A parallel plate capacitor of area A, plate separation d and capacitance C is filled with four dielectric materials hving dielectric constants `K_(1), K_(2), K_(3)` and `K_(4)` as shown in the figure below. 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. `K=K_(1)+K_(2)+K_(3)+3K_(4)`
B. `K=2/3 (K_(1)+K_(2)+K_(3))+2K_(4)`
C. `2/K=(3)/(K_(1)+K_(2)+K_(3))+1/K_(4)`
D. `1/K=1/K_(1)+1/K_(2)+1/K_(3)+3/(2K_(4))`

Answer

C