Q36. 200 \(\Omega\) resistance and 1H inductance are connected in series with an A.C. circuit. The frequency of the source is \(\frac{200}{2\pi}\text{ Hz}\). Then phase difference in between V and I will be :-

1. \(30^{\circ}\)
2. \(60^{\circ}\)
3. \(45^{\circ}\)
4. \(90^{\circ}\)

Correct Answer: C. \(45^{\circ}\)

Q37. Impedance of the following circuit will be :

[Circuit Diagram: Resistor \(R = 200\ \Omega\) in series with Inductive Reactance \(X_L = 150\ \Omega\)]

1. \(150\ \Omega\)
2. \(200\ \Omega\)
3. \(250\ \Omega\)
4. \(340\ \Omega\)

Correct Answer: C. \(250\ \Omega\)

Q38. In showing figure find \(V_{R}\):

[Circuit Details: Resistor \(V_R = ?\) in series with Inductor \(V_L = 176\text{ V}\), connected across a \(220\text{ V}\) AC supply]

1. 132 V
2. 396 V
3. 185 V
4. \(\sqrt{220\times176}\text{ V}\)

Correct Answer: A. 132 V

Q39. If alternating current of 60 Hz frequency is flowing through inductance of \(L=1\text{ mH}\) and drop in \(\Delta V_{L}\) is 0.6 V then alternating current :-

1. \(\frac{1}{\pi}\text{ A}\)
2. \(\frac{5}{\pi}\text{ A}\)
3. \(\frac{50}{\pi}\text{ A}\)
4. \(\frac{20}{\pi}\text{ A}\)

Correct Answer: B. \(\frac{5}{\pi}\text{ A}\)

Q40. An inductance of 1 mH, a condenser of \(10\ \mu\text{F}\) and a resistance of \(50\ \Omega\) are connected in series. The reactance of inductor and condensers are same. The reactance of either of them will be :-

1. \(100\ \Omega\)
2. \(30\ \Omega\)
3. \(3.2\ \Omega\)
4. \(10\ \Omega\)

Correct Answer: D. \(10\ \Omega\)

Q41. L, C and R represent physical quantities inductance, capacitance and resistance respectively. The combination representing dimension of frequency is

1. \(LC\)
2. \((LC)^{-1/2}\)
3. \((\frac{L}{C})^{-1/2}\)
4. \(\frac{C}{L}\)

Correct Answer: B. \((LC)^{-1/2}\)

Q42. A circuit contains R, L and C connected in series with an A.C. source. The values of the reactances for inductor and capacitor are \(200\ \Omega\) and \(600\ \Omega\) respectively and the impedance of the circuit is \(Z_{1}\). What happens to the impedance of the same circuit if the values of the reactances are interchanged:-

1. The impedance will remain unchanged
2. The impedance will increase
3. The impedance will decrease
4. Information insufficient

Correct Answer: A. The impedance will remain unchanged

Q43. When \(V=100\sin\omega t\) is applied across a series (R-L-C) circuit. At resonance the current in resistance (\(R=100\ \Omega\)) is \(i=i_{0}\sin\omega t\), then power dissipation in circuit is:-

1. 50 W
2. 100 W
3. 25 W
4. Can’t be calculated

Correct Answer: A. 50 W

Q44. At resonance in a series LCR circuit, which of the following statements is true:-

1. Current in the circuit is maximum and phase difference between E and I is \(\pi/2\)
2. Current in the circuit is maximum and phase difference between E and I is zero
3. Voltage is maximum and phase difference between E and I is \(\pi/2\)
4. Current is minimum and phase difference between E and I is zero

Correct Answer: B. Current in the circuit is maximum and phase difference between E and I is zero

Q45. An alternating voltage is connected in series with a resistance r and an inductance L. If the potential drop across the resistance is 200 volt and across the inductance is 150 volt, the applied voltage:

1. 350 volt
2. 250 volt
3. 500 volt
4. 300 volt

Correct Answer: B. 250 volt

Q46. For a series R-L-C circuit :-
(a) Voltage across L and C differ by \(\pi\)
(b) Current through L and R are in same phase
(c) Voltage across R and L differ by \(\pi/2\)
(d) Voltage across L and current through C differ by \(\pi/2\)

