Question

The natural frequency ($\omega_0$) of oscillations in $LC$ circuit is given by

• A. $\frac{1}{2\pi} \frac{1}{\sqrt{LC}}$
• B. $\frac{1}{\pi} \frac{1}{\sqrt{2LC}}$
• C. $\frac{1}{\sqrt{LC}}$
• D. $\sqrt{LC}$

Answer 1

Answer: (C)

Let natural frequency $=\omega_{0}$
Condition $- X _{ C }= X _{ L }$
$\frac{1}{\omega_{0} C } =\omega_{0} L$
$\Rightarrow \omega_{0}^{2} =\frac{1}{ LC } $
$\Rightarrow \omega_{0} =\sqrt{\frac{1}{ LC }}$