In an oscillating LC circuit, the maximum charge on the capacitor is 'Q'. 'When the energy is stored equally…

In an oscillating LC circuit, the maximum charge on the capacitor is 'Q'. 'When the energy is stored equally between the electric and magnetic fields, the charge on the capacitor becomes
  1. $\frac{\mathrm{Q}}{4}$
  2. $\frac{\mathrm{Q}}{2}$
  3. $\frac{\mathrm{Q}}{\sqrt{2}}$
  4. $\frac{\mathrm{Q}}{\sqrt{3}}$

Solution

Maximum energy stored in a capacitor, $\mathrm{E}_1=\frac{\mathrm{Q}^2}{2 \mathrm{C}}$ When energy is stored equally between the electric and magnetic fields, then energy in the capacitor is $\mathrm{E}_2=\frac{1}{2} \mathrm{E}_1$ If $\mathrm{Q}^{\prime}$ is the charge on the capacitor in this case, then $\mathrm{E}_2=\frac{\mathrm{Q}^{\prime 2}}{2 \mathrm{C}}$. $\begin{aligned} \therefore \quad & \frac{\mathrm{Q}^{\prime 2}}{2 \mathrm{C}}=\frac{1}{2} \frac{\mathrm{Q}^2}{2 \mathrm{C}} \\ & \mathrm{Q}^{\prime}=\frac{\mathrm{Q}}{\sqrt{2}} . \end{aligned}$

Asked in: MHT CET 2023 (13 May Shift 1)

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