Question

In an oscillating $LC$ circuit the maximum charge on the capacitor is $Q$. The charge on the capacitor when the energy is stored equally between the electric and magnetic field is

• A. $Q/2$
• B. $Q/\surd 3$
• C. $Q/\surd 2$
• D. $Q$

Answer 1

Answer: (C)

$Q/\surd 2$

[C] When capacitor is full charge, total energy of LC circuit is with capacitor

$\begin{array}{c}E=\frac{1}{2}\frac{Q^2}{C},Q\to maxchargeoncapacitor\\ maxenergyinInductor=\frac{L{I}_0^2}{2},I_0=current\end{array}$

According to the question

Let q charge on capacitor when charge in equally shared between inductor and capacitor.

$\begin{array}{c}\therefore \frac{1}{2}\left(\frac{1}{2}\frac{Q^2}{C}\right)=\frac{1}{2}\frac{q^2}{C}\\ \Rightarrow Q^2=2q^2\\ \therefore q=\frac{Q}{\sqrt{2}}\end{array}$