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. `1/k=1/k_(1)+1/k_(2)+1/k_(3)=3/(2k_(4))`
B. `k=k_(1)+k_(2)+k_(3)+3k_(4)`
C. `k=2/3(k_(1)+1/k_(2)+1/k_(3))=k_(4)`
D. `2/k=3/(k_(1)+k_(2)/k_(3))+1/k_(4)`

Answer

D