Q. An inductance of $1 \,mH$ and a capacitance of $10 \,\mu F$ are connected in a circuit. The angular frequency of circuit will be
AMUAMU 2000
Solution:
At resonance,
inductive reactance $\left(X_{L}\right)$ is equal to capacitive reactance
$\left(X_{C}\right) .$ Therefore,
$X_{L}=X_{C}$
$\omega L = \frac{1}{\omega C} \Rightarrow \omega = \frac{1}{\sqrt{LC}}$
Given, $ L=1 \,mH =1 \times 10^{-3} H , $
$ C=10 \,\mu F =10 \times 10^{-6} F $
$\therefore \omega=\frac{1}{\sqrt{10^{-3} \times 10 \times 10^{-6}}} $
$\Rightarrow \omega=10^{4} rad / s$
