MHT CET · Physics · Alternating Current

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

A \(\frac{\mathrm{Q}}{4}\)
B \(\frac{\mathrm{Q}}{2}\)
C \(\frac{\mathrm{Q}}{\sqrt{2}}\)
D \(\frac{\mathrm{Q}}{\sqrt{3}}\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(\frac{\mathrm{Q}}{\sqrt{2}}\)

Step-by-step Solution

Detailed explanation

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 \(\mathrm{E}_2=\frac{\mathrm{Q}^{\prime 2}}{2 \mathrm{C}}\).
\(
\begin{aligned}
\therefore & \frac{\mathrm{Q}^{\prime 2}}{2 \mathrm{C}}=\frac{1}{2} \frac{\mathrm{Q}^2}{2 \mathrm{C}} \\
& \mathrm{Q}^{\prime}=\frac{\mathrm{Q}}{\sqrt{2}} .
\end{aligned}
\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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