Question

The frequency of oscillations of current in the below LC circuit is -

• A. $\frac{1}{3\pi \sqrt{LC}}$
• B. $\frac{1}{6\pi \sqrt{LC}}$
• C. $\frac{1}{\pi \sqrt{LC}}$
• D. $\frac{1}{2\pi \sqrt{LC}}$

Answer 1

The correct option is B $\frac{1}{6\pi \sqrt{LC}}$


Equivalent inductance is,

$L_{\text{eq}}=L+2L=3L$

Equivalent capacitance is,

$C_{\text{eq}}=C+2C=3C$

$\therefore$ Frequency of oscillations of current,

$f=\frac{1}{2\pi \sqrt{L_{\text{eq}}{C}_{\text{eq}}}}=\frac{1}{2\pi \sqrt{\left(3L\right)\left(3C\right)}}$

$\Rightarrow f=\frac{1}{6\pi \sqrt{LC}}$

Hence, option $\left(B\right)$ is the correct answer.