JEE Physics 2025 Question with Solution

Given: A circuit contains a resistor $R$, an air capacitor with plates $A$ and $B$, a key, and a $5 \, \text{V}$ battery. We must identify the valid statements at the instant the key is closed.

Find: Which of the statements $A, B, C, D$ are correct at the initial instant.

At the instant the key is closed, the capacitor is initially uncharged, so it behaves like a short circuit. Therefore, the potential difference across the capacitor is zero initially, and the charging current is maximum.

Now analyze each statement:

1. Statement A: "There will be no current through resistor $R$" is incorrect. At the initial instant, current is maximum in the circuit, so current does pass through $R$.
2. Statement B: "There will be maximum current in the connecting wires" is correct.
3. Statement C: "Potential difference between the capacitor plates $A$ and $B$ is minimum" is correct because initially

which is the minimum value. 4. Statement D: "Charge on the capacitor plates is minimum" is correct because initially

which is the minimum charge.

Therefore, the correct combination is $B, C, D$ only. Hence, the correct option is B.

Given: The key is closed at $t = 0$ in a resistor-capacitor circuit connected to a $5 \, \text{V}$ battery.

Find: The valid statements about current, potential difference, and charge at that instant.

A capacitor cannot acquire charge instantaneously. So at the very first instant,

and hence

Therefore the capacitor acts like a conducting path initially.

Because the capacitor behaves like a short circuit at that instant, the current in the circuit is maximum. This means the claim of no current through resistor $R$ is false, while the claim of maximum current in the connecting wires is true.

Also, since both the charge and capacitor voltage start from zero, the potential difference across plates $A$ and $B$ is minimum and the charge on the plates is minimum at that instant.

Thus, statements B, C, and D are valid. The correct option is B.