For an RLC circuit driven with voltage of amplitude v _ m and...

The quality factor of an L.C.R. circuit is given by,

(Quality factor) $Q = \dfrac{1}{R}\sqrt{\dfrac{L}{C}} . . . ( i )$

Where $L, R, C$ are the inductance, resistance, and conductance of the L.C.R. circuit. The given resonance frequency is, ${\text{\omega}}_{0} = \dfrac{1}{\sqrt{LC}}$

$⇒ \sqrt{C} = \dfrac{1}{{\text{\omega}}_{0}\sqrt{L}} . . . ( ii )$

From $( i )$ and $( ii )$

$⇒ Q = \dfrac{1}{R}\sqrt{L} \times {\text{\omega}}_{0}\sqrt{L} ⇒ Q = \dfrac{{\text{\omega}}_{0}L}{R}$