1. a, b, c
2. b, c, d
3. c, d, a
4. All of the above

Correct Answer: D. All of the above

Q47. A series \(R-L-C\) (\(R=10\ \Omega\), \(X_{L}=20\ \Omega\), \(X_c=20\ \Omega\)) circuit is supplied by \(V=10\sin\omega t\) volt then power dissipation in circuit is :-

1. Zero
2. 10 watt
3. 5 watt
4. 2.5 watt

Correct Answer: C. 5 watt

Q48. The self inductance of the motor of an electric fan is 10 H. In order to impart maximum power at 50 Hz, it should be connected to a capacitance of :-

1. \(2\times10^{-6}\text{ F}\)
2. \(3\times10^{-6}\text{ F}\)
3. \(10^{-4}\text{ F}\)
4. \(10^{-6}\text{ F}\)

Correct Answer: D. \(10^{-6}\text{ F}\)

Q49. In a series resonant R-L-C circuit, if L is increased by 25% and C is decreased by 20%, then the resonant frequency will :-

1. Increases by 10%
2. Decreases by 10%
3. Remain unchanged
4. Increases by 2.5%

Correct Answer: C. Remain unchanged

Q50. The value of quality factor is :-

1. \(\frac{\omega L}{R}\)
2. \(\frac{\omega}{RC}\)
3. \(\sqrt{LC}\)
4. L/R

Correct Answer: A. \(\frac{\omega L}{R}\)

Q51. If value of R is changed in a series resonant LCR circuit with \(V_L = 10\text{ V}\) and \(V_C = 10\text{ V}\), then :-

1. Voltage across L remains same
2. Voltage across C remains same
3. Voltage across LC combination remains same
4. Voltage across LC combination changes

Correct Answer: C. Voltage across LC combination remains same

Q52. In a series LCR circuit voltage across resistor, inductor and capacitor are 1V, 3V and 2V respectively. At the instant t when the source voltage is given by \(V=V_{0}\cos\omega t\), the current in the circuit will be:-

1. \(I=I_{0}\cos(\omega t+\frac{\pi}{4})\)
2. \(I=I_{0}\cos(\omega t-\frac{\pi}{4})\)
3. \(I=I_{0}\cos(\omega t+\frac{\pi}{3})\)
4. \(I=I_{0}\cos(\omega t-\frac{\pi}{3})\)

Correct Answer: B. \(I=I_{0}\cos(\omega t-\frac{\pi}{4})\)

Q53. In an AC Circuit decrease in impedance with increase in frequency indicates that circuit has/have :-

1. Only resistance
2. Resistance & inductance
3. Resistance & capacitance
4. Resistance, capacitance & inductance

Correct Answer: C. Resistance & capacitance

Q54. In the given LCR circuit, the voltage across the terminals of a resistance and current will be :-
[Circuit Details: \(R = 50\ \Omega\), \(V_L = 400\text{ V}\), \(V_C = 400\text{ V}\), Supply = \(100\text{ V, 50 Hz}\)]

1. 400 V, 2 A
2. 800 V, 2 A
3. 100 V, 2 A
4. 100 V, 4 A

Correct Answer: C. 100 V, 2 A

Q55. Phase of current in LCR circuit :-

1. Is in the phase of potential
2. Leading from the phase of potential
3. Lagging from the phase of potential
4. Before resonance frequency, leading from the phase of potential and after resonance frequency, lagging from the phase of potential

Correct Answer: D. Before resonance frequency, leading from the phase of potential and after resonance frequency, lagging from the phase of potential

Q56. In LCR circuit, the voltage across the terminals of a resistance, inductance & capacitance are 40V, 30V & 60V, then the voltage across the main source will be :-

1. 130 volt
2. 100 volt
3. 70 volt
4. 50 volt

Correct Answer: D. 50 volt

Q57. For an alternating current of frequency \(\frac{500}{\pi}\text{ Hz}\) in L-C-R series circuit with \(L=1\text{ H}\), \(C=1\ \mu\text{F}\), \(R=100\ \Omega\), impedance is :-

1. 100 \(\Omega\)
2. \(100\sqrt{\pi}\ \Omega\)
3. \(100\sqrt{2\pi}\ \Omega\)
4. \(100\pi\ \Omega\)

