Obtain the resonant frequency $\left({\omega }_r\right)$ of a series LCR circuit withL = 2.0 H, C = 32 $\mu F$ and R = 10 ohm. What is the Q value of this circuit ?

Solution: Inductive, L=2.0H
Capacitance, C=$32\mu F=32\times {10}^{-6}F$
Resistance, R=$10\Omega$
Resonant frequency is given by the relation,
${\omega }_r=\frac{1}{\sqrt{LC}}$
$=\frac{1}{10}\sqrt{\frac{2}{32\times {10}^{-6}}}=\frac{1}{10}\times \frac{1}{4\times {10}^{-3}}=25$ ltbr gt Hence, the Q-value of this circuit is 25.