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

Options

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

Answer

D

Explanation

`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)`