Question

The following arrangement consists of five identical metal plates marked $1$, $2$, $3$, $4$ and $5$ parallel to each other. Area of each plates is $A$ and separation between the successive plates is $d$. The capacitance between $P$ and $Q$ is

• A. $5\frac{{\epsilon }_{0}A}{d}$
• B. $\frac{7}{3}\frac{{\epsilon }_{0}A}{d}$
• C. $\frac{5}{3}\frac{{\epsilon }_{0}A}{d}$
• D. $\frac{4}{3}\frac{{\epsilon }_{0}A}{d}$

Answer 1

Answer: (C)

The arrangement will work as a system of capacitors shown in figures (a) and (b) below


Capacitance of each capacitor in figure (a) is
$C=\frac{{\epsilon }_{0}A}{d}$
Equivalent capacitance between $P$ and $Q$ is
$C^{\prime }=C+\frac{C\times 2C}{C+2C}=\frac{5}{3}C=\frac{5}{3}$
$\frac{{\epsilon }_{0}A}{d}$