Question

Four metallic plates each with a surface area of one side $A$, are placed at a distance $d$ from each other. The two outer plates are connected to one point $A$ and the two other inner plates to another point $B$ as shown in the figure. Then the capacitance of the system is :

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

Answer 1

The correct option is B $\frac{2{ϵ}_{0}A}{d}$

There are two capacitors with capacitance $C_1=C_2=\frac{A{ϵ}_0}{d}$.
As they are in parallel so the net capacitance $C=C_1+C_2=\frac{A{ϵ}_0}{d}+\frac{A{ϵ}_0}{d}=\frac{2A{ϵ}_0}{d}$