Question

In an $L-C-R$ series resonant circuit which one of the following cannot be the expression for the $Q$-factor

• A. $ \frac{\omega L}{R} $
• B. $ \frac{1}{\omega \,CR} $
• C. $ \sqrt{\frac{L}{C}}\frac{1}{R} $
• D. $ \frac{R}{LC} $

Answer 1

Answer: (C)

Q-factor $=\frac{V_{L}}{V_{R}}$
or $\frac{V_{C}}{V_{R}}=\frac{\omega_{0} L}{R}$
or $\frac{1}{\omega_{0} C R}$
$\Rightarrow Q$-factor $=\frac{1}{R} \sqrt{\frac{L}{C}}$