Animated Solution for Physics - Electrostatics: For the circuit shown, which of the following statements is true ?

Imagine you have two water tanks, both filled to different levels, but the valves connecting them to the pipes are completely shut. Even if you connect a pipe between the two tanks, if the other ends of the tanks are sealed, no water can flow. This is exactly what's happening in our circuit!

Let's break down the initial state. We have two capacitors, $C_1$ and $C_2$. Using the fundamental formula $q=CV$, we can find the initial charge on each.

For $C_1$, the charge is $q_1=2\text{ pF}\times 30\text{ V}=60\text{ pC}$. For $C_2$, the charge is $q_2=3\text{ pF}\times 20\text{ V}=60\text{ pC}$.

Now, what happens when we close switch $S_3$? The right plate of $C_1$ and the left plate of $C_2$ become connected. But notice that switches $S_1$ and $S_2$ are still open! This means the outer plates of both capacitors are completely isolated from the rest of the universe.

Because the outer plates are isolated, their charges are trapped. They cannot change. And because a capacitor must maintain equal and opposite charges on its facing plates, the charges on the inner plates are also trapped!

Therefore, absolutely no charge flows when $S_3$ is closed. The potential differences across the capacitors remain exactly as they were: $V_1=30\text{ V}$ and $V_2=20\text{ V}$.

This is a classic trap in JEE. It tests your fundamental understanding of charge conservation and isolated systems. Don't rush to apply formulas when a simple conceptual check reveals the answer!