Question

Three identical, parallel conducting plates $A,B$ and $C$ are placed as shown. Switches $S_1$ and $S_2$ are open, and can connect $A$ and $C$ to earth when closed. $+Q$ charge is given to $B$:

• A. If $S_1$ is closed with $S_2$ open, a charge of amount $Q$ will pass through $S_1$
• B. If $S_2$ is closed with $S_1$ open, a charge of amount $Q$ will pass through $S_2$
• C. If $S_1$ and $S_2$ are closed together, a charge of amount Q/3 will pass through $S_1$, and a charge of amount $2Q/3$ will pass through $S_2$
• D. All the above statements are incorrect

Answer 1

Answer: (A), (B), (C)

The correct options are
A If $S_1$ is closed with $S_2$ open, a charge of amount $Q$ will pass through $S_1$
B If $S_2$ is closed with $S_1$ open, a charge of amount $Q$ will pass through $S_2$
C If $S_1$ and $S_2$ are closed together, a charge of amount Q/3 will pass through $S_1$, and a charge of amount $2Q/3$ will pass through $S_2$

When only one of the plates is earthed, a parallel plate capacitor is formed with +Q and -Q charges on the inner surface. There is no role of the outer plate here.
When both the given plates are earthed, the two capacitors forms are now in parallel with capacitances in the ratio $1:2$ and hence share the charge Q in the same ratio.