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. $2a{\epsilon }_0/d$
• B. $a{\epsilon }_0/(2d)$
• C. $a{\epsilon }_0/d$
• D. $4a{\epsilon }_0/d$

Answer 1

Answer: (A)

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 $C_4$ are connected to positive plate of $C_2$ and negative plate to negative. Therefore $C_1$ and $C_2$ are in parallel.
So, $C_p=C_1+C_2=2C=\frac{2{\epsilon }_{0}a}{d}$