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