Q. The natural frequency $(\omega_{0})$ of oscillations in L - C circuit is given by
A) $\frac{1}{2\pi}\frac{1}{\sqrt{LC}}$
B) $\frac{1}{2\pi}\sqrt{LC}$
C) $\frac{1}{\sqrt{LC}}$
D) $\sqrt{LC}$
Explanation
(a) Natural frequency is nothing but resonant frequency.
In this case $X_{L} = X_{C}$
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ \omega_{0}L = \frac{1}{\omega_{0}C}$
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\ \ \omega}_{0}^{2} = \frac{1}{LC}$
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\ \omega}_{0} = \frac{1}{\sqrt{LC}}$
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ 2\pi f = \frac{1}{\sqrt{LC}}$
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ f = \frac{1}{2\pi\sqrt{LC}}\ $
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.