Question

Four identical plates each of area $a$ are separated by a distance $d$. The connection is shown below. What is the capacitance between $P$ and $Q$?

• A. $\frac{2a{\epsilon }_0}{d}$
• B. $\frac{a{\epsilon }_0}{2d}$
• C. $\frac{{\epsilon }_0}{d}$
• D. $\frac{4a{\epsilon }_0}{d}$

Answer 1

The correct option is A $\frac{2a{\epsilon }_0}{d}$

Suppose the pair of plates is connected to positive terminal of the battery and the pair of plates $Q$ is connected to the negative terminal of the battery.
From figure, it is clear that we have two capacitors $C_1$ and $C_2$. Positive plates of $C_1$ are connected to positive plate of $C_2$ and negative plate to negative. Therefore $C_1$ and $C_2$ are in parallel.
So, $C_p=C_1+C_2=2C=\frac{2{\epsilon }_{0}a}{d}$