Electromagnetic Induction PYQs Set 4 (PDF)

Set 4 of 11 · Questions 91-120 of 319

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Mere Teacher · Previous Year Questions JEE Main Physics · Electromagnetic Induction · Set 4 (Q91-120)
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91. $An aeroplane is travelling horizontally towards west with a speed of 540 kmh^{- 1} . The wing span of the plane is 20 m . If the horizontal component of the earth's magnetic field at the location is 2.5 3 \times 10^{- 4} T and the dip angle is 30^{\circ}, the potential difference developed between the ends of the wing is$ (1) $1 V$ (2) $1.5 V$ (3) $0.75 V$ (4) $0.5 V$ 92. $In a pair of adjacent coils if the current in one coil changes from 10 A to 2 A in a time 0.2 s, an emf of 120 V is induced in another coil. The mutual inductance of the pair of the coils is$ (1) $2 H$ (2) $3 H$ (3) $6 H$ (4) $9 H$ 93. $Assertion (A): It is more difficult to push a magnet into a coil with more number of turns. Reason (R): The emf induced in a coil opposes the motion of a magnet when it is moved towards the coil.$ (1) $A is false, R is true$ (2) $Both A and R are true. R is correct explanation of A$ (3) $A is true, R is false$ (4) $Both A and R are true. R is not correct explanation of$ 94. $A circular coil has 100 turns, radius 3 cm and resistance 4Ω . The coil is co-axial with a solenoid of 200 turns / cm and diameter 4 cm . If the solenoid current is decreased from 2 A to zero in 0.04 s, then the current induced in the coil is$ (1) $4 π^{2} mA$ (2) $8 πmA$ (3) $30.3 mA$ (4) $45.5 mA$ 95. $Two coils ‘P’ and ‘Q’ are separated by some distance. When a current of 3A flows through coil 'P', a magnetic flux of 10^{- 3} Wb passes through 'Q'. No current is passed through 'Q'. When no current passes through 'P' and a current of 2A passes through 'Q', the flux through 'P' is?$ (1) $6.67 \times 10^{- 4} Wb$ (2) $3.67 \times 10^{- 3} Wb$ (3) $6.67 \times 10^{- 3} Wb$ (4) $3.67 \times 10^{- 4} Wb$ 96. $The magnetic flux through a loop of resistance 10Ω is varying according to the relation φ = 6 t^{2} + 7 t + 1, where φ is in milliweber, time is in second then at time t = 1 s the induced e.m.f. is$ (1) $12 mV$ (2) $7 mV$ (3) $19 mV$ (4) $19 V$ 97. $Physically, the self-inductance plays the role of$ (1) $inertia$ (2) $kinetic energy$ (3) $potential energy$ (4) $velocity$ 98. $The coefficient of mutual inductance between the primary and the secondary coil of a transformer is 0.2 H . When the current in the primary changes by 5 As^{- 1}, then the induced emf in the secondary will be$ (1) $5 V$ (2) $1 V$ (3) $25 V$ (4) $10 V$ 99. $The self induced emf of a coil is 25 volts. When the current in it is changed at uniform rate from 10 A to 25 A is 1s, the change in the energy of the inductance is:$ (1) $740 J$ (2) $437.5 J$ (3) $540 J$ (4) $637.5 J$ 100. $Two coils of self inductance 2 mH and 8 mH are placed so close together that the effective flux in one coil is completely linked with the other. The mutual inductance between these coils is$ (1) $16 mH$ (2) $10 mH$ (3) $6 mH$ (4) $4 mH$ 101. $A coil of resistance 50Ω is connected across a 5.0 V battery. If the current in the coil is found to be 50 mA after time t = 0.1 s battery is connected, then the inductance of the coil is$ (1) $\frac{5}{ln ( 2 )}$ (2) $10 ln (2)$ (3) $5 e^{4}$ (4) $\frac{10}{e ^{4}}$ 102. $The magnetic flux linked with a coil varies as φ = 3 t^{2} + 4 t + 9 . The magnitude of the emf induced at t = 2 seconds is$ (1) $8 V$ (2) $16 V$ (3) $32 V$ (4) $64 V$ 103. $A conducting circular loop made a thin wire, has area 3.5 \times 10^{- 3} m^{2} and resistance 10Ω. It is placed perpendicular to a time dependent magnetic field B (t) = (0.4 T) sin (50 πt) . The field is uniform in space. Then the net charge flowing through the loop during t = 0 s and t = 10 ms is close to:$ (1) $14 mC$ (2) $7 mC$ (3) $0.14 mC$ (4) $6 mC$ 104. $A copper disc of radius 0.1 m rotates about an axis passing through its centre and perpendicular to its plane with 10 revolutions per second in a uniform transverse magnetic field of 0.1 T . The emf induced across the radius of the disc is$ (1) $\frac{π}{10} V$ (2) $\frac{2 π}{10} V$ (3) $10 πmV$ (4) $20 πmV$ 105. $The self inductance ' L' of a solenoid of length ' l' and area of cross-section ' A' with a fixed number of turns ' N, increases as$ (1) $l decreases and A increases$ (2) $both l and A decrease$ (3) $both l and A increase$ (4) $l increases and A decreases.