iitians pace

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http://slidepdf.com/reader/full/iitians-pace 1/8Head Office: Andheri: 26245223 MUMBAI / DELHI/ AKOLA / KOLKATA / LUCKNOW

ANDHERI / BORIVALI / DADAR / CHEMBUR / THANE / MULUND/ NERUL / POWAI

IIT – JEE 2014 TW TEST MARKS: 65

TIME: 1HR TOPIC:EMI DATE:

SECTION-I

This section contains 10multiple choice questions. Each question has 4 choices (A), (B), (C)and (D) for its answer, out which ONLY ONE is correct.

(+3, - 1)

1. A coil has 2000 turns and area of 270cm . The magnetic field perpendicular to the plane of the coil is2/3.0 mWb and takes 0.1sec to rotate through o180 . The value of the induced e.m.f. will be

(a) V 4.8 (b) V 84

(c) V 42 (d) V 2.4

2. A coil having n turns and resistance R is connected with a galvanometer of resistance R4 . This

combination is moved in time tseconds from a magnetic field W 1 weber to W 2weber . The induced

current in the circuit is

(a) Rnt

W W

5

12 (b)

Rt

W W n

5

)( 12

(c) Rnt

W W )( 12 (d)

Rt

W W n )( 12

3. Two rails of a railway track insulated from each other and the ground are connected to a milli

voltmeter. What is the reading of voltmeter, when a train travels with a speed of 180 km/hr along the

track. Given that the vertical component of earth's magnetic field is 24 /102.0 mweber and the rails

are separated by 1 metre

(a) volt 2

10

(b) volt 4

10

(c) volt

310 (d) 1 volt

4. A conducting square loop of side l and resistance R moves in its plane with a uniform velocity v

perpendicular to one of its sides. A magnetic induction B constant in time and space, pointing

perpendicular and into the plane at the loop exists everywhere with half the loop outside the field, as

shown in figure. The induced e.m.f. is

(a) Zero

(b) RvB

(c) VBl/R

(d) VBl

5. If electric flux varies according to 23t 4t 2 , find emf at t = 2s.

(a) 22 V (b) 18 V

(c) 20 V (d) 16 V.

6. A 50 turns circular coil has a radius of cm3 , it is kept in a magnetic field acting normal to the area of

the coil. The magnetic field B increased from 0.10 tesla to 0.35 tesla in 2 milliseconds. The average

induced e.m.f. in the coil is

(a) volts77.1 (b) volts7.17 (c) volts177 (d) volts177.0

A

B C

D

v

l


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7. In the diagram shown if a bar magnet is moved along the common axis of two single turn coils A and

B in the direction of arrow

(a) Current is induced only in A& not in B

(b) Induced currents in A& B are in the same direction

(c) Current is induced only in B and not in A

(d) Induced currents in A& B are in opposite directions

8. An electric potential difference will be induced between the ends of the conductor shown in the

diagram, when the conductor moves in the direction

(a)P (b) Q (c) L (d) M

9. A copper disc of radius 0.1 m is rotated about its centre with 10 revolutions per second in a uniform

magnetic field of 0.1 Tesla with its plane perpendicular to the field. The e.m.f. induced across the

radius of disc is

(a) V 10

(b) V 10

2

(c) V 210 (d) V

2102

10. In the following circuit, the bulb will become suddenly bright if

(a) Contact is made or broken

(b) Contact is made

(c) Contact is broken

(d) Won't become bright at all

SECTION-II

This section contains 7 multiple choice questions. Each question has 4 choices (A), (B), (C)and (D) for its answer, out which ONE OR MORE is/are correct.

(+3, 0)

11. A super conducting loop having an inductance 'L' is kept in a magnetic field which is varying with

respect to time. If is the total flux, = total induced emf, then:(a) = constant (b) I = 0 (c) = 0 (d) 0

12. A conducting rod of length slides at constant velocity ‘v’ on two

parallel conducting rails, placed in a uniform constant magnetic field B

perpendicular to the plane of the rails as shown in figure. A resistance R

is connected between the two ends of the rail. Then which of the

following is/are correct:

(a) The thermal power dissipated in the resistor is equal to rate of work done by external force

B

A

N S

N S

L

M

Q

P



(b) If applied external force is doubled than a part of external power increases the velocity of rod.

(c) Lenz’s Law is not satisfied if the rod is accelerated by external force

(d) If resistance R is doubled then power required to maintain velocity becomes half.

13 . Whenever a magnet is moved either towards or away from a conducting coil, an emf is induced, the

magnitude of which is independent of

(a) the strength of the magnetic field

(b) the speed with which the magnet is moved

(c) the resistance of the coil

(d) the area of cross-section of the coil.

14. Choose the correct statements from the following.

(a) A circuit consisting of an inductance is carrying a current. When the circuit is suddenly switched

off, the direction of the induced current will be the same as that of the main current

(b) Sparking is observed in the switch when an electrical appliance is suddenly switched off because

the induced emf suddenly falls to zero

(c) A coil is connected in series with a bulb and this combination is connected to a dc source. When

an iron core is inserted in the coil, there will be no change in the brightness of the bulb.

(d) A coil is connected in series with a bulb and this combination is connected to an ac source.

When an iron core is inerted in the coil, the brightness of the bulb will increase.

15. L, C and R respectively represent inductance, capacitance and resistance. Which of the following

combinations have the dimensions of frequency?

