Question:
For an RLC circuit driven with voltage of amplitude \(v_m\) and frequency \(\omega_0 = \frac{1}{\sqrt{LC}}\) the current exhibits resonance. The quality factor, Q is given by :
For an RLC circuit driven with voltage of amplitude \(v_m\) and frequency \(\omega_0 = \frac{1}{\sqrt{LC}}\) the current exhibits resonance. The quality factor, Q is given by :
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The quality factor of a series RLC circuit at resonance is the ratio of the reactance of the inductor at resonance to the resistance.
Updated On: Nov 11, 2026
- \(\frac{CR}{\omega_0}\)
- \(\frac{\omega_0 L}{R}\)
- \(\frac{\omega_0 R}{L}\)
- \(\frac{R}{\omega_0 C}\)
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The Correct Option is B
Solution and Explanation
For a series RLC circuit at resonance \(\omega_0 = \frac{1}{\sqrt{LC}}\).
The quality factor is defined as \(Q = \frac{\omega_0}{\Delta\omega}\), where the half-power bandwidth is \(\Delta\omega = \frac{R}{L}\).
So \(Q = \frac{\omega_0 L}{R}\).
Also, since \(\omega_0 L = \frac{1}{\omega_0 C}\), \(Q = \frac{1}{\omega_0 C R}\), which is consistent with option (2).
Answer: (2) \(\frac{\omega_0 L}{R}\)
The quality factor is defined as \(Q = \frac{\omega_0}{\Delta\omega}\), where the half-power bandwidth is \(\Delta\omega = \frac{R}{L}\).
So \(Q = \frac{\omega_0 L}{R}\).
Also, since \(\omega_0 L = \frac{1}{\omega_0 C}\), \(Q = \frac{1}{\omega_0 C R}\), which is consistent with option (2).
Answer: (2) \(\frac{\omega_0 L}{R}\)
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