For an RLC circuit driven with voltage of amplitude v m and frequency ω 0 = 1 L C the current exhibits…

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

(Quality factor) $Q=\frac{1}{R}\sqrt{\frac{L}{C}}...\left(\mathrm{i}\right)$

Where $L,R,C$ are the inductance, resistance, and conductance of the L.C.R. circuit. The given resonance frequency is, ${\mathit{\text{ω}}}_0=\frac{1}{\sqrt{LC}}$

$\Rightarrow \sqrt{C}=\frac{1}{{\mathit{\text{ω}}}_0\sqrt{L}} ...\left(\mathrm{ii}\right)$

From $\left(\mathrm{i}\right)$ and $\left(\mathrm{ii}\right)$

$\Rightarrow Q=\frac{1}{R}\sqrt{L}\times {\mathit{\text{ω}}}_0\sqrt{L}\Rightarrow Q=\frac{{\mathit{\text{ω}}}_{0}L}{R}$