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Question

(B) The quality factor ($Q$-factor) of a resonant circuit is defined as the ratio of resonant frequency to the bandwidth of the circuit.Mathematically

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$\frac{1}{R} \sqrt{\frac{L}{C}}$

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(B) The quality factor ($Q$-factor) of a resonant circuit is defined as the ratio of resonant frequency to the bandwidth of the circuit.Mathematically,$Q = \frac{\omega_{0} L}{R}$.At resonance,the angular frequency is given by $\omega_{0} = \frac{1}{\sqrt{LC}}$.Substituting the value of $\omega_{0}$ into the $Q$-factor formula:$Q = \frac{1}{\sqrt{LC}} \cdot \frac{L}{R} = \frac{1}{R} \cdot \frac{\sqrt{L}}{\sqrt{C}} = \frac{1}{R} \sqrt{\frac{L}{C}}$.

The $Q$-factor of a resonant circuit is equal to

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