CUET · PHYSICS · PYQ PAPER 2023

To reduce the resonant frequency in an LCR series circuit with a generator.

A the generator frequency should be reduced
B another capacitor should be added in parallel to the first
C the iron core of the inductor should be removed
D dielectric in the capacitor should be removed

Verified Solution

Answer & Solution

Correct Answer

(B) another capacitor should be added in parallel to the first

Step-by-step Solution

Detailed explanation

"another capacitor should be added in parallel to the first" \( f_0 = \frac{1}{2\pi\sqrt{LC}} \) To reduce \( f_0 \), C must increase. Adding capacitors in parallel increases total capacitance: \( C_{total} = C_1 + C_2 \).

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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