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

1. For a series RLC circuit, excited by voltage V = 20 sinωt. The values of R = 2 Ω, L = 1mH and C = 0.4 µF. The quality factor and bandwidth of the circuit is ______________

a) 25, 2

b) 30, 5

c) 40, 10

d) 50, 2

2. An ideal transformer is rated as 2400/120 V, 9.6 kVA and has 50 turns on the secondary side. The turns ratio is ____________

a) 0.04

b) 0.05

c) 0.06

d) 0.07

3. For a series RLC circuit, excited by voltage V = 20 sinωt. The values of R = 2 Ω, L = 1mH and C = 0.4 µF. The resonant frequency of the circuit is ______________

a) 20 krad/s

b) 30 krad/s

c) 40 krad/s

d) 50 krad/s

4. In the circuit shown in the figure, if ω = 40 rad/s, then Z_{in} is _____________

a) 4.77 – j1.15 Ω

b) 2.96 – j0.807 Ω

c) 2.26 – j3.48 Ω

d) 2.26 – j3.48 Ω

5. The circuit shown in the figure below will act as an ideal source with respect to terminal A and B when the frequency is ___________

a) Zero

b) 1 rad/s

c) 4 rad/s

d) 16 rad/s

6. The RL circuit in the below figure is fed from a constant magnitude, variable frequency sinusoidal voltage source V_{IN}. At 50 Hz, the R and L elements each have a voltage drop V_{rms}. If the frequency of the source is changed to 25 Hz, the new voltage drop across R is ___________

a) 58−−√ V_{rms}

b) 23−−√ V_{rms}

c) 85−−√ V_{rms}

d) 2–√ V_{rms}

7. For the circuit shown in the figure below, the value of R for critical damping will be?

a) 10.5 Ω

b) 8.57 Ω

c) 3.5 Ω

d) 3 Ω

8. An ideal capacitor is charged to a voltage V and connected at t=0 across an ideal inductor L. If we take ω = 1LC√, the voltage across the capacitor at time t>0 will be?

a) V

b) V cos(ωt)

c) V sin(ωt)

d) Ve^{-ωt} cos(ωt)

9. In a series circuit with R = 10Ω and C = 25 μF, at what frequency will the current lead the voltage by 30°?

a) 11.4 kHz

b) 4.5 kHz

c) 1.1 kHz

d) 24.74 kHz

10. The time constant for the given circuit under resonance condition will be?

a) 19 s

b) 14 s

c) 4 s

d) 9 s

11. An ideal transformer is rated as 2400/120 V, 9.6 kVA and has 50 turns on the secondary side. The number of turns on the primary side is ____________

a) 1000

b) 2000

c) 3000

d) 4000

12. The frequency for the given circuit when the circuit is in a state of resonance will be?

a) 1 rad/s

b) 2 rad/s

c) 3 rad/s

d) 4 rad/s

13. A 50 μF capacitor, when connected in series with a coil having a resistance of 40Ω, resonates at 1000 Hz. The circuit is in resonating condition. The voltage across the capacitor is __________

a) 8.04 V

b) 7.96 V

c) 5.68 V

d) 1.25 V

14. A 50 μF capacitor, when connected in series with a coil having resistance of 40Ω, resonates at 1000 Hz. The circuit current if the applied voltage is 100 V for the resonant circuit is ___________

a) 2.5 A

b) 3.5 A

c) 4.5 A

d) 0.5 A

15. A 50 μF capacitor, when connected in series with a coil having resistance of 40Ω, resonates at 1000 Hz. The circuit is in resonating condition. The voltage across the coil is __________

a) 100.31 V

b) 200.31 V

c) 300.31 V

d) 400.31 V