Question

For an $RLC$ circuit driven with voltage of amplitude $V_{m}$ and frequency $\omega_{0}=\frac{1}{\sqrt{L C}}$ the current exhibits resonance. The quality factor $Q$ is

• A. $\frac{\omega_{0} R}{L}$
• B. $\frac{R}{\omega_{0} C}$
• C. $\frac{C R}{\omega_{0}}$
• D. $\frac{\omega_{0} L}{R}$

Answer 1

Answer: (D)

The quality factor of a $R-L-C$ circuit is
$Q=\frac{1}{R} \sqrt{\frac{L}{C}}$
At resonance, $X_{L}=X_{C}$
$\Rightarrow \omega_{0} L=\frac{1}{\omega_{0} C}$
$\Rightarrow \omega_{0}=\frac{1}{\sqrt{L C}}$
or $\sqrt{\frac{L}{C}}=\omega_{0} L$
$\therefore Q=\frac{1}{R} \sqrt{\frac{L}{C}}=\frac{\omega_{0} L}{R}$