CUET · PHYSICS · PYQ PAPER 2023

A parallel plate capacitor with air between the plates has a capacitance of 6 pF. What will be the capacitance if the distance between the plates is reduced to half and the space between them is filled with a substance of dielectric constant 5?

A 30 pF
B 60 pF
C 15 pF
D 120 pF

Verified Solution

Answer & Solution

Correct Answer

(B) 60 pF

Step-by-step Solution

Detailed explanation

\(C_0 = \frac{\epsilon_0 A}{d_0}\) \(C_1 = \frac{k \epsilon_0 A}{d_1} = \frac{5 \epsilon_0 A}{d_0/2} = 10 \frac{\epsilon_0 A}{d_0}\) \(C_1 = 10 C_0 = 10 \times 6 \text{ pF} = 60 \text{ pF}\)

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 :

List - I	List - II
(A) Electric potential due to point charge	(I) \( \propto \frac{1}{r^2} \)
(B) Electric potential due to a dipole on axial line	(II) \( \propto \frac{1}{r^3} \)
(C) Electric field intensity due to a dipole on axial line	(III) \( \propto \frac{1}{r} \)
(D) Electric field intensity due to a quadrapole	(IV) \( \propto \frac{1}{r^4} \)

Choose the correct answer from the options given below :

CUET 2023 Medium

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List-I (Materials)	List-II (Band Gap (eV))
(A) Germanium	(I) 1.42 eV
(B) Gallium Arsenide	(II) > 3 eV
(C) Insulator	(III) 1.1 eV
(D) Silicon	(IV) 0.7 eV