Three parallel plate air capacitors are connected in parallel each capacitor has plate area `('A')/(3)` and the separation between the plates is 'd', '2d' and '3d' respectively. The equivalaent capacity of combination is (`epsi_(0)`=absolute permittivity of free space).

Options

A. `(7epsi_(0)A)/(18d)`
B. `(11epsi_(0)A)/(18d)`
C. `(13epsi_(0)A)/(18d)`
D. `(17epsi_(0)A)/(18d)`

Answer

B

Explanation

For a parallel plate capacitor, `C=(Aepsi_(0))/(d)`
and since the three capacitors are joined in parallel
`C_(P)=C_(1)+C_(2)+C_(3)`
`=(Aepsi_(0))/(3d)+(Aepsi_(0))/(3xx2d)+(Aepsi_(0))/(3xx3d)`
`=(A epsi_(0))/(3d)[1+(1)/(2)+(1)/(3)]=(Aepsi_(0))/(3d)xx(11)/(6)`
`therefore C_(P)=(11 A epsi_(0))/(18d)`