of current in the primary coil from 2 A to zero in 0.01s, the e.m.f. generated in the secondary coil is 1000 V. The mutual inductance of the two coil is (1) 1.25 H
(2)
2.50 H
(3)
5.00 H
(4)
10.00 H
Sol. Answer (3) = Mi d dt
Mdi
dt
1000
M
1 2
M 2
0.01
10 5.00 H
34. Two coaxial coils are very close to each other and their mutual inductance is 5 mH. If a current 50 sin 500 t is passed in one of the coils then the peak value of induced e.m.f. in the secondary coil will be (1) 5000 V
(2)
500 V
(3)
150 V
(4)
125 V
Sol. Answer (4) = Mi d dt
Mdi dt
5 10 –3 50 50 0 cos t
= 125 V
max
35. The coefficient of self induction of two inductor coils are 20 mH and 40 mH respectively. If the coils are connected in series so as to support each other and the resultant inductance is 80 mH then the value of mutual inductance between the coils will be (1) 5 mH
(2) 10 mH
(3)
20 mH
(4)
40 mH
Sol. Answer (2) L1 = 20 mH, L2 = 40 mH L
L1 L2 2 M
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Solution of Assignment
Electromagnetic Induction
63
SECTION - B
Objective Type Questions 1.
A conducting rod AB of length l is projected on a frictionless frame PSRQ with velocity v 0 at any instant. The velocity of the rod after time t is
(1) v = v 0
(2)
v > v 0
(3)
v < v 0
(4)
None of these
Sol. Answer (3) The rod will experience magnetic force in the direction opposite to initial force. So velocity will decrease with time. 2.
In the given circuit, bulb will become suddenly bright, if
L
V
Bulb
S
(1) Switch is closed or opened
(2)
Switch is closed
(3) Switch is opened
(4)
None of these
Sol. Answer (3) Sudden decrease in current due to circuit breaking (opening) will be compensated by sudden induced current flow (as per Lenz's law) and hence sudden brightness. 3.
What will be the direction of current in the coil A as the switch S is closed? B
A S
V
(1) Clockwise
(2)
Anticlockwise
(3) Anticlockwise and then clockwise
(4)
Clockwise and then anticlockwise
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4.
Electromagnetic Induction
Solution of Assignment
The armature of a generator of resistance 1 is rotated at its rated speed and produces 125 V with out load and 115 V with full load. The current in the armature coil is (1) 240 A
(2)
10 A
(3)
1A
(4)
2A
Sol. Answer (2) l
5.
125 115
1
10 A
A copper disc of radius 0.1 m is rotated about its centre with 10 rev/s in a uniform magnetic field of 0.1T with its plane perpendicular to field. The emf induced across the radius of disc is
(1)
10
volt
(2)
100
volt
(3)
1000
volt
(4)
Zero
Sol. Answer (2)
1 2 1 2
2
BR , R
0.1 m, B 0.1 T, W 20
s
2 0.1 0.1 20
volt
100
6.
A frame CDEF is placed in a region where a magnetic field B is present. A rod of length one metre moves with constant velocity 20 m/s and strength of magnetic field is one tesla. The power spent in the process is (take R = 0.2 and all other wires and rod have zero resistance) P D
C
B v
R
E
(1) 1 kW
(2)
2 kW
Q
(3)
F
3 kW
(4)
4 kW
Sol. Answer (2) 2
P = F .V
2
B l v
2
R
11
2
20
2
0.2
2 kW
7.
An ideal solenoid of cross-sectional area 10–4 m2 has 500 turns per metre. At the centre of this sol enoid, another coil of 100 turns is wrapped closely around it. If the current in the coil changes from 0 to 2 A in 3.14 ms, the emf developed in the second coil is (1) 1 mV
(2)
2 mV
(3)
3 mV
(4)
4 mV
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Solution of Assignment
Electromagnetic Induction
65
Sol. Answer (4) M
0 n1n 2 A
4 10
–
8.
