Physics · Capacitors and R-C Circuits

JEE Main 2026 — 23 January, Evening Shift — Question 33

A parallel plate capacitor with plate separation 5 mm is charged by a battery. On introducing a mica sheet of 2 mm and maintaining the connections of the plates with the terminals of the battery, it is found that it draws $25 \%$ more charge from the battery. The dielectric constant of mica is $\_\_\_\_$ .

Option A:
2.5
Option B:
2
Correct
Option C:
1.5
Option D:
1

Answer: B

Step-by-step solution

C = \frac{\epsilon_0 A}{d}

Q_1 = CV

Q_2 = C_{\text{eq}} V

Q_2 = 1.25\,CV

C_{\text{eq}} = \frac{C_1 C_2}{C_1 + C_2} = \frac{\left(\frac{\epsilon_0 A}{3}\right) \left(\frac{K \epsilon_0 A}{2}\right)} {\left(\frac{\epsilon_0 A}{3}\right) + \left(\frac{K \epsilon_0 A}{2}\right)}

C_{\text{eq}} = \frac{\frac{K \epsilon_0^2 A^2}{6}} {\frac{\epsilon_0 A (2 + 3K)}{6}}

C_{\text{eq}} = \frac{K \epsilon_0 A}{2 + 3K}

1.25 \times \frac{\epsilon_0 A}{5} = \frac{K \epsilon_0 A}{2 + 3K}

0.25(2 + 3K) = K

2 + 3K = 4K

K = 2

Answer key and solution verified before publishing.

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Exam: JEE Main 2026
Paper: 23 January, Evening Shift
Subject: Physics
Chapter: Capacitors and R-C Circuits
Topic: Effect of Dielectrics