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In the figure a capacitor is filled with...

In the figure a capacitor is filled with dielectrics. The resultant capacitance is

A

`(2epsilon_0A)/d[1/k_1+1/k_2+1/k_3]`

B

`(epsilon_0A)/d[1/k_1+1/k_2+1/k_3]`

C

`(2epsilon_0A)/d[k_1+k_2+k_3]`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
D
`C_1=(k_1(A/2)epsilon_0)/(d//2)=(k_1Aepsilon_0)/(d) , C_2 = (k_2Aepsilon_0)/d`
`C_3=(k_3Aepsilon_0)/(2d)`
`C_(eq) = C_3 +(C_1xxC_2)/(C_1+C_2) = (k_3/2+(k_1k_2)/(k_1+k_2))(epsilon_0A)/d`
`k_(eq)=k_3/2 +(k_1k_2)/(k_1+k_2)`
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