Mdi
–7
dt
500 100 10 –4
M 2 3.14
4 mV
A positive charge q moves along the line AB, which lies in the same plane as a circular loop of conducti ng wire as shown in the figure. The direction of current induced in the loop is B
q
A
(1) Clockwise
(2)
First anticlockwise then clockwise
(3) First clockwise then anticlockwise
(4)
No current is induced
Sol. Answer (3) B
0 qv 4
r 2
when q approaches the loop 'r ' decreases when q goes away from the loop 'r ' increases so using Lenz law induced current will be first clockwise then anticlockwise. 9.
Figure shows an L-R circuit. When the switch S is closed, the current through resistor R 1, R 2 and R 3 are I 1, I 2 and I 3 respectively. The value of I 1, I 2 and I 3 at t = 0 s is I 1
I 2
I 3
R 3 R 2
E
L2
R 1 L1 S
(1) I 1 = I 2 = I 3 = 0
(3)
I 1
0, I 2
E R 2
, I 3
E R 3
(2)
I 1
(4)
I 1
E R 1
, I 2 I 3 0
E R 1
,
I 2
E R 2
L1
,
I 3
E R 3
L3
Sol. Answer (2) At t = 0, inductor offers infinite resistance So ,
I1
E R 1
, I 2 I 3 0
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Electromagnetic Induction
Solution of Assignment
10. Two coils A and B are wound on the same iron core as shown in figure. The number of turns in the coil A and B are N A and N B respectively. Identify the correct statement A
B
I A
I B
(1) Both the coils have same magnitude of magnetic flux (2) The magnetic flux linked are in the ratio
A B
N A N B
(3) The induced emf across each coil are in the ratio
E A E B
N A N B
2
(4) Both the coils have same magnitude of induced emf Sol. Answer (2) A B
11.
N A
N B
A simple pendulum with bob of mass m and conducting wire of length L swings under gravity through an angle 2. The earth’s magnetic field component in the direction perpendicular to swing is B. The maximum potential difference induced across the pendulum is
L
h
(1)
. gL 2
2BL sin
(2)
BL sin (gl ) 2
(3)
BL sin .(gL) 3/ 2 2
(4)
BL sin .(gL)2 2
Sol. Answer (2) Using conservation of energy mgl 1– cos
mgl 1 – cos
2gl 2 sin
2
1 2
g
2
2 1 2
I 2
mI 2 2
2 2 l 2
sin
l
2
B l 2
Bl sin
1
2
1 2
2
g l
sin
2 l B 2
gl
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Solution of Assignment
Electromagnetic Induction
67
12. The switch shown in the circuit is closed at t = 0. The current drawn from the battery by the circuit at t = 0 and t = are in the ratio
L
C
E R
(1) 2 : 1
(2)
R
S
1:2
R
(3)
1:1
(4)
1:4
Sol. Answer (3) At t = 0, L offers infinite resistance At t , C offers infinite resistance So, in both the cases,
l
2R
Hence ratio is 1 : 1. 13. A small square loop of wire of side l is placed inside a large square loop of wire of side L (>>l ). The loops are coplanar and their centres coincide. The mutual inductance of the system is
l
2
2 2 0 L
(1)
L
(2)
l
2 2 0 L
l
(3)
2 2 0 l
L
(4)
2 2 0 l
2
L
Sol. Answer (4) M
i
due to outer loop in the smaller loop will be due to magnetic field Vector sum of all the four sides of bigger square. 2
So
M
2 2 0 l i
L i
14. A uniform magnetic field exists in the region given by B 3 iˆ 4 ˆj 5kˆ . A rod of length 5 m placed along y
axis is moved along x -axis with constant speed 1 ms –1. Then induced e.m.f. in the rod is (1) Zero
(2)
25 V
(3)
5V
(4)
10 V
Sol. Answer (2)
v B .l
ˆ .5 ˆj 1i ˆ 3iˆ 4 jˆ 5k
4kˆ – 5 j ˆ .5 ˆj
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Electromagnetic Induction
Solution of Assignment
15. A copper rod AB of length l , pivoted at one end A, rotates at constant angular velocity , at right angles to a uniform magnetic field of induction B. The emf, developed between the mid point C of the rod and end B is
A 2
Bl
(1)
(2)
8
3 4
B
C
2
Bl
2
(3)
Bl 4
3
(4)
8
2
B l
Sol. Answer (4) l
∫ Bxdx
l
2
x 2 B 2
B 2
3 8
l
l
2 l – l
Bl
2
2
4
2
16. Radius of a circular loop placed in a perpendicular uniform magnetic field is increasing at a constant rate of r 0 ms –1. If at any instant radius of the loop is r , then emf induced in the loop at that instant will be (1) –2Brr 0
(2)
–2Br
(3)
–Br 0r
(4)
–2Br 0r
Sol. Answer (4) dr dt
r0
⇒
–d
dt
Br
–B 2r
2
dr dt
–2Brr 0
17.
