CUET · PHYSICS · PYQ PAPER 2025

A parallel plate air capacitor has a capacitance C. When it is half filled with a dielectric of dielectric constant 5, the percentage increase in the capacitance will be

A 200%
B 400%
C 66.6%
D 33.3%

Verified Solution

Answer & Solution

Correct Answer

(A) 200%

Step-by-step Solution

Detailed explanation

\(C_0 = \frac{\epsilon_0 A}{d}\) \(C_{new} = \frac{\epsilon_0 (A/2)}{d} + \frac{k \epsilon_0 (A/2)}{d}\) \(C_{new} = \frac{\epsilon_0 A}{2d}(1+k)\) \(C_{new} = C_0 \frac{1+k}{2}\) \(C_{new} = C_0 \frac{1+5}{2} = 3 C_0\)…

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.

Same subject

Match List-I with List-II for convex lens (symbols have their usual meanings)

List-I (Frequency Range)	List-II (EM Waves)
(A) \(4 \times 10^{14} Hz-7.5 \times 10^{14} Hz\)	(l) Infrared rays
(B) \(3 \times 10^{17} Hz-3 \times 10^{20} Hz\)	(II) Microwaves
(C) \(3 \times 10^9 Hz-3 \times 10^{11} Hz\)	(III) Visible Light
(D)\(3 \times 10^{11} Hz-4 \times 10^{14} Hz\)	(IV) X-rays

Choose the correct answer from the options given below :

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A diverging lens of glass (\( \mu = 1.5 \)) has both surfaces of the same radius of curvature (R). On immersion in a medium of refractive index (\( \mu = 1.8 \)), it will behave as:

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