Q1. When 100 volts d.c. is applied across a solenoid a current of 1.0 amp. flows in it. When 100 volt a.c. is applied across the same coil, the current drops to 0.5 amp. If the frequency of the a.c. source is 50 Hz the impedance and inductance of the solenoid are :-

1. 200 ohm and 0.55 H
2. 100 ohm and 0.86 H
3. 200 ohm and 1.0 H
4. 100 ohm and 0.93 H

Correct Answer: A. 200 ohm and 0.55 H

Q2. Time constant of the given circuit is \(\tau\). If the battery is replaced by an ac source having voltage \(V=V_{0} \cos \omega t\), power factor of the circuit will be :-

1. \(\omega\tau\)
2. \(\frac{1}{\sqrt{1+(\omega\tau)^{2}}}\)
3. \(\sqrt{1+(\omega\tau)^{2}}\)
4. None

Correct Answer: B. \(\frac{1}{\sqrt{1+(\omega\tau)^{2}}}\)

Q3. An alternating emf of angular frequency \(\omega\) is applied across an inductance. The instantaneous power developed in the circuit has an angular frequency:

1. \(\omega/4\)
2. \(\omega/2\)
3. \(\omega\)
4. \(2\omega\)

Correct Answer: D. \(2\omega\)

Q4. The self inductance of a choke coil is 10 mH. when it is connected with a 10 V D.C. source, then the loss of power is 20 watt. When it is connected with 10 volt A.C. source loss of power is 10 watt. The frequency of A.C. source will be :

1. 50 Hz
2. 60 Hz
3. 80 Hz
4. 100 Hz

Correct Answer: C. 80 Hz

Q5. An inductance L, a capacitance C and resistance R may be connected to an AC source of angular frequency \(\omega\), in three different combinations of RC, RL and RLC in series. Assume that \(\omega L = \frac{1}{\omega C}\). The power drawn by the three combinations are \(P_{1}\), \(P_{2}\), \(P_{3}\) respectively. Then :-

1. \(P_{1} > P_{2} > P_{3}\)
2. \(P_{1} = P_{2} < P_{3}\)
3. \(P_{1} = P_{2} > P_{3}\)
4. \(P_{1} = P_{2} = P_{3}\)

Correct Answer: B. \(P_{1} = P_{2} < P_{3}\)

Q6. In the L-C circuit shown in figure, the current is in direction shown in the figure and charges on the capacitor plates have sign shown in the figure. At this time :-

1. \(i\) as well as \(Q\) increasing
2. \(i\) as well as \(Q\) decreasing
3. \(i\) is increasing but \(Q\) is decreasing
4. \(i\) is decreasing but \(Q\) is increasing

Correct Answer: C. \(i\) is increasing but \(Q\) is decreasing

Q7. The switch in the circuit pictured is in position a for a long time. At \(t=0\) the switch is moved from a to b. The current through the inductor will reach its first maximum after moving the switch in a time:-

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

Correct Answer: C. \(\frac{\pi}{2}\sqrt{LC}\)

Q8. The inductance of the oscillatory circuit of a radio station is 10 milli henry and its capacitance is \(0.25\ \mu\text{F}\). Taking the effect of the resistance negligible, wavelength of the broadcasted waves will be (velocity of light \(= 3.0 \times 10^{8}\text{ m/s}\), \(\pi = 3.14\)):-

1. \(9.42 \times 10^{4}\text{ m}\)
2. \(18.8 \times 10^{4}\text{ m}\)
3. \(4.5 \times 10^{4}\text{ m}\)
4. None of these

Correct Answer: A. \(9.42 \times 10^{4}\text{ m}\)

Q9. A coil has an inductance of 0.7 henry and is joined in series with a resistance of \(220\ \Omega\). When the alternating emf of 220 V at 50 Hz is applied to it then the phase through which current lags behind the applied emf and the wattless component of current in the circuit will be respectively :-

1. \(30^{\circ}\), 1 A
2. \(45^{\circ}\), 0.5 A
3. \(60^{\circ}\), 1.5 A
4. None of these

Correct Answer: B. \(45^{\circ}\), 0.5 A

Q10. In the circuit shown in the figure, the A.C. source gives a voltage \(V=20 \cos (2000 t)\) volt neglecting source resistance, the voltmeter and ammeter readings will be :