$ 106. $In an ac circuit an alternating voltage 2002 sin 100 t volts is connected to a capacitor of capacity 1 μF . The r.m.s. value of the current in the circuit is$ (1) $10 mA$ (2) $100 mA$ (3) $200 mA$ (4) $20 mA$ 107. $A long solenoid of diameter 0.1 m has 2 \times 1 0^{4} turns per meter. At the centre of the solenoid, a coil of 100 turns and radius 0.01 m is placed with its axis coinciding with the solenoid axis. The current in the solenoid reduces at a constant rate to 0 A from 4 A in 0.05 s . Ifthe resistance ofthe coil is 10 π^{2} Ω, the total charge flowing through the coil during this time is$ (1) $16 μC$ (2) $32 μC$ (3) $16 πμC$ (4) $32 πμC$ 108. $How many meters of a thin wire are required to design a solenoid of length 1m and L = 1mH? Assume cross-sectional diameter is very small-$ (1) $10 m$ (2) $40 m$ (3) $70 m$ (4) $100 m$ 109. $Power dissipated in an LCR series circuit connected to an A.C. source of emf ϵ is$ (1) $\frac{ϵ ^{2} R ^{2} + ( Lω - \frac{1}{Cω} ) ^{2}}{R}$ (2) $\frac{ϵ ^{2} [ R ^{2} + ( Lω - \frac{1}{Cω} ) ^{2}}{R}$ (3) $\frac{ϵ ^{2} R}{R ^{2} + ( Lω - \frac{1}{Cω} ) ^{2}}$ (4) $\frac{ϵ ^{2} R}{[ R ^{2} + ( Lω - \frac{1}{Cω} ) ^{2}}$ 110. $The core of a transformer is laminated because$ (1) $ratio of voltage in primary and secondary may be increased$ (2) $energy losses due to eddy currents may be minimized$ (3) $the weight of the transformer may be reduced$ (4) $rusting of the core may be prevented.$ 111. $The mutual inductance (M) of the two coils is 3 H, The self inductances of the coils are 4 H and 9 H respectively. The coefficient of coupling between the coils is$ (1) $0.3$ (2) $0.4$ (3) $0.5$ (4) $0.6$ 112. $An series L - C - R circuit is connected to a source of A . C . current. At resonance, the phase difference between the applied voltage and the current in the circuit, is$ (1) $π$ (2) $zero$ (3) $π /4$ (4) $π /2$ 113. $A coil of 40 henry inductance is connected in series with a resistance of 8 ohm and the combination is joined to the terminals of a 2 volt battery. The time constant of the circuit is$ (1) $5 seconds$ (2) $1/5 seconds$ (3) $40 seconds$ (4) $20 seconds.$ 114. $The potential differences across the resistance, capacitance and inductance are 80 V, 40 V and 100 V respectively in an L - C - R circuit. The power factor of this circuit is$ (1) $0.4$ (2) $0.5$ (3) $0.8$ (4) $1.0$ 115. $An infinitely long cylinder is kept parallel to a uniform magnetic field B directed along positive z -axis. The direction of induced current on the surface of cylinder as seen from the z -axis will be$ (1) $clockwise of the +ve z -axis$ (2) $anticlockwise of the +ve z -axis$ (3) $zero$ (4) $along the magnetic field$ 116. $If N is the number of turns in a coil, the value of self inductance varies as$ (1) $N^{0}$ (2) $N$ (3) $N^{2}$ (4) $N^{- 2}$ 117. $Regarding self-inductance: (A) The self-inductance of the coil depends on its geometry. (B) Self-inductance does not depend on the permeability of the medium. (C) Self-induced e.m.f. opposes any change in the current in a circuit. (D) Self-inductance is electromagnetic analogue of mass in mechanics. (E) Work needs to be done against self-induced e.m.f. in establishing the current. Choose the correct answer from the options given below:$ (1) $A, B, C, E only$ (2) $B, C, D, E only$ (3) $A, C, D, E only$ (4) $A, B, C, D only$ 118. $If 2.5 \times 10^{- 6} N average force is exerted by a light wave on a non-reflecting surface of 30 cm^{2} area during 40 minutes of time span, the energy flux of light just before it falls on the surface is_______W / cm^{2} (Round off to the Nearest Integer) (Assume complete absorption and normal incidence conditions are there)$ 119. $Two coils have mutual inductance 0.002 H . The current changes in the first coil according to the relation i = i_{0} sin ωt, where i_{0} = 5 A and ω = 50 πrad / s . The maximum value of emf in the second coil is \frac{π}{α} V . The value of α is$ 120. $Two concentric circular coils with radii 1 cm and 1000 cm and number of turns 10 and 200 respectively are placed coaxially with centers coinciding. The mutual inductance of this arrangement will be_____x 1 0^{- 8} H. (Take, π^{2} = 10)$