This set of Network Theory Multiple Choice Questions & Answers (MCQs) focuses on “Problems of Series Resonance Involving Quality Factor”.

1. A circuit tuned to a frequency of 1.5 MHz and having an effective capacitance of 150 pF. In this circuit, the current falls to 70.7 % of its resonant value. The frequency deviates from the resonant frequency by 5 kHz. Effective resistance of the circuit is?

a) 2 Ω

b) 3 Ω

c) 5.5 Ω

d) 4.7 Ω

2. Consider a circuit consisting of two capacitors C_{1} and C_{2}. Let R be the resistance and L be the inductance which are connected in series. Let Q_{1} and Q_{2} be the quality factor for the two capacitors. While measuring the Q value by the Series Connection method, the value of the Q factor is?

a) Q = (C1–C2)Q1Q2Q1C1−Q2C2

b) Q = (C2–C1)Q1Q2Q1C1−Q2C2

c) Q = (C1–C2)Q1Q2Q2C2−Q1C1

d) Q = (C2–C1)C1C2Q1C1−Q2C2

3. A circuit tuned to a frequency of 1.5 MHz and having an effective capacitance of 150 pF. In this circuit, the current falls to 70.7 % of its resonant value. The frequency deviates from the resonant frequency by 5 kHz. Q factor is?

a) 50

b) 100

c) 150

d) 200

4. Consider a circuit consisting of two capacitors C_{1} and C_{2}. Let R be the resistance and L be the inductance which are connected in series. Let Q_{1} and Q_{2} be the quality factor for the two capacitors. While measuring the Q value by the Parallel Connection method, the value of the Q factor is?

a) Q = (C1–C2)Q1Q2Q1C1−Q2C2

b) Q = (C2–C1)Q1Q2Q1C1−Q2C2

c) Q = (C1–C2)Q1Q2Q2C2−Q1C1

d) Q = (C2–C1)C1C2Q1C1−Q2C2

5. For the resonant circuit given below, the value of the quality factor of the circuit is __________

a) 5.6

b) 7.1

c) 8.912

d) 12.6

6. For the series resonant circuit given below, the value of the quality factor is ___________

a) 15

b) 36

c) 25

d) 10

7. A 50 Hz voltage is measured with a moving iron voltmeter and a rectifier type AC voltmeter connected in parallel. If the meter readings are V_{a} and V_{b} respectively. Then the form factor may be estimated as?

a) VaVb

b) 1.11VaVb

c) 2√VaVb

d) πVaVb

8. For the series resonant circuit shown below, the value of the resonant frequency is _________

a) 36.84 kHz

b) 40.19 kHz

c) 25.28 kHz

d) 15.9 kHz

9. For the series resonant circuit given below, the bandwidth is ____________

a) ±351 Hz

b) ±796 Hz

c) ±531 Hz

d) ±225 Hz

10. In a series resonance type BPF, C = 1.8 pf, L = 25 mH, R_{F} = 52 Ω and R_{L} = 9 kΩ. The Resonant frequency f is __________

a) 75.1 kHz

b) 751 kHz

c) 575 kHz

d) 57.5 kHz

11. A 50 μF capacitor, when connected in series with a coil having a resistance of 40Ω, resonates at 1000 Hz. The inductance of the coil for the resonant circuit is ____________

a) 2.5 mH

b) 1.2 mH

c) 0.5 mH

d) 0.1 mH

12. For the series circuit given below, the value of the cut-off frequencies are ____________

a) 78.235 kHz; 16.215 kHz

b) 13.135 kHz; 81.531 kHz

c) 16.716 kHz; 15.124 kHz

d) 50.561 kHz; 18.686 kHz

13. In a series resonance type BPF, C = 1.8 pf, L = 25 mH, R_{F} = 52 Ω and R_{L} = 9 kΩ. The Bandwidth is ___________

a) 331 kHz

b) 575 kHz

c) 331 Hz

d) 575 Hz

14. A coil (which can be modelled as a series RL circuit) has been designed for a high Quality Factor (Q) performance. The voltage is rated at and a specified frequency. If the frequency of operation is increased 10 times and the coil is operated at the same rated voltage. The new value of Q factor and the active power P will be?

a) P is doubled and Q is halved

b) P is halved and Q is doubled

c) P remains constant and Q is doubled

d) P decreases 100 times and Q is increased 10 times

15. A 50 Hz, bar primary CT has a secondary with 800 turns. The secondary supplies 7 A current into a purely resistive burden of 2 Ω. The magnetizing ampere-turns are 300. The phase angle is?

a) 3.1°

b) 85.4°

c) 94.6°

d) 175.4°