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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 four dielectric materials hving dielectric constants `K_(1), K_(2), K_(3)` and `K_(4)` as shown in the figure below. If a single dielectric material is to be used to have the same capacitance c in this capacitor, then its dielectric constant K is given by

A

`k=k_(1)+k_(2)+k_(3)+3k_(4)`

B

`k=(2)/(3)(k_(1)+k_(2)+k_(3))+2k_(4)`

C

`(2)/(k)=(3)/(k_(1)+k_(2)+k_(3))+(1)/(k_(4))`

D

`(1)/(k)=(1)/(k_(1))+(1)/(k_(2))+(1)/(k_(3))+(3)/(2k_(4))`

Text Solution

Verified by Experts

The correct Answer is:
C

`(1)/(C)=(1)/(C_(1))+(1)/(C_(2))`
`(d)/(kAin_(0))=(3d)/(2(k_(1)+k_(2)+k_(3))Ain_(0))+(d)/(2k_(4)Ain_(0))`
`(d)/(kAin_(0))=(d)/(Ain_(0))[(3)/(2(k_(1)+k_(2)+k_(3)))+(1)/(2k_(4))]`
`(2)/(k)=(3)/(k_(1)+k_(2)+k_(3))+(1)/(k_(4))`
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