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Three parallel plate air capacitors are ...

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)

A

`(7in_(0)A)/(18d)`

B

`(11in_(0)A)/(18d)`

C

`(13in_(0)A)/(18d)`

D

`(17in_(0)A)/(18d)`

Text Solution

Verified by Experts

The correct Answer is:
B
`C_(p)=C_(1)+C_(2)+C_(3)`
`=(A_(1)epsi_(0))/(d_(1))+(A_(2)epsi_(0))/(d_(2))+(A_(3)epsi_(0))/(d_(3))`
`=(Aepsi_(0))/(3d)+(Aepsi_(0))/(6d)+(Aepsi_(0))/(9d)`
`=(Aepsi_(0))/(3d)(1+(1)/(2)+(1)/(3))=(Aepsi_(0))/(3d)=((6+3+2)/(6))`
`=(11)/(18)(Aepsi_(0))/(d)`.
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