This set of Network Theory Multiple Choice Questions & Answers (MCQs) focuses on “Problems of Series Resonance Involving Frequency Response of Series Resonant Circuit”.

1. A series RLC circuit has R = 50 Ω, L = 0.01 H and C = 0.04 × 10^{-6} F. System voltage is 100 V. At this frequency, the circuit impedance is?

a) 50 – j2.5 Ω

b) 50 – j2.8 Ω

c) 50 + j2.5 Ω

d) 50 + j2.8 Ω

2. Given, R = 10 Ω, L = 100 mH and C = 10 μF. The values of ω_{0}, ω_{1} and ω_{2} respectively are?

a) ω_{0} = 1000 rad/s, ω_{1} = 951.25 rad/s, ω_{2} = 1075.54 rad/s

b) ω_{0} = 1000 rad/s, ω_{1} = 975.25 rad/s, ω_{2} = 1051.25 rad/s

c) ω_{0} = 1000 rad/s, ω_{1} = 951.25 rad/s, ω_{2} = 1051.25 rad/s

d) ω_{0} = 1000 rad/s, ω_{1} = 825.30 rad/s, ω_{2} = 1075.54 rad/s

3. A series RLC circuit has R = 50 Ω, L = 0.01 H and C = 0.04 × 10^{-6} F. System voltage is 100 V. The frequency, at which the maximum voltage appears across the capacitor, is?

a) 5937.81 Hz

b) 7370 Hz

c) 7937.81 Hz

d) 981 Hz

4. Given, R = 10 Ω, L = 100 mH and C = 10 μF. Selectivity is?

a) 10

b) 1.2

c) 0.15

d) 0.1

5. A 440 V, 50 HZ AC source supplies a series LCR circuit with a capacitor and a coil. If the coil has 100 mΩ resistance and 15 mH inductance, then at a resonance frequency of 50 Hz, the half power frequencies of the circuit are?

a) 50.53 Hz, 49.57 Hz

b) 52.12 HZ, 49.8 Hz

c) 55.02 Hz, 48.95 Hz

d) 50 HZ, 49 Hz

6. A 440 V, 50 HZ AC source supplies a series LCR circuit with a capacitor and a coil. If the coil has 100 mΩ resistance and 15 mH inductance, then at a resonance frequency of 50 Hz, what is the value of the capacitor?

a) 676 μF

b) 575 μF

c) 591 μF

d) 610 μF

7. Two series resonant filters are shown below. Let the 3 dB bandwidth of filter 1 be B_{1} and that of filter 2 be B_{2}. The value of B1B2 is ____________

a) 0.25

b) 1

c) 0.5

d) 0.75

8. At what frequency will the current lead the voltage by 30° in a series circuit with R = 10Ω and C = 25 μF?

a) 11.4 kHz

b) 4.5 kHz

c) 1.1 kHz

d) 24.74 kHz

9. A 440 V, 50 HZ AC source supplies a series LCR circuit with a capacitor and a coil. If the coil has 100 mΩ resistance and 15 mH inductance, then at a resonance frequency of 50 Hz, the Q factor of the circuit is?

a) 82.63

b) 47.115

c) 27.38

d) 92.38

10. In the circuit given below, the magnitudes of V_{L} and V_{C} are twice that of V_{K}. Calculate the inductance of the coil, given that f = 50.50 Hz.

a) 6.41 mH

b) 5.30 mH

c) 3.18 mH

d) 2.31 mH

11. A series RLC circuit has a resonance frequency of 1 kHz and a quality factor Q = 50. If R and L are doubled and C is kept same, the new Q of the circuit is?

a) 25.52

b) 35.35

c) 45.45

d) 20.02

12. For the circuit given below, if the frequency of the source is 50 Hz, then a value of t_{o} which results in a transient free response is?

a) 0

b) 1.78 ms

c) 7.23 ms

d) 9.21 ms

13. A circuit with a resistor, inductor and capacitor in series is resonant with frequency f Hz. If all the component values are now doubled, then the new resonant frequency will be?

a) 2 f

b) f

c) f4

d) f2

14. In a series RLC circuit R = 10 kΩ, L = 0.5 H and C = 1250 μF. Calculate the frequency when the circuit is in a state of resonance.

a) 4.089 × 10^{4} Hz

b) 11111.1πHz

c) 4.089π × 10^{4} Hz

d) 1π × 10^{4} Hz

15. In a series RLC circuit for lower frequency and for higher frequency, power factors are respectively ______________

a) Leading, Lagging

b) Lagging, Leading

c) Independent of Frequency

d) Same in both cases