The expression for the equivalent capacitance of the system shown in Fig. is (A is the corss-sectional area of one of the planes) :

Options

A. `in_(0)A//3d`
B. `(3 in_(0)A)/(d)`
C. `in_(0)A//6d`
D. none of the above

Answer

D

Explanation

`C_(1) = (in_(0)A)/(d), C_(2) = (in_(0)A)/(2d)`
`C_(3) = (in_(0)A)/(3d)`
As three condensers are in parallel. Fig
`:. C_(p) = C_(1) + C_(2) + C_(3) = (in_(0) A)/(d) + (in_(0) A)/(2d) + (in_(0)A)/(3d)`
`C_(p) = (in_(0)A)/(d) [1 + (1)/(2) + (1)/(3)] = (11 in_(0) A)/(6d)`
Choice (d) is correct.