The Q-factor of a resonant LCR series AC circuit is given by

The correct answer is Option (2) → $Q=\frac{1}{R}\sqrt{\frac{L}{C}}$

Quality factor, $Q=\frac{ωr}{Δω}$

where,

$ω_r$ = Resonant frequency

$Δω$ = Bandwidth

$ω_r=\frac{1}{\sqrt{LC}}$ and $Δω=\frac{R}{L}$

$∴Q=\frac{1}{\sqrt{LC}}×\frac{L}{R}=\frac{1}{R}\sqrt{\frac{L}{C}}$