1. 0 V, 1.4 A
2. 5.6 V, 1.4 A
3. 0 V, 0.47 A
4. 1.68 V, 0.47 A

Correct Answer: B. 5.6 V, 1.4 A

Q11. An inductor and a resistor in series are connected to an A.C. supply of variable frequency. As the frequency of the source is increased, the phase angle between current and the potential difference across source will be :

1. First increase and then decrease
2. First decrease and then increase
3. Go on decreasing
4. Go on increasing

Correct Answer: D. Go on increasing

Q12. The diagram shows a capacitor C and a resistor R connected in series to an AC source, \(V_{1}\) and \(V_{2}\) are voltmeters and A is an ammeter. Consider now the following statements :

Statements:
(I) Readings in A and \(V_{2}\) are always in phase
(II) Reading in \(V_{1}\) is ahead with reading in \(V_{2}\)
(III) Readings in A and \(V_{1}\) are always in phase

Which of these statements is/are correct :

1. I only
2. II only
3. I and II only
4. II and III only

Correct Answer: A. I only

Q13. A capacitor of capacitance \(2\ \mu\text{F}\) is connected in the tank circuit of an oscillator oscillating with a frequency of 1 kHz. If the current flowing in the circuit is 2 mA, the voltage across the capacitor will be:-

1. 0.16 V
2. 0.32 V
3. 79.5 V
4. 159 V

Correct Answer: A. 0.16 V

Q14. If an alternating current \(i=i_{m}\sin\omega t\) is flowing through a capacitor then voltage drop \(\Delta V_{c}\) across capacitor C will be ?

1. \(-\frac{i_{m}}{\omega C}\sin\omega t\)
2. \(-\frac{i_{m}}{\omega C}\cos\omega t\)
3. \(-\frac{i_{m}}{\omega C}\left(\sin\omega t+\frac{\pi}{4}\right)\)
4. \(\frac{i_{m}}{\omega C}\left(\sin\omega t-\frac{\pi}{4}\right)\)

Correct Answer: B. \(-\frac{i_{m}}{\omega C}\cos\omega t\)

Q15. If an alternating current \(i=i_{m}\sin\omega t\) is flowing through an inductor then voltage drop \(\Delta V_{L}\) across inductor L will be :-

1. \(i_{m} c\sin\omega t\)
2. \(i_{m}\omega L\cos\omega t\)
3. \(i_{m}\omega L\sin\left(\omega t+\frac{\pi}{4}\right)\)
4. \(i_{m}\omega L\cos\left(\omega t-\frac{\pi}{4}\right)\)

Correct Answer: B. \(i_{m}\omega L\cos\omega t\)

Q16. If frequency of alternating source is made zero then which of the following statement is true :

1. Current through capacitor will be zero
2. Current through resistance will be zero
3. Current through inductance will be zero
4. All

Correct Answer: A. Current through capacitor will be zero

Q17. The figure shows a LCR network connected to 300 V a.c. supply. The circuit elements are such that \(R=X_{L}=X_{c}=10\ \Omega\). \(V_{1}\), \(V_{2}\) and \(V_{3}\) are three a.c. voltmeters connected as shown in the figure. Which of the following represents the correct set of readings of the voltmeters ?

1. \(V_{1}=100\text{ V}\), \(V_{2}=100\text{ V}\), \(V_{3}=100\text{ V}\)
2. \(V_{1}=150\text{ V}\), \(V_{2}=0\text{ V}\), \(V_{3}=150\text{ V}\)
3. \(V_{1}=300\text{ V}\), \(V_{2}=100\text{ V}\), \(V_{3}=100\text{ V}\)
4. \(V_{1}=300\text{ V}\), \(V_{2}=300\text{ V}\), \(V_{3}=300\text{ V}\)

Correct Answer: D. \(V_{1}=300\text{ V}\), \(V_{2}=300\text{ V}\), \(V_{3}=300\text{ V}\)

Q18. A \(1.5\ \mu\text{F}\) capacitor is charged to 60 V. The charging battery is then disconnected and a 15 mH coil is connected in series with the capacitor so that LC oscillations occur. Assuming that the circuit contains no resistance, the maximum current in this coil shall be close to :

1. 1.4 A
2. 1.2 A
3. 0.8 A
4. 0.6 A

Correct Answer: D. 0.6 A