Question

Five identical plates of equal area $A$ are placed parallel to each other and at equal distance $d$ from each other as shown in the figure. The effective capacity of the system between the terminals $A$ and $B$ is

• A. $\frac{3}{5}\frac{\epsilon _{0} A}{d}$
• B. $\frac{5}{4}\frac{\epsilon _{0} A}{d}$
• C. $\frac{5}{3}\frac{\epsilon _{0} A}{d}$
• D. $\frac{4}{5}\frac{\epsilon _{0} A}{d}$

Answer 1

Answer: (C)

Plates 1-2, 2-3, 3-4 and 4-5 form a total of four capacitors.
The capacity of each capacitor is, $C_{0} \, = \, \frac{\epsilon _{0} A}{d}$
From figure, it is clear that, $C_{e q} \, = \, \frac{5}{3}C_{0} \, = \, \frac{5}{3}\frac{\epsilon _{0} A}{d}$