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The $Q$ -factor of a resonant circuit is equal to
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Verified Answer
The correct answer is:
$\frac{1}{R} \sqrt{\frac{L}{C}}$
The quality factor (Q-factor) of a resonant circuit
$$
Q=\frac{\omega_{0} L}{R}
$$
At resonance, $\omega_{0}=\frac{1}{\sqrt{L C}}$
$$
Q=\frac{1}{\sqrt{L} C} \cdot \frac{L}{R}=\frac{1}{R} \sqrt{\frac{L}{C}}
$$
$$
Q=\frac{\omega_{0} L}{R}
$$
At resonance, $\omega_{0}=\frac{1}{\sqrt{L C}}$
$$
Q=\frac{1}{\sqrt{L} C} \cdot \frac{L}{R}=\frac{1}{R} \sqrt{\frac{L}{C}}
$$
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