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(D) The quality factor $Q$ of an $R-L-C$ series circuit is defined as the ratio of the voltage drop across the inductor (or capacitor) to the voltage

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$\frac{\omega_0 L}{R}$

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(D) The quality factor $Q$ of an $R-L-C$ series circuit is defined as the ratio of the voltage drop across the inductor (or capacitor) to the voltage drop across the resistor at resonance.$Q = \frac{V_L}{V_R} = \frac{I X_L}{I R} = \frac{\omega_0 L}{R}$.At resonance,the resonant frequency is given by $\omega_0 = \frac{1}{\sqrt{LC}}$.Substituting $\sqrt{LC} = \frac{1}{\omega_0}$,we can also write $Q = \frac{1}{R} \sqrt{\frac{L}{C}}$.Comparing this with the given options,the expression for the quality factor is $\frac{\omega_0 L}{R}$.

For an $R-L-C$ 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

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