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 fields is

• A. $Q/2$
• B. $Q/\sqrt{3}$
• C. $Q/\sqrt{2}$
• D. $Q$

Answer 1

Answer: (C)

In an $LC$ circuit the energy oscillates between inductor (in the magnetic field) and capacitor (in the electric field). $U_{E\max }$ [Maximum energy stored in capacitor] $=\frac{Q^2}{2C}$ $U_{B\max }$ [Maximum energy stored in inductor] $=\frac{L{i}_0^2}{2}$ where $I_0$ is the current at this time. For the given instant $U_E=U_B$ $ie,$ $\frac{q^2}{2C}=\frac{L{i}^2}{2}$ From energy conservation $U_E+U_B=U_{E\max }=U_{B\max }$ $\Rightarrow$ $2\frac{q^2}{2C}=\frac{Q^2}{2C}$ $\Rightarrow$ $q=\frac{Q}{\sqrt{2}}$