(a)R

L (b)

1

RC (c)

R

LC (d)

1

LC

16. In a coil of self inductance 10 mH, the current I (in ampere) varies with time t(in second) as i = 8t +

2 amp

(a) The induced emf increases with time(b) The induced emf has a constant value of 80 mV

(c) The power supplied to the inductor at t = 1 s is 0.8W

(d) The power supplied to the inductor at t = 2 s is 1.6W

17. The SI unit of inductance (which is henry) can also be written as

(a) weber/ampere (b) volt second/ampere

(c) joule/(ampere)2 (d) ohm second

18. A circular loop of radius R carrying current I lies in x-y plane with its centre at origin. The total

magnetic flux through x-y plane is kR. Find the value of k.(a) 1 (b) 0 (c) 2 (d) 4

19. Two coils have a mutual inductance 0.005 H . The current changes in the first coil according to

equation t I I sin0 , where A I 100 and = 100 radian/sec. The maximum value of e.m.f. in the

second coil is k volts. Find the value of k.

(a) 2 (b) 4 (c) 5 (d) 3



SECTION-III (Paragraph Type)

This section contains 2 groups of questions. Each question has 4 choices (A), (B), (C) and (D)for its answer, out of which ONLY ONE is correct.

(+3, -1)

A person wants to roll a solid non-conducting spherical ball of mass m and radius r on a surface

whose coefficient of static friction is . He placed the ball on the surface wrapped with n turns ofclosely packed conducting coils of negligible mass at the diameter. By some arrangement he is able

to pass a current i through the coils either in the clockwise direction or in the anti-clockwise

direction. A constant horizontal magnetic field B

is present throughout the space as shown in the fig.

(Assume is large enough to help rolling motion)

iB

x

y

20. If current i is passed through the coils the maximum torque in the coil is

(a) nir 2 B k̂ (b) nir 2B ˆ j (c) nir 2B ˆ j (d) nir 2B k̂

21. Angular acceleration of the ball after it has rotated through an angle (< 180o), is

(a)5

7

niB

m

cos (b)

2

5

niB

m

cos (c)

7

5

niB

m

cos (d)

5

2

niB

m

cos



ANDHERI / BORIVALI / DADAR / CHEMBUR / THANE / MULUND/ NERUL / POWAI

TOPICS:EMI PAPER I(ANSWER KEY)

1. b 2. b 3. c 4. d 5. d

6. b 7. d 8. d 9. c 10. c

11. a, c 12. a, b, d 13. d 14. a, b, c 15. a, b, d

16. b, c 17. a, b, c, d 18. B 19. c 20. a

21. a



EMI PAPER I Solution

1. (b)

t

NBAe

)cos(cos 12

1.0

)0cos180(cos10703.02000 4

V e 84

2. (b)

Rt

W W n

t R

N

R

ei

5

)()( 1212

3. (c)

vl Bev. 1

3600

1000180102.0 4

V 310

4. (d)

emf due to motion of AB = B V

5. (d)

Given 23st 4t 2

d

emf 6t 4dt

t 2

d 16Vdt

6. (b)

t

A B B N e

cos)( 12

3

22

102

0cos)103()10.035.0(50

o V 7.17 .

7. (d)

is increasing in one loop and decreasing in other.

8. (d)

Conductor cuts the flux only when, if it moves in the direction of M .

9. (c)

22 )1.0(1021.02

1

2

1 r Be V

210



10. (c)

EMF is induced due to coil

11. (A, C)

12. (A, B, D)

(D), (A) conservation of e nergy

(B) excess energy shows in kinetic energy.

13. (d)

The magnitude of induced emf

d e N

dt

d BAe N

dt

Time interval dt, depends on the speed with which the magnet is moved.

Therefore, the induced emf is independent of the resistance of the coi l.

14. (a, b, c)

Statement (a) is correct. This follows from Lenz’s law

Statement (b) is correct. The sparking is caused because a large induced emf is developed at the

breaking of the circuit.

Statement (c) is correct. A coil offers no reactance to direct currents, i.e. inductance plays no role in

dc circuits. Hence there will be no change in the brightness of the bulb when an iron core is inserted

in the coil.

Statement (d) is incorrect. The coil will offer reactance L to alternating current. When an iron core

is inserted in the coil the inductance L increases due to increase in flux, hence the reactance of the

coil increases, causing a decrease in current in the circuit. As a result the brightness of the bulb will

be reduced.

15. (a, b, d)

The dimensions nof L and

1

C are the same as those of resistance, where = 2v.

16 (b, c)

3 3dI d| e| L (10 10 ) (2 8t) 80 10 80mV

dt dt

Power P = eI = (80 10 –3) (2 + 8t)

Power at t = 1 s is (80 10 –3) (2 + 8) = 0.8 W



Power at t = 2s is (80 10 –3) (2 + 16) = 1.44 W.

So the correct choice are (b & c)

17. (a, b, c, d)

From = LI, the SI unit of L is weber/ampere

From |e| = LdI

dt, the SI unit of L is

volt second/ampere

From 21U LI

2 , the SI unit of L is

Joule/(ampere)2

Since ohm = volt/ampere, volt second/ampere = ohm second. Hence all the four choices are correct.

18. (a)

= B

= ni (r 2) ˆ ˆ j Bi

= nir 2B k̂

19. (a)

B cosfr = I ……(A)

f = macm = m r ……(B)

=5 niB

cos7 m

20. (0)

2B A AR B cos90º 0

21. (5)

max 0 0

max max

d d MI sin t MI 5volts

dt dt

B

r

f

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