Question

For an $RLC$ circuit driven with voltage of amplitude $V_m$ and frequency ${\omega }_0=\frac{1}{\sqrt{LC}}$ the current exhibits resonance. The quality factor $Q$ is

• A. $\frac{{\omega }_{0}R}{L}$
• B. $\frac{R}{{\omega }_{0}C}$
• C. $\frac{CR}{{\omega }_0}$
• 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, $X_L=X_C$
$\Rightarrow {\omega }_{0}L=\frac{1}{{\omega }_{0}C}$
$\Rightarrow {\omega }_0=\frac{1}{\sqrt{LC}}$
or $\sqrt{\frac{L}{C}}={\omega }_{0}L$
$\therefore Q=\frac{1}{R}\sqrt{\frac{L}{C}}=\frac{{\omega }_{0}L}{R}$