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A parallel plate capacitor is of area 6 ...

A parallel plate capacitor is of area 6 `cm^(2)` and a separation 3 mm. The gap is filled with three dielectric materials of equal thickness (see figure) with dielectric constant `K_(1)=10`, `K_(2)=12 and K_(3) = 14`. The dielectric constant of a material which when fully inserted in above capacitor, gives same capacitance would be :

A

4

B

14

C

36

D

12

Text Solution

Verified by Experts

The correct Answer is:
D
`C=(epsilon_(0)A)/(d)`
`C_(1)=(K_(1)epsilon_(0)A)/(3d)=(K_(1)C)/(3)`
`C_(2)=(K_(2)C)/(3)`
`C_(3)=(K_(3)C)/(3)`
`C_(eq)=K_(eq)=(C)/(3)(K_(1)+K_(2)+K_(3))`
`K_(eq)=(K_(1)+K_(2)+K_(3))/(3)=(36)/(3)=12`.
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