JEE Main 2025 Jan 28 Shift 1, Physics Q1: Energy Stored In A Capacitor

JEE Main2025Jan 28, Shift 1Physics

Two capacitors $C_{1}$ and $C_{2}$ are connected in parallel to a battery. Charge-time graph is shown below for the two capacitors. The energy stored with them are $U_{1}$ and $U_{2}$ , respectively. Which of the given statements is true ?

A
$C_{1} > C_{2}$ , $U_{1} > U_{2}$
B
$C_{2} > C_{1}$ , $U_{2} < U_{1}$
C
$C_{1} > C_{2}$ , $U_{1} < U_{2}$
D
$C_{2} > C_{1}$ , $U_{2} > U_{1}$

Solution

Both capacitors are connected in parallel to the same battery, so they reach the same final potential difference $V$ .

From the graph, the saturation charge of $C_{2}$ exceeds that of $C_{1}$ . Since $q = C V$ with $V$ common, the capacitance ordering follows the charge ordering: $C_{2} > C_{1}$ .

Energy stored is $U = \frac{1}{2} C V^{2}$ . With the same $V$ , larger $C$ gives larger $U$ , so $U_{2} > U_{1}$ .

$∴ C_{2} > C_{1}$ and $U_{2} > U_{1}$ .

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JEE Main 2025 Jan 28 Shift 1, Physics Q1: Energy Stored In A Capacitor

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