A parallel -plate capacitor of area `A`, plate separation `d` and capacitance `C` is filled with four dielectric materials having dielectric constant `k_(1), k_(2), k_(3)` and `k_(4)` as shown in the figure below. If a single dielectric materical 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