Alternating Current PYQs Set 3 (PDF)

Set 3 of 10 · Questions 61-90 of 290

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Mere Teacher · Previous Year Questions JEE Main Physics · Alternating Current · Set 3 (Q61-90)
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61. $A series LCR circuit has L = 0.01 H, R = 10 Ω and C = 1 μ F and it is connected to ac voltage of amplitude (V_{m}) 50 V. At frequency 60% lower than resonant frequency, the amplitude of current will be approximately:$ (1) $466mA$ (2) $312mA$ (3) $238mA$ (4) $196mA$ 62. $The LC parallel resonant circuit$ (1) $has a very high impedance$ (2) $has a very high current$ (3) $acts as resistance of very low value$ (4) $has zero impedance$ 63. $The instantaneous values of alternating current and voltages in a circuit are given as i = \frac{1}{2} sin (100 πt) ampe r e = \frac{1}{2} sin (100 πt + π /3) Vol t The average power in Watts consumed in the circuit is:$ (1) $\frac{1}{4}$ (2) $\frac{3}{4}$ (3) $\frac{1}{2}$ (4) $\frac{1}{8}$ 64. $A circuit connected to an ac source of emf e_{0} sin (100 t) with t in seconds, gives a phase difference of \frac{π}{4} between the emf e and current i . Which of the following circuits will exhibit this?$ (1) $RL circuit with R = 1 kΩ and L = 10 mH$ (2) $RL circuit with R = 1 kΩ and L = 1 mH$ (3) $RC circuit with R = 1 kΩ and C = 1 μF$ (4) $RC circuit with R = 1 kΩand C = 10 μF$ 65. $A multimeter reads a voltage of a certain A.C. source as 100 V . What is the peak value of voltage of A.C. source?$ (1) $141.4 V$ (2) $200 V$ (3) $400 V$ (4) $100 V$ 66. $An e.m.f. E = 4 cos (1000 t) volt is applied to an LR circuit of inductance 3 mH and resistance 4Ω . The maximum current in the circuit is$ (1) $\frac{4}{7} A$ (2) $1.0 A$ (3) $\frac{4}{7} A$ (4) $0.8 A$ 67. $The average power dissipated in A.C. circuit is 2 watt. If a current flowing through a circuit is 2 A and impedance is 1Ω, what is the power factor of the A.C. circuit?$ (1) $0$ (2) $0.5$ (3) $\frac{1}{2}$ (4) $1$ 68. $For a series LCR circuit at resonance, the statement which is not true is$ (1) $wattless current is zero$ (2) $power factor is zero$ (3) $peak energy stored by a capacitor = peak energy stored by an inductor$ (4) $average power = apparent power$ 69. $A 100Ω resistance and a capacitor of 100Ω reactance are connected in series across a 220 V source. When the capacitor is 50 % charged, the peak value of the displacement current is [NEET 2016]$ (1) $2.2 A$ (2) $11 A$ (3) $4.4 A$ (4) $112 A$ 70. $In the series LCR circuit, the power dissipation is through$ (1) $R$ (2) $L$ (3) $C$ (4) $both L and C$ 71. $A 0.07 H inductor and a 12 Ω resistor are connected in series to a 220V, 50Hz ac source. The approximate current in the circuit and the phase angle between current and source voltage are respectively. [Take π as \frac{22}{7}]$ (1) $8.8A and tan^{- 1} (\frac{11}{6})$ (2) $88A and tan^{- 1} (\frac{11}{6})$ (3) $0.88A and tan^{- 1} (\frac{11}{6})$ (4) $8.8A and tan^{- 1} (\frac{6}{11})$ 72. $A sinusoidal earner voltage is amplitude modulated. The resultant amplitude modulated wave has maximum and minimum amplitude of 120 V and 80 V respectively. The amplitude of each sideband is:$ (1) $15V$ (2) $10 V$ (3) $20 V$ (4) $5V$ 73. $An alternating current is given by i = i_{1} sin ωt + i_{2} cos ωt . The r.m.s. current is given by$ (1) $\frac{i _{1}^{2} + i _{2}^{2}}{2}$ (2) $\frac{i _{1} + i _{2}}{2}$ (3) $\frac{i _{1}^{2} - i _{2}^{2}}{2}$ (4) $\frac{i _{1} - i _{2}}{2}$ 74. $A series L - C - R circuit containing 5.0 H inductor, 80 μF capacitor and 40Ω resistor is connected to 230 V variable frequency AC source. The angular frequencies of the source at which power transferred to the circuit is half the power at the resonant angular frequency are likely to be [NEET 2021]$ (1) $25 rad/s and 75 rad / s$ (2) $50 rad / s and 25 rad/s$ (3) $46 rad / s and 54 rad / s$ (4) $42 rad / s and 58 rad / s$ 75. $Given below are two statements: Statement I: Maximum power is dissipated in a circuit containing an inductor, a capacitor and a resistor connected in series with an AC source, when resonance occurs. Statement II: Maximum power is dissipated in a circuit containing pure resistor due to zero phase difference between current and voltage. In the light