CUET · PHYSICS · PYQ PAPER 2025

Two parallel plate capacitors, X and Y, have the same area of plates and the same separation between them. They are connected in series across a 12 V battery. X has air between the plates while Y contains a dielectric medium of dielectric constant 4. The ratio of electrostatic energy stored in X and Y is

A \(4:1\)
B \(1:4\)
C \(2:1\)
D \(1:2\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(4:1\)

Step-by-step Solution

Detailed explanation

\(C_X = C_0\) \(C_Y = 4 C_0\) \(Q_X = Q_Y = Q\) (series connection) \(\frac{U_X}{U_Y} = \frac{\frac{1}{2}Q^2/C_X}{\frac{1}{2}Q^2/C_Y}\) \(\frac{U_X}{U_Y} = \frac{C_Y}{C_X} = \frac{4 C_0}{C_0} = 4\) Ratio: \(4:1\)

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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