Correct Answer: A. 100 \(\Omega\)

Q58. A sinusoidal A.C. current flows through a resistor of resistance R. If the peak current is \(I_{P}\), then the power dissipated is :-

1. \(I_p^2 R \cos \theta\)
2. \(\frac{1}{2} I_p^2 R\)
3. \(\frac{4}{\pi} I_p^2 R\)
4. \(\frac{1}{\pi^2} I_p^2 R\)

Correct Answer: B. \(\frac{1}{2} I_p^2 R\)

Q59. An AC circuit draws 5 A at 160 V and the power consumption is 600 W. Then the power factor is :-

1. 1
2. 0.75
3. 0.50
4. Zero

Correct Answer: B. 0.75

Q60. Which is not correct for average power P at resonance :-

1. \(P = I_{rms} V_{rms}\)
2. \(P = \frac{V}{\sqrt{2}}\frac{I}{\sqrt{2}}\)
3. \(P = VI\)
4. \(P = I^2_{rms} R\)

Correct Answer: C. \(P = VI\)

Q61. In an A.C. circuit inductance, capacitance and resistance are connected. If the effective voltage across inductance is \(V_{L}\), across capacitance is \(V_{C}\) and across resistance is \(V_{R}\), then the total effective value of voltage is :-

1. \(V_{R}+V_{L}+V_{C}\)
2. \(V_{R}+V_{L}-V_{C}\)
3. \(\sqrt{{V_{R}}^{2}+(V_{L}-V_{C})^{2}}\)
4. \(\sqrt{{V_{R}}^{2}-(V_{L}-V_{C})^{2}}\)

Correct Answer: C. \(\sqrt{{V_{R}}^{2}+(V_{L}-V_{C})^{2}}\)

Q62. In an a.c. circuit V and I are given by \(V = 100 \sin (100 t)\text{ volts}\) and \(I = 100 \sin(100 t+\pi/3)\text{ mA}\). The power dissipated in the circuit is :-

1. \(10^4\text{ watt}\)
2. 10 watt
3. 2.5 watt
4. 5.0 watt

Correct Answer: C. 2.5 watt

Q63. For a series LCR circuit the power loss at resonance is :-

1. \(\frac{V^{2}}{\left[\omega L-\frac{1}{\omega C}\right]}\)
2. \(I^{2} L \omega\)
3. \(I^{2}R\)
4. \(\frac{V^{2}}{C\omega}\)

Correct Answer: C. \(I^{2}R\)

Q64. In an alternating circuit applied voltage and flowing current are \(E=E_{0} \sin\omega t\) and \(I=I_{0} \sin(\omega t+\pi/2)\) respectively. Then the power consumed in the circuit will be :-

1. Zero
2. \(E_{0}I_{0}/2\)
3. \(E_{0}I_{0}/\sqrt{2}\)
4. \(E_{0}I_{0}/4\)

Correct Answer: A. Zero

Q65. In which of the following cases will the power factor be negligible :-

1. Inductance and resistance both high
2. Inductance and resistance both low
3. Low resistance and high inductance
4. High resistance and low inductance

Correct Answer: C. Low resistance and high inductance

Q66. If \(V=100\sin(100t)\text{ V}\) and \(I=100\sin(100t+\frac{\pi}{6})\text{ A}\), then find the wattless power in watt :-

1. \(10^{4}\)
2. \(10^{3}\)
3. \(10^{2}\)
4. \(2.5\times10^{3}\)

Correct Answer: D. \(2.5\times10^{3}\)

Q67. An A.C. supply gives 30V r.m.s. which passes through a \(10\ \Omega\) resistance. The power dissipated in it is :-

1. \(90\sqrt{2}\text{ W}\)
2. 90 W
3. \(45\sqrt{2}\text{ W}\)
4. 45 W

Correct Answer: B. 90 W

Q68. An inductor of inductance L and resistor of resistance R are joined in series and connected by a source of voltage V and angular frequency \(\omega\). Power dissipated in the circuit is :-