of the above statements, choose the correct answer from the options given below:$ (1) $Statement I is false but Statement II is true$ (2) $Both Statement I and Statement II are true$ (3) $Statement I is true but Statement II is false$ (4) $Both Statement I and Statement II are false$ 76. $In a series L - C - R circuit, the inductance L is 10 mH, capacitance C is 1 μF and resistance R is 100Ω . The frequency at which resonance occurs is [NEET 2023]$ (1) $15.9 kHz$ (2) $1.59 rad / s$ (3) $1.59 kHz$ (4) $15.9 rad / s$ 77. $An L - C circuit contains 196 pF capacitor and a 441 μH inductor. The frequency of electromagnetic radiation emitted by antenna coupled to the L- C circuit is$ (1) $7.96 \times 10^{5} Hz$ (2) $54.1 \times 10^{5} Hz$ (3) $79.6 \times 10^{5} Hz$ (4) $5.41 \times 10^{5} Hz$ 78. $Given below are two statements: Statement I: In an LCR series circuit, current is maximum at resonance. Statement II: Current in a purely resistive circuit can never be less than that in a series LCR circuit when connected to same voltage source. In the light of the above statements, choose the correct from the options given below:$ (1) $Statement I is false but Statement II is true$ (2) $Statement I is true but Statement II is false$ (3) $Both Statement I and Statement II are true$ (4) $Both Statement I and Statement II are false$ 79. $The power factor of an R - L circuit is \frac{1}{2} . If the frequency of AC is doubled power factor will now be$ (1) $\frac{1}{3}$ (2) $\frac{1}{5}$ (3) $\frac{1}{7}$ (4) $\frac{1}{11}$ 80. $The peak voltage of the AC source is equal to [NEET 2022]$ (1) $the rms value of the AC source$ (2) $2 times the rms value of the AC source$ (3) $1/ 2 times the rms value of the AC source$ (4) $the value of voltage supplied to the circuit$ 81. $In an a.c circuit, the instantaneous e.m.f and current are given by e = 100 sin 30 t i = 20 sin (30 t - \frac{π}{4}) In one cycle of a.c the average power consumed by the circuit and the wattless current are, respectively:$ (1) $\frac{50}{2}, 0$ (2) $50,0$ (3) $50,10$ (4) $\frac{1000}{2}, 10$ 82. $LCR circuit, the resonance frequency of circuit increases two times of the initial circuit by changing C and C^{’} and R from 100Ω to 400Ω, while the inductance was kept the same. The ratio C / C^{’}, is$ (1) $2$ (2) $8$ (3) $16$ (4) $4$ 83. $For a given series LCR circuit it is found that maximum current is drawn when value of variable capacitance is 25 nF . If resistance of 200Ω and 100 mH inductor is being used in the given circuit. The frequency of ac source is ______\times 10^{3} Hz . (given π^{2} = 10)$ 84. $An inductor of reactance 100Ω, a capacitor of reactance 50Ω, and a resistor of resistance 50Ω are connected in series with an AC source of 10 V, 50 Hz . Average power dissipated by the circuit is ____ w.$ 85. $An oscillating LC circuit consists of a 75 mH inductor and a 1.2 μ F capacitor. If the maximum charge to the capacitor is 2.7 μ C. The maximum current in the circuit will be_______mA.$ 86. $An inductor of inductance 2 μ H is connected in series with a resistance, a variable capacitor and an AC source of frequency 7 kHz. The value of capacitance for which maximum current is drawn into the circuit is \frac{1}{x} F_{,} where the value of x is______. (Take π = \frac{22}{7})$ 87. $In a series LR circuit power of 400 W is dissipated from a source of 250V, 50 Hz. The power factor of the circuit is 0.8. In order to bring the power factor to unity, a capacitor of value of C is added in series to the L and R. Taking the value of C as (\frac{n}{3 π}) μF, then value of n is:$ 88. $An inductor of 10mH is connected to a 20V battery through a resistor of 10 kΩ and a switch After a long time, when maximum current is set up in the circuit, the current is switched off. The current in the circuit after 1 μs is \frac{x}{100} . Then is equal to (Take e^{- 1} = 0.37)$ 89. $An inductor of 0.5 mH, a capacitor of 200 µF and a resistor of 2 π, are connected in series with a 220 V ac source. If the current is in phase with the emf, the frequency of ac source will be x 1 0^{2} Hz.$ 90. $An inductor of self inductance 1 H is connected in series with a resistor of 100 π ohm and an ac supply of 100 π volt, 50 Hz. Maximum current flowing in the circuit is _______ A.$