Question

Three parallel plate air capacitors are connected in parallel. Each capacitor has plate area `"A"/3` and separation between the plates is 'd', '2d', '3d' respectively. The equivalent capacity of combination is ______ 

(ε₀ = absolute permittivity of free space)

Options

• 7A ε₀/18d 

• 5A ε₀/9d 

• 11A ε₀/18d 

• 9A ε₀/17d 

Answer 1

Three parallel plate air capacitors are connected in parallel. Each capacitor has plate area `"A"/3` and separation between the plates is 'd', '2d', '3d' respectively. The equivalent capacity of the combination is 11A ε₀/18d.

Explanation:

 

`"C"_1 = (epsilon_0"A")/(3"d")`

`"C"_2 = (epsilon_0"A")/(6"d")`

`"C"_3 = (epsilon_0"A")/(9"d")`

∴ `"C"_1 + "C"_2 + "C"_3 = (epsilon_0"A")/"d" [1/3 + 1/6 + 1/9]`

= `(epsilon_0"A")/"d" ((6 + 3 + 2))/18`

= `(11epsilon_0"A")/(18"d")`