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 70 cm 2 . The magnetic field perpendicular to the plane of the coil is o 0. 3Wb / m 2 and takes 0.1 sec to rotate through 180 . The value of the induced e.m.f. will be (a) 8 . 4 V (b) 84 V (c) 42 V (d) 4 .2 V
2.
A coil having n turns and resistance R is connected connected with a galvanometer of resistance resistance 4 R . 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)
(c)
W 2 W 1
5 Rnt
(W 2 W 1 ) Rnt
(b)
(d)
n(W 2 W 1 )
5 Rt n(W 2 W 1 ) Rt
3.
Two rails of a railway track insulated insulated from each other and the ground are connected connected to a milli milli voltmeter. What is the reading of voltmeter, when a train travels with a speed of 180 km/hr along along the 4 2 track. Given that the vertical component of earth's magnetic field is 0.2 10 weber / m and the rails are separated by 1 metre (a) 10 2 volt (b) 10 4 volt (c) 10 3 volt (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 out side the field, as shown in figure. The induced indu ced e.m.f. is (a) Zero B C (b) RvB v l (c) VBl/R (d) VBl
5.
A
D
If electric flux varies according to 3t 2 4t 2 , find emf at t = 2s. (a) 22 V (c) 20 V
6.
(b) 18 V (d) 16 V.
A 50 turns circular coil has a radius of
3 cm ,
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) 1.77 volts (b) 17 .7 volts (c) 177 volts (d) 0.177 volts Head Office: Andheri: 26245223
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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 B
N
(a) (b) (c) (d) 8.
S
Current is induced only in A& not in B Induced currents in A& B are in the same direction Current is induced only in B and not in A Induced currents in A& B are in opposite directions
An electric potential difference will be induced between the ends of the conductor shown in the diagram, when the conductor moves in the direction M L N
Q S
P
(a)P 9.
(c) L
(d) M
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) (c)
10.
(b) Q
10
V
10 2 V
(b) (d)
2 10
V
2 10 2 V
In the following circuit, the bulb will become suddenly bright if (a) Contact is made or broken (b) Contact is made made (c) Contact is broken (d) Won't become bright bright at all
SECTION-II This section contains 7 contains 7 multiple choice questions. Each 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 having an inductance inductance 'L' is is kept kept in a magnetic magnetic field field which which is varying 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 p laced in a uniform constant magnetic field B perpendicular to the plane of the rails as shown s hown 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) If applied external force is doubled than a part p art of external power increases the velocity of rod. (c) Lenz’s Law is not satisfied if the rod is accelerated by b y external external force (d) If resistance R is doubled then power po wer required to maintain velocity becomes half. 13 .
Whenever a magnet magnet is moved moved either either towards or away away from from a conducting coil, an emf is induced, the the magnitude of which is independent of (a) the strength of the the magnetic field (b) the speed with which which the magnet is moved (c) the resistance resistance of the coil (d) the area of cross-section of the the coil.
14.
Choose the correct statements statements from the following. (a) A circuit consisting consisting of an inductance inductance is carrying a current. When the circuit is suddenly switched switched off, the direction of the induced current will be the same as that of the t he main current (b) Sparking is observed 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 connected in series with a bulb and this combination is connected to a dc source. When 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 connected to an ac source. When an iron core is inerted in the t he coil, the brightness of the bulb will increase.
15.
L, C and R respectively represent inductance, inductance, capacitance and resistance. Which of the the following following combinations have the dimensions of frequency? (a)
R L
(b)
1
(c)
RC
R LC
(d)
1 LC
16.
In a coil coil of self inductance 10 mH, mH, the current I (in ampere) ampere) varies varies with time t(in second) as i = 8t + 2 amp (a) The induced emf increases increases with time (b) The induced induced emf has a constant value value of 80 mV (c) The power supplied supplied to the inducto inductorr at t = 1 s is 0.8W 0.8W (d) The power supplied supplied to the inductor inductor at t = 2 s is 1.6W 1.6W
17.
The SI unit of inductance (which is henry) can also be written as (a) weber/ampere (b) volt second/ampere 2 (c) joule/(ampere) (d) ohm second
18.
A circular loop of radius R carrying current I lies lies in x-y plane with its centre at origin. The total magnetic flux through t hrough x-y plane is kR. Find the value of k. (a) 1
19.
(b) 0
(c) 2
(d) 4
Two coils have a mutual inductance 0.005 H . The current changes in the first coil according to equation I I 0 sin t , where I 0 10 A and = = 100 radian/sec. The maximum value of e.m.f. in the
second coil is k volts. Find the value of o f k. (a) 2
(b) 4
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(c) 5
(d) 3
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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 of closely 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) mot ion) y
i
B
x
20.
If current i is passed through the coils the maximum torque in the coil is ˆ ˆ (a) nir 2 B k (b) nir 2B jˆ (c) nir 2B jˆ (d) nir 2B k
21.
Angular acceleration of the ball after it has rotated through an angle (< 180 ), is 5 niB 2 niB 7 niB 5 niB (a) cos (b) cos (c) cos (d) cos 7 m 5 m 5 m 2 m
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o
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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
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EMI PAPER I Solution
1.
(b) e
NBA (cos 2
cos 1 )
t
2000 0. 3 70 10 4
e 84
2.
e R
N ( 2 1 ) n(W 2 W 1 ) R t 5 Rt
(c) e
4.
V
(b) i
3.
(cos 180 cos 0 ) 0.1
180 1000 Bv .vl 0. 2 10 4 1 10 3 V 3600
(d) emf due to motion of AB = BV
5.
(d) Given 3st 2 4t 2
emf
d 16V dt t 2
6.
(b) e
7.
d 6t 4 dt
N ( B 2
B1 ) A cos t
50 (0. 35 0. 10 ) (3 10 2 )2 cos 0 o 17 .7 2 10 3
V
.
(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) e
1 1 2 0 .1 2 10 (0 .1)2 10 2 V B r r 2 2
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 e N
d dt
e N
d BA 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 T his 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. 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
16
1 are the same as those of resistance, where = 2v. C
(b, c) | e | L
dI d 8t ) 80 80 103 80mV (10 103 ) (2 8t 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| = L
dI , the SI unit of L is dt
volt second/ampere 1 2
From U LI2 , 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) jˆ Biˆ ˆ = nir 2B k
19.
(a) B
r f
B cosfr = I ……(A) f = macm = m r ……(B)
=
5 niB cos 7 m
20. (0)
B A AR 2 B co cos 90º 0 21. (5)
max
d d s in t MI0 5volts MI0 si dt max dt max