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A parallel plate capacitor having plates...

A parallel plate capacitor having plates of area S and plate separation d, has capacitance `C_1` in air. When two dielectrics of different relative primitivities (`epsilon_1=2epsilon_0` and `epsilon_2=4epsilon_0`) are introduced between the two plates as shown in the figure, the capacitance becomes `C_2`. The ratio `C_2/C_1` is

A

`6/5`

B

`5/3`

C

`7/5`

D

`7/3`

Text Solution

Verified by Experts

The correct Answer is:
D
`c_1=(epsilon_0s)/d,c=(2epsilon_0(s)/2)/((d)/2)=(2epsilon_0s)/d`
`c '=(eepsilon_0(s)/2)/((d)/2)=(4epsilon_0s)/d`
and `c '' =(2epsilon_0s/2)/d=(epsilon_0s)/d`
`c_2=(c c')/(c+c)+c''=4/3 (epsilon_0s)/d+(epsilon_0s)/d=7/3(epsilon_0s)/d(c_2)/c_1=7/3`
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