A parallel plate capacitor of area A, plate separation d and capacitance C is filled with three different dielectric materials having dielectric constants `k_1 k_2 and k_3` as shown in the following figure. 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

Options

A. `1/k=1/k_1+1/k_2+1/(2k_3)`
B. `1/k=1/(k_1+k_2)+1/(2k_3)`
C. `k=(k_1k_2)/(k_1+k_2)+2k_3`
D. `k=(k_1 k_3)/(k_1+k_3)+(k_2 k_3)/(k_2+k_1)`

Answer

B