Question

In an L-C-R series AC circuit, if $\omega_0$ is the resonant angular frequency, then the quality factor (Q-factor) is given by

• A. $\omega_0 L/C$
• B. $(1/R) \sqrt{ \frac{ L}{ C}}$
• C. $\omega_0 C/R$
• D. $L/ \omega_0 R$

Answer 1

Answer: (B)

$(1/R) \sqrt{ \frac{ L}{ C}}$

Answer 2

Quality factor
$Q=\frac{X_{L}}{R}=\frac{\omega_{0}L}{R}$
At resonance
$\omega_{0}=\frac{1}{\sqrt{LC}}$
$\therefore Q=\frac{L}{R}\times\frac{1}{\sqrt{LC}}=\frac{1}{R}\sqrt{\frac{L}{C}}$