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. If a isngle dielectric material is to be used to have the same capacitance C in this capacitor, then its dielectic constant k is given by

Options

A. `k=k_(1)+k_(2)+2k_(3)`
B. `k=(k_(1)k_(2))/(k_(1)+k_(2))+2k_(3)`
C. `(1)/(k)=(1)/(k_(1))+(1)/(k_(2))+(1)/(2k_(3))`
D. `(1)/(k)=(1)/(k_(1)+k_(2))+(1)/(2k_(3))`

Answer

D