Physics · Capacitors and R-C Circuits

JEE Main 2025 — 29 January, Evening Shift — Question 30

A capacitor, $\mathrm{C}_{1}=6 \mu \mathrm{~F}$ is charged to a potential difference of $\mathrm{V}_{0}=5 \mathrm{~V}$ using a 5 V battery. The battery is removed and another capacitor, $\mathrm{C}_{2}=12$ $\mu \mathrm{F}$ is inserted in place of the battery. When the switch ' S ' is closed, the charge flows between the capacitors for some time until equilibrium condition is reached. What are the charges ( $\mathrm{q}_{1}$ and $\mathrm{q}_{2}$ ) on the capacitors $\mathrm{C}_{1}$ and $\mathrm{C}_{2}$ when equilibrium condition is reached.

Option A:
$q_{1}=15 \mu \mathrm{C}, \mathrm{q}_{2}=30 \mu \mathrm{C}$
Option B:
$q_{1}=30 \mu \mathrm{C}, \mathrm{q}_{2}=15 \mu \mathrm{C}$
Option C:
$\mathrm{q}_{1}=10 \mu \mathrm{C}, \mathrm{q}_{2}=20 \mu \mathrm{C}$
Correct
Option D:
$q_{1}=20 \mu \mathrm{C}, \mathrm{q}_{2}=10 \mu \mathrm{C}$

Answer: C

Step-by-step solution

$6 \mathrm{~V}_{\mathrm{C}}+12 \mathrm{~V}_{\mathrm{c}}=30+0$

$18 \mathrm{~V}_{\mathrm{c}}=30$

$\mathrm{V}_{\mathrm{C}}=\frac{30}{18}=\frac{5}{3} \mathrm{Volt}$

$\Rightarrow \mathrm{q}_{1}=\frac{6 \times 5}{3}=10 \mu \mathrm{C}$

$\Rightarrow \mathrm{q}_{2}=\frac{12 \times 5}{3}=20 \mu \mathrm{C}$

Answer key and solution verified before publishing.

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Exam: JEE Main 2025
Paper: 29 January, Evening Shift
Subject: Physics
Chapter: Capacitors and R-C Circuits
Topic: Combination of Capacitors and Circuit Analysis