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. `(1)/(K)=(1)/(K_(1))+(1)/(K_(2))+(1)/(2K_(3))`
B. `(1)/(K)=(1)/(K_(1)+K_(2))+(1)/(2K_(3))`
C. `(1)/(K)=(K_(1)K_(2))/(K_(1)+K_(2))+2K_(3)`
D. `K=(K_(1)K_(3))/(K_(1)+K_(3))+(K_(2)K_(3))/(K_(2) +K_(3))`

Answer

D

Explanation

`K=(K_(1)K_(2))/(K_(1)+K_(2))+(K_(2)K_(3))/(K_(2)+K_(3))(Conceptual)`.