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 $-X_C=X_L$
$\frac{1}{{\omega }_{0}C}={\omega }_{0}L$
$\Rightarrow {\omega }_0^2=\frac{1}{LC}$
$\Rightarrow {\omega }_0=\sqrt{\frac{1}{LC}}$