1
2
3
The figure shows three circuits with identical batteries, inductors and resistances. Rank the circuits according to the currents through the battery just after the switch is closed, greatest first (1) I 2 > I 3 > I 1
(2)
I 2 > I 1 > I 3
(3)
I 1 > I 2 > I 3
(4)
I 1 > I 3 > I 2
Sol. Answer (1) l1
0, l 2
R
, l 3
2R
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Solution of Assignment
Electromagnetic Induction
69
18. In an inductor, the current I varies with time t as I = 5 A + 16 (A/s) t . If induced emf in the inductor is 5 mV, the self inductance of the inductor is (1) 3.75 × 10–3 H
(2)
3.75 × 10–4 H
(3)
3.125 × 10–3 H
(4)
3.125 × 10–4 H
Sol. Answer (4) l
5 16t
di ⇒
dt
16
5 10 –3 V Ldi
dt
So,
L 16 5 10
L 3.125 10
–4
–3
H
19. A magnet is moved in the direction indicated by an arrow between two coils AB and CD as shown in figure. The direction of induced current in the straight wire is A
C
B
N
(1) A to B and C to D
(2)
D
S
B to A and C to D
(3)
A to B and D to C
(4)
B to A and D to C
Sol. Answer (3) Using Lenz's law 20. Two coils of self inductance L1 and L2 are placed near each other so that the total flux in one coil is completely linked with the other. Their mutual inductance (M ) will be given by (1) M = L1 L2
(2)
M
(3)
L1 L2
M
(4)
L1 L2
M
L1 L2
Sol. Answer (2) M
L1L2
21. The network shown in figure is a part of a complete circuit. If at a certain instant, the current i is 4 A and is increasing at a rate of 10 3 A/s. Then V B – V A will be i
A
1
(1) –11 V
(2)
11 V
B
12 V
5 mH
(3)
–21 V
(4)
21 V
Sol. Answer (3) di dt
So,
10
3
V A – 4 1 – 12 – 5 10
–3
10 V 3
B
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Electromagnetic Induction
Solution of Assignment
22. The magnetic flux through a stationary loop with resistance R varies during interval of time T as = at (T – t ). The heat generated during this time neglecting the inductance of loop will be 2
a T
(1)
3
2
a T
(2)
3R
2
2
3R
3
a T
(3)
3R
a T
(4)
2
3R
Sol. Answer (1) at T – t aTt – at 2 d
–
– aT – 2at
dt
P –
2
R
aT
T
∫
Pdt 0
aT
∫
– 2at
2
R
0
2
2
R
T
H
– 2at
a T
3
3R
23. A short-circuited coil is placed in a time-varying magnetic field. Electrical power is dissipated due to the current induced in the coil. If the number of turns were to be quadrupled and the wire radius halved, the electric power dissipated would be (1) Halved
(2)
The same
(3)
Doubled
(4)
Quadrupled
Sol. Answer (2) nBr 2
dB dt
r ' 4nB 2 nBr 2 '
P
'
'
dB
2
R
2
dt
dB dt
2 R
24. A small square loop of wire of side l is placed inside a large circular loops of radius r . The loop are coplanar and their centre coincide. The mutual inductance of the system is proportional to 2
(1)
2
l
(2)
r
l
r
2
(3)
r 2
l
(4)
r
2
l
Sol. Answer (1) Using Mi M
i
2
2
l 0 i l . i r 2r
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Solution of Assignment
Electromagnetic Induction
71
SECTION - C
Previous Years Questions 1.
