Q53 / 75 · JEE Main 2025 (28 Jan Shift 1) · Physics

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? Figure

  • A
    $\mathrm{C}_2\gt\mathrm{C}_1, \mathrm{U}_2 \lt \mathrm{U}_1$
  • B
    $\mathrm{C}_1\gt\mathrm{C}_2, \mathrm{U}_1\gt\mathrm{U}_2$
  • C
    $\mathrm{C}_1\gt\mathrm{C}_2, \mathrm{U}_1 \lt \mathrm{U}_2$
  • Correct answer
    D
    $\mathrm{C}_2\gt\mathrm{C}_1, \mathrm{U}_2\gt\mathrm{U}_1$

Solution

For a capacitor at steady state $q=C V \text { and } U=\frac{1}{2} C V^2$ Since $C_1$ and $C_2$ are connected in parallel, $V_1=V_2$. Also from graph $q_1 < q_2$ $\begin{aligned} & \Rightarrow \quad C_1 V_1 < C_2 V_2 \\ & \text { i.e. } C_1 < C_2 \text { or } C_2>C_1 \\ & \qquad \frac{U_1}{U_2}=\frac{C_1 V_1^2}{C_2 V_2^2}=\frac{C_1}{C_2} < 1 \end{aligned}$ or $U_1 < U_2$ or $U_2>U_1$

Hence, the correct answer is option: 'D'.

Relevant Questions