MHT CET · Physics · Alternating Current

An alternating voltage of frequency ' \(\omega\) ' is induced in electric circuit consisting of an inductance ' \(\mathrm{L}\) ' and capacitance ' \(\mathrm{C}\) ', connected in parallel. Then across the inductance coil

A current is maximum when \(\omega^2=\frac{1}{\text { LC }}\)
B current is zero
C voltage is minimum when \(\omega^2=\frac{1}{\text { LC }}\)
D voltage is maximum when \(\omega^2=\frac{1}{\text { LC }}\)

Verified Solution

Answer & Solution

Correct Answer

(D) voltage is maximum when \(\omega^2=\frac{1}{\text { LC }}\)

Step-by-step Solution

Detailed explanation

In a parallel LC circuit
at \(\omega^2=\frac{1}{\mathrm{LC}}\), the current is minimum.
As current and voltage are out of phase by \(90^{\circ}\), the voltage would be maximum.

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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