An electron moves on a straight line path XY as shown. The abcd is a coil adjacent to the path of electron. [Re-AIPMT-2015] What will be the direction of current, if any, induced in the coil? a
b
d
c X
Y
electron
(1) No current induced (2) abcd (3) adcb (4) The current will reverse its direction as the electron goes past the coil Sol. Answer (4) When electron goes in straight line electric flux first increases then decreases. 2.
A conducting square frame of side a and a long straight wire carrying current I are located in the same plane as shown in the figure. The frame moves to the right with a constant velocity V. The emf induced in the frame [AIPMT-2015] will be proportional to x I V
a
(1)
1 (2 x a )(2x a )
(2)
1
1
(3)
2
x
(4)
2
(2 x a )
1 (2 x a )2
Sol. Answer (1) e ABCD = e AB + eCD
0I a 2 x 2
av
0I a 2 x 2
x av
A +
D + V
0Iav
2 2 2 2 x a 2x a
0Iav 2 x a 2 x a
(2 x a )(2 x a)
x –
V
a
2
B–
a 2
x +
a a
– C
2
2
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3.
Electromagnetic Induction
Solution of Assignment
A thin semicircular conducting ring (PQR ) of radius r is falling with its plane vertical in a horizontal magnetic field B, as shown in figure. The potential difference developed across the ring when its speed is v is ×
×
×
B
Q ×
×
×
×
[AIPMT-2014]
×
×
×
×
×
r
P
R
(1) Zero
(2)
Bv r 2/2 and P is at higher potential
(3) rBv and R is at higher potential
(4)
2rBv and R is at higher potential
Sol. Answer (4) = BLeff v (Leff = Diameter)
= B 2Rv 4.
A coil of self-inductance L is connected in series with a bulb B and an AC source. Brightness of the bulb decrease [NEET-2013] when (1) Number of turns in the coil is reduced (2) A capacitance of reactance X C = X L is included in the same circuit (3) An iron rod is inserted in the coil (4) Frequency of the AC source is decreased
Sol. Answer (3) 5.
A wire loop is rotated in a magnetic field. The frequency of change of direction of the induced e.m.f. is [NEET-2013] (1) Twice per revolution
(2)
Four times per revolution
(3) Six times per revolution
(4)
Once per revolution
Sol. Answer (1) BA cos t d
6.
dt
BA sin t
A coil of resistance 400 is placed in a magnetic field. if the magnetic flux (Wb) linked with the coil varies [AIPMT (Prelims)-2012] with times t (s) as = 50t 2 + 4. The current in the coil at t = 2 s is (1) 2 A
(2)
1A
(3)
0.5 A
(4)
0.1 A
Sol. Answer (3) 50t 2 4 d
l
dt
t 2
100t
100 2 200 V
R
200 400
0.5 A
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Solution of Assignment
7.
Electromagnetic Induction
73
The current (I ) in the inductance is varying with time according to the plot shown in figure.
I T /2 t
T
Which one of the following is the correct variation of voltage with time in the coil?
[AIPMT (Prelims)-2012]
v
v
v
v t
t
(1)
(2)
T
T /2
(3)
T /2
T
(4)
t T
T /2
T /2
T t
Sol. Answer (2) Ldi
Use for 0 to
dt
T 2
and from 8.
,
T 2
di dt
is constant and positive
to T ,
di dt
is constant and negative.
In a coil of resistance of 10 , the induced current developed by changing magnetic flux through it,is shown in figure as a function of time. The magnitude of change in flux through the coil in Weber is [AIPMT (Mains)-2012] i (A)
4
0 (1) 8
(2)
2
0.1 (3)
t (s)
6
(4)
4
Sol. Answer (2)
t .R
l
l tR
or
d
ldt R
Total flux R
∫ ldt
∫ idt represents area under i – t curve 1 2
So R 0.1 4 2 Aakash Educational Services Pvt. Ltd. - Regd. Office : Aakash Tower, Plot No.-4, Sector-11, Dwarka, New Delhi-75 Ph.011-47623456
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9.
