MHT CET · Physics · Alternating Current

In the given circuit, when \(\mathrm{S}_1\) is closed, the capacitor gets fully charged. Now \(\mathrm{S}_1\) is open and \(\mathrm{S}_2\) is closed. Then

A there is no exchange of energy between L and C .
B the current in the circuit is in the same direction.
C the instantaneous current in the circuit may be \(\mathrm{V}\left(\sqrt{\frac{\mathrm{C}}{\mathrm{L}}}\right)\).
D the energy stored in the circuit is purely in the form of magnetic energy.

Verified Solution

Answer & Solution

Correct Answer

(C) the instantaneous current in the circuit may be \(\mathrm{V}\left(\sqrt{\frac{\mathrm{C}}{\mathrm{L}}}\right)\).

Step-by-step Solution

Detailed explanation

Maximum energy in capacitor \(=\) Maximum energy in inductor
\(\frac{1}{2} \mathrm{CV}^2=\frac{1}{2} \mathrm{LI}^2\)
\(\begin{array}{ll}\therefore & I^2=\frac{C}{L} V^2 \\ \therefore & I=V \sqrt{\frac{C}{L}}\end{array}\)

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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