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


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  $