Electromagnetic Induction
Solution of Assignment
The current i in a coil varies with time as shown in the figure. The variation of induced emf with time would be [AIPMT (Prelims)-2011] i
t
0
T /4
T /2
3T/4
emf
emf
T /2 3 T/4 T
(1)
0
t
T /4
(2)
0
0
T /4
t T /2 3 T/4 T
emf
emf
(3)
T
t T /4
T /2
3T/4
T /4
(4)
T
T /2
3T /4
T
t
0
Sol. Answer (2) di dt
–Ldi dt
is slope of l – t curve.
10. A conducting circular loop is placed in a uniform magnetic field, B = 0.025 T with its plane perpendicular to the loop. The radius of the loop is made to shrink at a constant rate of 1 mms –1. The induced emf when the [AIPMT (Prelims)-2010] radius is 2 cm is (1) 2 V
(2)
V
(3)
2
V
2V
(4)
Sol. Answer (2) 11.
A conducting circular loop is placed in a uniform magnetic field 0.04 T with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at 2 mm/s. The induced emf in the loop when the radius [AIPMT (Prelims)-2009] is 2 cm is (1) 4.8 V
(2)
0.8 V
(3)
1.6 V
3.2 V
(4)
Sol. Answer (4)
12. A circular disc of radius 0.2 m is placed in a uniform magnetic field of induction
1 Wb
2
m
in such a way that its
axis makes an angle of 60° with (1) 0.01 Wb
(2)
B.
[AIPMT (Prelims)-2008]
The magnetic flux linked with the disc is
0.02 Wb
(3)
0.06 Wb
(4)
0.08 Wb
Sol. Answer (2) Aakash Educational Services Pvt. Ltd. - Regd. Office : Aakash Tower, Plot No.-4, Sector-11, Dwarka, New Delhi-75 Ph.011-47623456
Solution of Assignment
Electromagnetic Induction
75
13. A long solenoid has 500 turns. When a current of 2 A is passed through it, the resulting magnetic flux linked with [AIPMT (Prelims)-2008] each turn of the solenoid is 4 × 10 –3 Wb. The self-inductance of the solenoid is (1) 4.0 H
(2)
2.5 H
(3)
2.0 H
(4)
1.0 H
Sol. Answer (4) N = 500, l = 2 L
N i
500 4 10 –3 2
14. What is the value of inductance L for which the current is a maximum in a series LCR circuit with C = 10 F [AIPMT (Prelims)-2007] and = 1000 s–1? (1) 10 mH
(2)
100 mH
(3) 1 mH
(4)
Cannot be calculated unless R is known
Sol. Answer (2) 15. Two coils of self-inductances 2 mH and 8 mH are placed so close together that the effective flux in one coil is [AIPMT (Prelims)-2006] completely linked with the other. The mutual inductance between these coils is (1) 10 mH
(2)
6 mH
(3)
4 mH
(4)
16 mH
Sol. Answer (3) L1 = 2mH, L2 = 8 mH M
L1L2
16 4 mH
16. A metal ring is held horizontally and a bar magnet is dropped through the ring with its length along the axis of the ring. The acceleration of the falling magnet is (1) More than g
(2)
Equal to g
(3)
Less than g
(4)
Either (1) or (3)
Sol. Answer (3) S N
due to Lenz's law a < g 17. The magnetic flux through a circuit of resistance R changes by an amount in a time t . Then the total quantity of electric charge Q that passes any point in the circuit during the time t is represented by (1) Q
1
.
