1)

Four identical metal plates are located in the air at equal distance d from each other . The area of each plate in S. If the outermost plates are connected by a  conducting  wire as shown in the figure the  capacitance between points A and B will be

A) $\frac{\epsilon_{0}S}{d}$

B) $\frac{3}{2}\frac{\epsilon_{0}S}{d}$

C) $\frac{1}{2}\frac{\epsilon_{0}S}{d}$

D) $\frac{2}{3}\frac{\epsilon_{0}S}{d}$

Option B

### Explanation:

The equivalent arrangement of given combination  is shown in the following figure,

We know that the capaciance , $C=\frac{\epsilon_{0}S}{d}$

where, S is the area of each plate and d is distance between two plates.

So, equivalent capacitance  between points A and B,

$C_{AB}= \frac{ C \times C}{C+C}+C$

$=\frac{C}{2}+C=\frac{3C}{2}=\frac{3}{2}\frac{\epsilon_{0}S}{d}$