Question

In the given circuit initially the charge on capacitor is $Q_0$ At t = 0 the switch S is closed Which of the following statement(s) is/are correct?

• A. Maximum current through the inductor is $\frac{Q_0}{\sqrt{LC}}$
• B. Charge on the capacitor is zero at $t=\frac{\pi }{2}\sqrt{LC}$
• C. Current through the inductor is maximum at $t=\frac{\pi }{2}\sqrt{LC}$
• D. Maximum magnetic energy can be stored in the inductor is $\frac{Q_0^2}{2C}$

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A Maximum current through the inductor is $\frac{Q_0}{\sqrt{LC}}$
B Charge on the capacitor is zero at $t=\frac{\pi }{2}\sqrt{LC}$
C Current through the inductor is maximum at $t=\frac{\pi }{2}\sqrt{LC}$
D Maximum magnetic energy can be stored in the inductor is $\frac{Q_0^2}{2C}$

The charge on the capacitor at t is $q=Q_0\cos \omega t$ where $\omega =\frac{1}{\sqrt{LC}}$

so the magnitude current $i_C=i_L=|\frac{dq}{dt}|=Q_0\omega \sin \omega t$

So at $t=\frac{\pi }{2}\sqrt{LC}$ , $q=0$ and $i_L{}_{max}=Q_0\omega =\frac{Q_0}{\sqrt{LC}}$

By energy conservation, energy stored in inductor $=$ energy stored in capacitor $=\frac{Q_0^2}{2C}$