A parallel plate capacitor has capacitance C , when there is vacuum within the parallel plates. A sheet having thickness (1/3 ) rd of the separation between the plates and relative permittivity K is introduced between the plates. The new capacitance of the system is :

Physics · Capacitors and R-C Circuits

JEE Main 2026 — 21 January, Morning Shift — Question 33

A parallel plate capacitor has capacitance C , when there is vacuum within the parallel plates. A sheet having thickness $\left(\frac{1}{3}\right)^{\text {rd }}$ of the separation between the plates and relative permittivity K is introduced between the plates. The new capacitance of the system is :

Option A:
$\frac{3 \mathrm{KC}}{2 \mathrm{~K}+1}$
Correct
Option B:
$\frac{\text { CK }}{2+\text { K }}$
Option C:
$\frac{3 \mathrm{CK}^{2}}{(2 \mathrm{~K}+1)^{2}}$
Option D:
$\frac{4 \mathrm{KC}}{3 \mathrm{~K}-1}$

Answer: A

Step-by-step solution

$\mathrm{C}_{1}=\frac{3 \mathrm{~A} \epsilon_{0}}{2 \mathrm{~d}}$ $\mathrm{C}_{2}=\frac{3 \mathrm{~A} \in_{0} \times \mathrm{K}}{\mathrm{d}}$ $\mathrm{C}_{1}=\frac{3}{2} \mathrm{C}$ $\mathrm{C}_{2}=3 \mathrm{KC}$

Ceq $=\frac{\text { C }_{1} \text { C }_{2}}{\text { C }_{1}+\text { C }_{2}}=\frac{\frac{3}{2} \mathrm{C} \times 3 \mathrm{KC}}{\frac{3}{2} \mathrm{C}+3 \mathrm{KC}}$ Ceq $=\frac{\frac{9}{2} \mathrm{KC}^{2}}{\frac{3}{2} \mathrm{C}(2 \mathrm{~K}+1)}=\frac{3 \mathrm{KC}}{2 \mathrm{~K}+1}$

Answer key and solution verified before publishing.

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Exam: JEE Main 2026
Paper: 21 January, Morning Shift
Subject: Physics
Chapter: Capacitors and R-C Circuits
Topic: Combination of Capacitors and Circuit Analysis