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 equivalent capacity of combination is `(epsilon_0` = absolute permittivity of free space)

Options

A. `(7epsilon_(0)A)/(18d)`
B. `(1epsilon_(0)A)/(18d`
C. `(13epsilon_(0)A)/(18d)`
D. `(17epsilon_(0)A)/(18d)`

Answer

B

Explanation

According to question, capacitance of parallel plate
`"capacitor is given by C"=(epsilon_(0)A)/(d)`
`"For first capacitor, "C_(1)=(epsilon_(0)A)/(3d)`
`"For second capacitor, "C_(2)=(epsilon_(0)A)/(6d)`
`"For third capacitor," C_(3)=(epsilon_(0)A)/(9d)`
Again they are arranged in parallel combination, so equivalent capacitor is given by
`C_("eq")=C_(1)+C_(2)+C_(3)`
`=(epsilon_(0)A)/(d)xx(11)/(18)=(11epsilon_(0)A)/(18d)`