(2)
R t
Q
R
(3)
Q
t
(4)
Q R .
t
Sol. Answer (2) l
tR
⇒
⇒
Q t
Q
tR R
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76
Electromagnetic Induction
Solution of Assignment
18. As a result of change in the magnetic flux linked to the closed loop as shown in the figure, an e.m.f V volt is induced in the loop. The work done (in joule) in taking a charge Q coulomb once along the loop is
(1) QV
(2)
2QV
(3)
QV 2
(4)
Zero
Sol. Answer (1) W = QV (By the defination of e.m.f) 19. A rectangular, a square, a circular and an elliptical loop, all in the ( x -y ) plane, are moving out of a uniform magnetic field with a constant velocity V vi ˆ. The magnetic field is directed along the negative z -axis direction. The induced emf, during the passage of these loops, out of the field region, will not remain constant for
(1) Any of the four loops
(2)
The rectangular, circular and elliptical loops
(3) The circular and the elliptical loops
(4)
Only the elliptical loop
Sol. Answer (3) For circular and elliptical loop, area coming out from the field per unit time is not constant i.e.,
dA dt
constant
20. A conductor of 3 m length is moving perpendicular to its length as well as a magnetic field of 10 –3 T with a speed of 102 m/s, then the force required to move it with this constant speed is (1) 0. 3 N
(2)
0.9 N
(3)
0
(4)
3 × 10–3 N
Sol. Answer (3) Motional emf will induce ( = Bvl ). But loop is not closed so no current will flow, hence no magnetic field force will act upon it. 21. In a circular conducting coil, when current increases from 2 A to 18 A in 0.05 s, the induced emf is 20 V. The self inductance of the coil is (1) 62.5 mH
(2)
6.25 mH
(3)
50 mH
(4)
0
Sol. Answer (1)
Ldi dt
L 18 – 2 0.05
20
So L = 62.5 10–3 H 22. In the circuit given in figure, 1 and 2 are ammeters. Just after key K is pressed to complete the circuit, the reading will be R 1
1 L
R 2
2
K
(1) Zero in 1, maximum in 2
(2)
Maximum in both 1 and 2
(3) Zero in both 1 and 2
(4)
Maximum in 1, zero in 2
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Solution of Assignment
Electromagnetic Induction
77
Sol. Answer (4) At t = 0, C offers zero resistance L offers infinite resistance So reading of Ammeter (1) max Ammeter (2) Zero 23. For a coil having L = 2 mH, current flowing through it is I = t 2 e–t then the time at which emf become zero (1) 2 s
(2)
1s
(3)
4s
(4)
3s
Sol. Answer (1) Ldi
dt
When di
di
becomes zero, will becom zero.
dt
–t 2 e – t e – t 2t 0
dt
t = 2
24. When the number of turns and the length of a solenoid both are doubled, its self inductance becomes (1) Four times
(2)
Doubled
(3)
Halved
(4)
Unchanged
Sol. Answer (2) L
L
0 n 2 Al
0
N l
2
Al
2
2 0N A
l
So, on doubling N and l 2
L'
0 2N A 2l
2
2 0 N A l
L' = 2L
25. The time constant of L-R circuit is doubled if (1) Both L and R become two times (2) L becomes four times and R becomes two times (3) L becomes two times and R becomes four times (4) L becomes two times and R becomes eight times Sol. Answer (2)
L R
' 2
4L 2R
26. Two neighbouring coils A and B have a mutual inductance of 20 mH. The current flowing through A is given by, i = 3t 2 – 4t + 6. The induced emf at t = 2s is (1) 160 mV
(2)
200 mV
(3)
260 mV
(4)
300 mV
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78
Electromagnetic Induction
Solution of Assignment
Sol. Answer (1) M = 20 mH l
3t 2 – 4t 6
di dt
6t – 4
Mdi dt
20 10 –3 6 2 – 4 = 160 mV t 2
27. The self inductance L of a solenoid depends on the number of turns per uni t length ‘ n’ as (1) L n
(2)
L n2
(3)
L n –1
(4)
L n –2
Sol. Answer (2) 28. Two coils have a mutual inductance 0.005 H. The current changes in the first coil according to equation / = / 0 sin t , where /0 = 10 A and = 100 radian per second. The maximum value of e.m.f. (in volt) in the second coil is (1)
(2)
5
(3)
2
(4)
4
Sol. Answer (2) M = 0.005 H l
I 0 sin t 10 sin t
1 rad/s
Mdi dt
0.005 10 100 cos t 0.005 1000 = 5
29. A transformer has 500 primary turns and 10 secondary turns. If the secondary has resistive load of 15 , the currents in the primary and secondary respectively, are (1) 0.16 A, 3.2 × 10–3 A
