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  4. In an L-C-R series AC circuit, if ω0 is the resonant angular frequency, then the quality factor (Q-factor) is given by

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Q. In an L-C-R series AC circuit, if $\omega_0$ is the resonant angular frequency, then the quality factor (Q-factor) is given by

KEAMKEAM 2008Alternating Current

Solution:

Quality factor
$Q=\frac{X_{L}}{R}=\frac{\omega_{0}L}{R}$
At resonance
$\omega_{0}=\frac{1}{\sqrt{LC}}$
$\therefore Q=\frac{L}{R}\times\frac{1}{\sqrt{LC}}=\frac{1}{R}\sqrt{\frac{L}{C}}$