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_0A)/(18d)`
B. `(11epsilon_0A)/(18d)`
C. `(13epsilon_0A)/(18d)`
D. `(17epsilon_0A)/(18d)`

Answer

B

Explanation

According to question, capacitance of parallel plate capacitor is given by `C=(varepsilon_0A)/d`
For first capacitor, `C_1=(varepsilon_0A)/(3d)`
For second capacitor, `C_2=(varepsilon_0A)/(6d)`
For third capacitor, `C_3=(varepsilon_0A)/(9d)`
Again they are arranged in parallel combination, so equivalent capacitor is given by
`C_(eq)=C_1+C_2+C_3`
=`varepsilon_0A/d(1/3+1/6+1/9)= varepsilon_0A/(d)xx11/18=(11varepsilon_0A)/(18d)`