CUET · PHYSICS · PYQ PAPER 2023

The same current is flowing in two AC circuits. The first circuit contains a pure inductor and the second, a capacitor. If the frequency of the AC is increased, then the current will :

A increase in the first and increase in the second
B increase in both
C decrease in both
D decrease in the first but increase in the second

Verified Solution

Answer & Solution

Correct Answer

(A) increase in the first and increase in the second

Step-by-step Solution

Detailed explanation

For inductor, \( X_L = 2 \pi f L \). Current \( I \propto \frac{1}{X_L} \propto \frac{1}{f} \). If \( f \) increases, \( I \) decreases. For capacitor, \( X_C = \frac{1}{2 \pi f C} \). Current \( I \propto \frac{1}{X_C} \propto f \). If \( f \) increases, \( I \) increases.

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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