This set of Network Theory Multiple Choice Questions & Answers (MCQs) focuses on “Resonant Frequency for a Tank Circuit”.

1. For the tank circuit shown below, find the resonant frequency.

a) 157.35

b) 158.35

c) 159.35

d) 160.35

View Answer

Explanation: The parallel resonant circuit is generally called a tank circuit because of the fact that the circuit stores energy in the magnetic field of the coil and in the electric field of the capacitor. The resonant frequency f

_{r}= (1/2π) √((1/LC)-(R

^{2}/L

^{2}) ).

2. The expression of ωr in parallel resonant circuit is?

a) 1/(2√LC)

b) 1/√LC

c) 1/(π√LC)

d) 1/(2π√LC)

View Answer

Explanation: The stored energy is transferred back and forth between the capacitor and coil and vice-versa. The expression of ω

_{r}in parallel resonant circuit is ω

_{r}= 1/√LC.

3. The expression of bandwidth for parallel resonant circuit is?

a) 1/RC

b) RC

c) 1/R

d) 1/C

View Answer

Explanation: The expression of bandwidth for parallel resonant circuit is BW = 1/RC. the circuit is said to be in resonant condition when the susceptance part of admittance is zero.

4. The quality factor in case of parallel resonant circuit is?

a) C

b) ω_{r}RC

c) ω_{r}C

d) 1/ω_{r}RC

View Answer

Explanation: The quality factor in case of parallel resonant circuit is Q = 1/ω

_{r}RC. The impedance of parallel resonant circuit is maximum at the resonant frequency and decreases at lower and higher frequencies.

5. The quality factor is the product of 2π and the ratio of ______ to _________

a) maximum energy stored, energy dissipated per cycle

b) energy dissipated per cycle, maximum energy stored

c) maximum energy stored per cycle, energy dissipated

d) energy dissipated, maximum energy stored per cycle

View Answer

Explanation: At low frequencies X

_{L}is very small and X

_{C}is very large so the total impedance is essentially inductive. The quality factor is the product of 2π and the ratio of maximum energy stored to energy dissipated per cycle.

6. The maximum energy stored in a capacitor is?

a) CV^{2}

b) CV^{2}/2

c) CV^{2}/4

d) CV^{2}/8

View Answer

Explanation: The maximum energy stored in a capacitor is CV

^{2}/2. Maximum energy = CV

^{2}/2. As frequency increases the impedance also increases and the inductive reactance dominates until the resonant frequency is reached.

7. The expression of quality factor is?

a) I_{L}/I

b) I/I_{L}

c) IL

d) I

View Answer

Explanation: The expression of quality factor is I

_{L}/I. Quality factor = I

_{L}/I. At the the point X

_{L}= X

_{C}, the impedance is at its maximum.

8. The quality factor is defined as?

a) I

b) I_{C}

c) I/I_{C}

d) I_{C}/I

View Answer

Explanation: The quality factor is defined as I

_{C}/I. Quality factor = I

_{C}/I. As the frequency goes above resonance capacitive reactance dominates and impedance decreases.

9. In the circuit shown in the figure, an inductance of 0.1H having a Q of 5 is in parallel with a capacitor. Determine the value coil resistance (Ω) of at a resonant frequency of 500 rad/sec.

a) 10

b) 20

c) 30

d) 40

View Answer

Explanation: Quality factor Q = ω

_{r}L/R. L = 0.1H, Q = 5, ω

_{r}= 500 rad/sec. On solving, R = 10Ω. While plotting the voltage and current variation with frequency, at resonant frequency, the current is maximum.

10. Find the value of capacitance (µF) in the circuit shown in the question 9.

a) 10

b) 20

c) 30

d) 40

View Answer

Explanation: ω

^{2}

_{r}= 1/LC. L = 0.1H, ωr = 500 rad/sec. On solving, C = 40 µF. In order to tune a parallel circuit to a lower frequency the capacitance must be increased.

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