Alternating Current PYQs Set 2 (PDF)

Set 2 of 10 · Questions 31-60 of 290

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Mere Teacher · Previous Year Questions JEE Main Physics · Alternating Current · Set 2 (Q31-60)
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31. $An inductor and a resistor are connected in series to an ac source. If the power factor of the circuit is 0.5 , the ratio of the resistance of the resistor and the reactance of the inductor is$ (1) $1 : 1$ (2) $1 : 2$ (3) $1 : 3$ (4) $1 : 2$ 32. $A resistor of resistance 40Ω, a capacitor of capacitive 20Ω and an inductor of inductive reactance 50Ω are connected in series to an ac source of 100 V . The current through the circuit is$ (1) $0.5 A$ (2) $1 A$ (3) $1.5 A$ (4) $2 A$ 33. $The equation of current in a purely inductive circuit is 5 sin(49 π -30°). If the inductance is 30 mH then the equation for the voltage across the inductor, will be: (Let π = \frac{22}{7})$ (1) $147sin(49 π t - 30°)$ (2) $1.47sin(49 π t + 60°)$ (3) $23.1sin(49 π t - 30°)$ (4) $23.1sin(49 π t + 60°)$ 34. $A series combination of resistor (R), capacitor (C) is connected to an A.C. source of angular frequency ' ω'. Keeping the voltage same, if the frequency is changed to \frac{ω}{3}, the current becomes half of the original current. Then the ratio of the capacitive reactance and resistance at the former frequency is$ (1) $0.6$ (2) $3$ (3) $2$ (4) $6$ 35. $A coil is suspended in a uniform magnetic field, with the plane of the coil parallel to the magnetic lines of force. When a current is passed through the coil it starts oscillating; it is very difficult to stop. But if an aluminium plate is placed near to the coil, it stops. This is due to:$ (1) $developement of air current when the plate is placed.$ (2) $induction of electrical charge on the plate$ (3) $shielding of magnetic lines of force as aluminium is a paramagnetic material.$ (4) $Electromagnetic induction in the aluminium plate giving rise to electromagnetic damping.$ 36. $An ideal transformer has a turns ratio of 10 . When the primary is connected to 220 V, 50 Hz ac source, the power output is$ (1) $10 times the power input$ (2) $\frac{1}{10} th the power input$ (3) $equal to power input$ (4) $zero$ 37. $A inductor 20 mH a capacitor 100 µF and a resistor 50 Ω are connected in series across a source of emf, V = 10 sin 314 t. The power loss in the circuit is:$ (1) $0.79 W$ (2) $1.13 W$ (3) $2.74 W$ (4) $0.43 W$ 38. $A coil has inductance of 0.4 H and resistance of 8Ω . It is connected to an AC source with peak emf 4 V and frequency \frac{30}{π} Hz . The average power dissipated in the circuit is$ (1) $1 W$ (2) $0.5 W$ (3) $0.3 W$ (4) $0.1 W$ 39. $Given below are two statements: Statement I: When the frequency of an AC source in a series LCR circuit increases, the current in the circuit first increases, attains a maximum value and then decreases. Statement II: In a series LCR circuit, the value of power factor at resonance is one. In the light of given statements, choose the most appropriate answer from the options given below.$ (1) $Statement I is incorrect but Statement II is true$ (2) $Both Statement I and Statement II are false$ (3) $Both Statement I and Statement II are true$ (4) $Statement I is correct but Statement II is false$ 40. $In a series LCR circuit R = 200 Ω and the voltage and the frequency of the main supply is 220 V and 50 Hz respectively. On taking out the capacitance from the circuit the current lags behind the voltage by 30 ° . On taking out the inductor from the circuit the current leads the voltage by 30 ° . The power dissipated in the LCR circuit is$ (1) $305 W$ (2) $210 W$ (3) $Zero W$ (4) $242 W$ 41. $In which of the following devices, the eddy current effect is not used?$ (1) $electric heater$ (2) $induction furnace$ (3) $magnetic braking in train$ (4) $electromagnet$ 42. $A transformer is used to light 100 W - 110 V lamp from 220 V mains. If the main current is 0.5 A, the efficiency of the transformer is$ (1) $95 %$ (2) $99 %$ (3) $90 %$ (4) $96 %$ 43. $Which of the following represents the variation of inductive reactance (X_{L}) with the frequency of voltage source (v) ?