Key relation for capacitors in parallel

When two capacitors are connected in parallel to the same battery, both have the same potential difference $V$ across them.

Use the charge-time graph

For each capacitor, $Q = CV$ Since $V$ is the same for both capacitors, the capacitor that finally attains greater charge must have greater capacitance.

From the given charge-time graph, capacitor $C_2$ reaches a higher charge than capacitor $C_1$.

Therefore, $Q_2 > Q_1 \,\Rightarrow\, C_2V > C_1V$ $\Rightarrow C_2 > C_1$

Compare stored energies

Energy stored in a capacitor is $U = \frac{1}{2}CV^2$

Again, since both capacitors are connected in parallel, $V$ is the same for both. Hence energy is directly proportional to capacitance: $U \propto C$

Since $C_2 > C_1,$ we get $U_2 > U_1$

Check options

• A: $C_2 > C_1,\ U_2 > U_1$ ✅
• B: $C_1 > C_2,\ U_1 > U_2$ ❌
• C: $C_2 > C_1,\ U_2 < U_1$ ❌
• D: $C_1 > C_2,\ U_1 < U_2$ ❌

Final answer

The correct option is: $\boxed{A}$