The equivalent capacitance of the arrangement shown in figure, if `A` is the area of each plate is

Options

A. `(a in_(0))/(d)[(K_(1))/(2)+(K_(2)K_(3))/(K_(2)+K_(3))]`
B. `(a in_(0))/(2d)[(K_(2))/(2)+(K_(1)K_(3))/(K_(1)+K_(3))]`
C. `(a in_(0))/(3d)[(K_(3))/(2)+(K_(1)K_(2))/(K_(1)+K_(2))]`
D. `(a in_(0))/(d)[(K_(1))/(2)+(K_(1)+K_(2))/(K_(2)K_(3))]`

Answer

A

Explanation

`(K_(1) in_(o)((A)/(2)))/(d),C_(2)=(K_(2)in_(o)A)/(d),C_(3)=(K_(3) in_(o)A)/(d)`
`:. C=(C_(2)C_(3))/(C_(2)+C_(3))+C_(1)`.