Question

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

• A. $\frac{\epsilon _{0} A}{d}$
• B. $\frac{2ε_{0} A}{d}$
• C. $\frac{3ε_{0} A}{d}$
• D. $\frac{4ε_{0} A}{d}$

Answer 1

Answer: (C)

Plate $1$ is connected to plate $3$ and plate $2$ is connected to plate $4$ . Thus, there are three capacitors in parallel, each of capacitance
$C=\frac{\epsilon _{0} A}{d}$

The equivalent capacitance, as shown in the figure, is
$C^{′}=3C=\frac{3 \epsilon _{0} A}{d}$