1. \(\frac{(R^{2}+\omega^{2}L^{2})}{V}\)
2. \(\frac{V^{2}R}{(R^{2}+\omega^{2}L^{2})}\)
3. \(\frac{V}{(R^{2}+\omega^{2}L^{2})}\)
4. \(\frac{\sqrt{R^{2}+\omega^{2}L^{2}}}{V^{2}}\)

Correct Answer: B. \(\frac{V^{2}R}{(R^{2}+\omega^{2}L^{2})}\)

Q69. For the given circuit, the power factor is :-
[Circuit Details: Resistor \(R = 1100\ \Omega\) in series with Inductor \(L = 3.5\text{ H}\), AC Supply frequency = \(50\text{ Hz}\)]

1. 0
2. \(1/2\)
3. \(1/\sqrt{2}\)
4. None of these

Correct Answer: C. \(1/\sqrt{2}\)

Q70. In a purely capacitive circuit average power dissipated in the circuit is :-

1. \(V_{rms}I_{rms}\)
2. Depends on capacitance
3. Infinite
4. Zero

Correct Answer: D. Zero

Q71. Energy loss in pure capacitance in A.C. circuit is :-

1. \(\frac{1}{2}CV^{2}\)
2. \(CV\)
3. \(\frac{1}{4}CV^{2}\)
4. Zero

Correct Answer: D. Zero

Q72. Power dissipated in pure inductance will be :-

1. \(\frac{LI^{2}}{2}\)
2. \(2LI^{2}\)
3. \(\frac{LI^{2}}{4}\)
4. Zero

Correct Answer: D. Zero

Q73. The power factor of L-R circuit is :-

1. \(\frac{\omega L}{R}\)
2. \(\frac{R}{\sqrt{(\omega L)^{2}+R^{2}}}\)
3. \(LR\)
4. \(\sqrt{\omega LR}\)

Correct Answer: B. \(\frac{R}{\sqrt{(\omega L)^{2}+R^{2}}}\)

Q74. If alternating current of rms value ‘a’ flows through resistance R then power loss in resistance is :-

1. Zero
2. \(a^{2}R\)
3. \(\frac{a^{2}R}{2}\)
4. \(2a^{2}R\)

Correct Answer: B. \(a^{2}R\)

Q75. Which of the following devices in an alternating circuit provides maximum power dissipation :-

1. Only capacitor
2. Capacitor and resistor
3. Only inductor
4. Only resistor

Correct Answer: D. Only resistor

Q76. Comparing the L-C oscillations with the oscillations of a spring-block system (force constant of spring = \(k\) and mass of block = \(m\)), the physical quantity \(mk\) is similar to :-

1. \(CL\)
2. \(\frac{1}{CL}\)
3. \(\frac{C}{L}\)
4. \(\frac{L}{C}\)

Correct Answer: D. \(\frac{L}{C}\)

Q77. In an oscillating LC circuit the maximum charge on the capacitor is Q. The charge on the capacitor when the energy is stored equally between the electric and magnetic fields is :-

1. \(Q/2\)
2. \(Q/\sqrt{3}\)
3. \(Q/\sqrt{2}\)
4. \(Q\)

Correct Answer: C. \(Q/\sqrt{2}\)

Q78. A fully charged capacitor C with initial charge \(q_{o}\) is connected to a coil of self inductance L at \(t=0\). The time at which the energy is stored equally between the electric and the magnetic fields is :-

1. \(2\pi\sqrt{LC}\)
2. \(\sqrt{LC}\)
3. \(\pi\sqrt{LC}\)
4. \(\frac{\pi}{4}\sqrt{LC}\)

Correct Answer: D. \(\frac{\pi}{4}\sqrt{LC}\)

Q79. A LC circuit is in the state of resonance. If \(C=0.1\ \mu\text{F}\) and \(L=0.25\text{ henry}\). Neglecting ohmic resistance of circuit, what is the frequency of oscillations :-

1. 1007 Hz
2. 100 Hz
3. 109 Hz
4. 500 Hz

Correct Answer: A. 1007 Hz

Q80. A \(60\ \mu\text{F}\) capacitor is charged to 100 volts. This charged capacitor is connected across a 1.5 mH coil, so that LC oscillations occur. The maximum current in the coil is :-

1. 1.5 A
2. 2 A
3. 15 A
4. 20 A

Correct Answer: D. 20 A