JEE Physics 2025 Question with Solution

Given: Two capacitors $C_1$ and $C_2$ are connected in parallel to a battery, so both have the same potential difference $V$. The charge-time graph shows that capacitor $C_2$ reaches a higher final charge than capacitor $C_1$.

Find: The correct relation between capacitances and energies $U_1$ and $U_2$.

For capacitors connected in parallel,

$$Q = CV$$

At the same voltage, the capacitor with greater final charge has greater capacitance. From the graph,

$$Q_2 > Q_1$$

Therefore,

$$C_2 > C_1$$

The energy stored in a capacitor is

$$U = \frac{1}{2}CV^2$$

Since both capacitors have the same voltage $V$, energy is directly proportional to capacitance. Hence,

$$U_2 > U_1$$

Therefore, the correct option is B: $C_2 > C_1, U_2 > U_1$.

Note: The extracted solution text on the page contains an internal inconsistency with the displayed graph; the graph and the marked correct option both support option B.