$ (1) (2) (3) (4) 44. $A series AC circuit containing an inductor (20 mH), a capacitor (120 μ F) and a resistor (60Ω) is driven by an AC source of \frac{24 V}{50 Hz} . The energy dissipated in the circuit in 60 s is:$ (1) $3.39 \times 10^{3} J$ (2) $5.65 \times 10^{2} J$ (3) $5.17 \times 10^{2} J$ (4) $2.26 \times 10^{3} J$ 45. $An AC voltage V = 20 sin 200 πt is applied to a series LCR circuit which drives a current I = 10 sin (200 πt + \frac{π}{3}) . The average power dissipated is:$ (1) $21.6 W$ (2) $200 W$ (3) $173.2 W$ (4) $50 W$ 46. $A series LCR circuit is connected to an alternating source of emf E. The current amplitude at resonant frequency is I_{0} . If the value of resistance R becomes twice of its initial value then amplitude of current at resonance will be$ (1) $2 I_{0}$ (2) $I_{0}$ (3) $\frac{I _{0}}{2}$ (4) $\frac{I _{0}}{2}$ 47. $A fully charged capacitor ' C' with initial charge ' Q_{0}' is connected to a coil of self inductance ' L' at t = 0 . The time at which the energy is stored equally between the electricity and the magnetic field is$ (1) $π LC$ (2) $2 π LC$ (3) $\frac{π}{4} LC$ (4) $LC$ 48. $An alternating current is given by I = I_{A} sin ωt + I_{B} cos ωt . The r.m.s current will be$ (1) $\frac{( I _{A} + I _{B} )}{2}$ (2) $\frac{I _{A}^{2} + I _{B}^{2}}{2}$ (3) $I_{A}^{2} + I_{B}^{2}$ (4) $\frac{I _{A}^{2} + I _{B}^{2}}{2}$ 49. $The average power dissipated in a pure inductor is$ (1) $V I^{2}$ (2) $zero$ (3) $\frac{1}{2} VI$ (4) $\frac{V I ^{2}}{4}$ 50. $Why 220 V AC is more dangerous than 220 V DC?$ (1) $The DC attracts$ (2) $Peak voltage for AC is much larger$ (3) $The body offers less resistance to AC$ (4) $Due to some other reason$ 51. $A capacitor of capacitance 10 μF is connected to an AC source and an AC ammeter. If the source voltage varies as V = 502 sin 100 t, the reading of the am meter is$ (1) $50 mA$ (2) $70.7 mA$ (3) $5.0 mA$ (4) $7.07 mA$ 52. $An inductor 20 mH, a capacitor 50 μF and a resistor 40Ω are connected in series across a source of emf V = 10 sin 340 t . The power loss in AC circuit is [NEET 2016]$ (1) $0.67 W$ (2) $0.76 W$ (3) $0.89 W$ (4) $0.51 W$ 53. $The rms value of conduction current in a parallel plate capacitor is 6.9 μ A. The capacity of this capacitor, if it is connected to 230 V ac supply with an angular frequency of 600 rad/s, will be:$ (1) $5 pF$ (2) $50 pF$ (3) $100pF$ (4) $200pF$ 54. $A capacitor, an inductor and an electric bulb are connected in series to an a.c. supply of variable frequency. As the frequency of the supply is increased gradually, then the electric bulb is found to$ (1) $increase in brightness$ (2) $decrease in brightness$ (3) $increase, reach a maximum and then decrease in brightness.$ (4) $show no change in brightness.$ 55. $Assertion: It is more difficult to move a magnet into a coil with more loops. Reason: This is because emf induced in each current loop resists the motion of the magnet.$ (1) $Both A and R are true and R is a correct explanation for A .$ (2) $Both A and R are true but R is not a correct explanation for A .$ (3) $A is true and R is false.$ (4) $A is false, R is true.$ 56. $A series LCR circuit is subjected to an ac signal of 200 V, 50 Hz . If the voltage across the inductor (L = 10 mH) is 31.4 V, then the current in this circuit is$ (1) $68 A$ (2) $63 A$ (3) $10 A$ (4) $10 mA$ 57. $Primary side of a transformer is connected to 230 V, 50 Hz supply. Turns ratio of primary to secondary winding is 10 : 1 . Load resistance connected to secondary side is 46Ω . The power consumed in it is :$ (1) $12.5 W$ (2) $10.0 W$ (3) $11.5 W$ (4) $12.0 W$ 58. $A capacitor of capacitance 500 μ F is charged completely using a dc supply of 100 V. It is now connected to an inductor of inductance 50 mH to form an LC circuit. The maximum current in LC circuit will be______A.$ 59. $A telegraph line of length loo km has a capacity of 0.01 μ /km and it carries an alternating current at 0.5 kilo cycle per second. If minimum impedance is required, then the value of the inductance that needs to be introduced in series is________mH. (ifπ = 10)$ 60. $In an LCR series circuit, an inductor 30mH and a resistor 1Ω are connected to an AC source of angular frequency 300 rad/s. The value of capacitance for which, the current leads the voltage by 4 5^{0} is \frac{1}{x} \times 1 0^{- 3} F . Then the value of x is ___.$