Question

In the given LCR series circuit the quality factor is

 

• A. \(54.6\)
• B. \(64\)
• C. \(48\)
• D. \(50\)

Hint:

The quality factor \( Q \) represents the damping of the circuit, with higher values indicating lower energy losses relative to the stored energy.

Answer 1

The Correct Option is D

Given Values:

• Resistance (\( R \)) = 10 \( \Omega \)
• Inductance (\( L \)) = 4 H
• Capacitance (\( C \)) = 16 \( \mu \)F = \( 16 \times 10^{-6} \) F

1. Calculate the Resonant Angular Frequency (\( \omega_0 \)):
\[ \omega_0 = \frac{1}{\sqrt{LC}} \] \[ \omega_0 = \frac{1}{\sqrt{(4 \, \text{H}) \times (16 \times 10^{-6} \, \text{F})}} \] \[ \omega_0 = \frac{1}{\sqrt{64 \times 10^{-6}}} \] \[ \omega_0 = \frac{1}{8 \times 10^{-3}} \] \[ \omega_0 = 125 \, \text{rad/s} \] 2. Calculate the Quality Factor (Q):
\[ Q = \frac{\omega_0 L}{R} \] \[ Q = \frac{(125 \, \text{rad/s}) \times (4 \, \text{H})}{10 \, \Omega} \] \[ Q = \frac{500}{10} \] \[ Q = 50 \] Therefore, the quality factor of the LCR series circuit is 50. The correct answer is (4) 50.