(2)
3.2 × 10–3 A, 0.16 A
(3) 0.16 A, 0.16 A
(4)
3.2 × 10–3 A, 3.2 × 10 –3 A
Sol. Answer (2) Use
iP iS
n P n S
30. A magnet is made to oscillate with a particular frequency through a coil as shown in figure. The time variation of magnitude of emf generated across the coil during one cycle is S N
V
e
e
(1)
t
(2)
e
e
t
(3)
t
(4)
t
Sol. Answer (3) emf induced will be zero when magnet will be inside coil. Use Lenz's law. Aakash Educational Services Pvt. Ltd. - Regd. Office : Aakash Tower, Plot No.-4, Sector-11, Dwarka, New Delhi-75 Ph.011-47623456
Solution of Assignment
Electromagnetic Induction
79
31. Two coils have self inductance L1 = 4 mH and L2 = 1 mH respectively. The currents in the two coils are increased at the same rate. At a certain instant of time both coils are given the same power. If I 1 and I 2 are the currents in the two coils, at that instant of time respectively, then the value of 1
(1)
1
(2)
8
(3)
4
1 2
I 1 I 2
(4)
is
1
Sol. Answer (2) L1 = 4 mH, di 1 dt l 1 l 2
l1 l2
L2 = 1 mH
di 2 dt
∵
2 1 L2
L1
di 2 dt di 1
⇒
P
l1 l2
i ⇒
L2 L1
1 2
l 2
l 1
1 4
dt
SECTION - D
Assertion-Reason Type Questions 1.
A : Total induced emf in a loop is not confined to any particular point but it is distributed around the loop in direct proportion to the resistances of its parts. R : In general when there is no change in magnetic flux, no induced emf is produced.
Sol. Answer (2) 2.
A : The induced current flows so as to oppose the cause producing it. R : Lenz's law is based on energy conservation.
Sol. Answer (1) 3.
A : Faraday's law is an experimental law. R : Time varying magnetic field cannot generate induced emf.
Sol. Answer (3) 4.
A : Unlike electrostatic field the lines of induced field form closed loop. R : Electrostatic field is conservative unlike induced fields.
Sol. Answer (1) 5.
A : The mutual induction between the two coils infinitely apart is zero. R : If the mutual induction between the two coils is zero, it means that their self inductances are also zero.
Sol. Answer (3) 6.
A : An inductor is called the inertia of an electric circuit. R : An inductor tends to keep the flux constant.
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7.
Electromagnetic Induction
Solution of Assignment
A : At any instant, if the current through an inductor is zero, then the induced emf will also be zero. R : In one time constant, the current flows to 37 percent of its maximum value in a series LR circuit.
Sol. Answer (4) 8.
A : There may be an induced emf in a loop without induced current. R : Induced current depends on the resistance of the loop as well.
Sol. Answer (2) 9.
A : When the magnetic flux through a loop is maximum, induced emf is maximum. R : When the magnetic flux through a loop is minimum, induced emf is minimum.
Sol. Answer (4) 10. A : When a conducting loop is kept stationary in a non-uniform magnetic field an emf is induced. R : As per Faraday's law, whenever flux changes, an emf is induced. Sol. Answer (4) 11.
A : When an electric motor is started, a variable resistance (that decreases with time) is used in series. This resistance is known as motor starter. R : The back-emf in the beginning, when motor starts, is very small.
Sol. Answer (1) 12. A : When a bar magnet is dropped into a vertical long hollow metallic tube, the magnet ultimately moves with zero acceleration. R : The magnet falling into metallic tube causes the eddy currents in the metal tube, so the motion of the magnet is damped. Sol. Answer (1) 13. A : The power output of a practical transformer is always smaller than the power input. R : A transformer works on the principle of mutual induction. Sol. Answer (2) 14. A : Electrical power through transmission lines is transmitted at high voltage. R : At high voltage theft of power is checked. Sol. Answer (3) 15. A : The electric field induced due to changing magnetic field is non-conservative. R : The line integral of the electric field induced due to changing magnetic field along a closed loop is always zero. Sol. Answer (3)
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