Four identical metal plates each of area A are separated mutually by a distance d and are connected as shown. Find the capacity of the system between the terminals A and B.

Options

A. `(epsi_(0)S)/(d)`
B. `(3)/(2)(epsi_(0)S)/(d)`
C. `(1)/(2)(epsi_(0)S)/(d)`
D. `(2)/(3)(epsi_(0)S)/(d)`

Answer

B

Explanation

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

we know that the capacitance, `C=(epsi_(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)=(CxxC)/(C+C)+C`
`=(C)/(2)+C=(3C)/(2)=(3)/(2).(epsi_(0)S)/(d)`