Question

Obtain the resonant frequency and Q-factor of a series LCR circuit with L = 3.0 H, $C=27\mu F$, and $R=7.4\Omega$. It is desired to improve the sharpness of the resonance of the circuit by reducing its 'full width at half maximum' by a factor of 2. Suggest a suitable way.

Answer 1

The frequency and Q factor are given by
$\omega =\frac{1}{\sqrt{LC}}=\frac{1}{\sqrt{3\times 27}}=0.111rad/s$
$Q=\frac{1}{R}\sqrt{\frac{L}{C}}=\frac{1}{7.4}\sqrt{\frac{3}{27}}=0.045$
To double Q without changing $\omega$, reduce R to 3.7