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A parallel plate capacitor of area A, pl...

A parallel plate capacitor of area A, plate separation d and capacitance C is filled with three different dielectric materials having dielectric constants `k_1`, `k_2` and `k_3` as shown. If a isngle dielectric material is to be used to have the same capacitance C in this capacitor, then its dielectic constant k is given by

A

`1/k = 1/k_1 + 1/k_2 + 1/(2k_3)`

B

`1/k = 1/(k_1+k_2) + 1/(2k_3)`

C

`k = (k_1k_2)/(k_1+k_2) + 2k_3`

D

`k = k_1 +k_2 + 2k_3`

Text Solution

Verified by Experts

The effective capacitance is given by
`(epsilon_(0)A)/(d)[(1)/(k_(1)+k_(2))+(1)/(2k_(3))]^(-4)`
The capacitance of a single capacitor will be `(epsilon_(0)A//d)k`.
`k=[(1)/((k_(1)+k_(2)))+(1)/(2k_(3))]^(-1)` or `(1)/(k)=(1)/((k_(1)+k_(2)))+(1)/(2k_(3))`
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