Question

A capacitor is charged to a potential of $V_0$. It connected with an inductor through a switch $SX$. The switch is closed at time $t=0$. Which of the following statement is correct.

• A. maximumn current in the circuit is $V_0\sqrt{LC}$
• B. potential across capacitor becomes zero for the first time at $t=\pi \sqrt{LC}$
• C. energy stored in the inductor at time $\frac{\pi }{2}\sqrt{LC}$ is $\frac{1}{4}{CV}_0^2$
• D. maximum energy stored in the inductor is $\frac{1}{2}{CV}_0^2$

Answer 1

The correct option is D maximum energy stored in the inductor is $\frac{1}{2}{CV}_0^2$

We know,

$Q=C{V}_0$

Let $I$ is max current.

$\begin{array}{c}\Rightarrow \frac{1}{2}\angle I^2=\frac{Q^2}{2c}\\ \Rightarrow \frac{1}{2}\angle I^2=\frac{C^2{V}_0^2}{2c}\\ \Rightarrow I=V_0\sqrt{\frac{C}{L}}\end{array}$

$\therefore$ Option $A$ is incorrect.

Now,

$max$ energy shoved in capacitor $=\frac{1}{2}\angle I^2=\frac{1}{2}C{V}_0^2$

$\therefore$ Option $D$ is correct.