Question

Four metal plates numbered $1,2,3$ and $4$ are arranged as shown below. The area of each plate is $A$ and separation between adjacent plates is $d$. The capacitance of the arrangement is

• A. $\frac{{\epsilon }_{o}A}{d}$
• B. $\frac{2{\epsilon }_{o}A}{d}$
• C. $\frac{3{\epsilon }_{o}A}{d}$
• D. $\frac{4{\epsilon }_{o}A}{d}$

Answer 1

The correct option is B $\frac{2{\epsilon }_{o}A}{d}$

Connecting the points A and B to the terminals of a battery.




The inner plates 2 and 3 are connected together due to which they act as a single conductor. Since the outer plates 1 and 4 are connected together, there are effectively two capacitors:

1. Between plates 1 & 2.
2. Between plates 3 & 4.

These two capacitors are in parallel as shown below:


Capacitance of a parallel plate capacitor having area $A$ and distance $d$ between plates is given by,
$C=\frac{{\epsilon }_{o}A}{d}$

Both the capacitors are connected in parallel.

$C_{eq}=C_1+C_2=2C$

So equivalent capacitance,
$C_{\text{eq}}=\frac{2{\epsilon }_{o}A}{d}$