A parallel-plate capacitor of area A, plate separation d and capacitance C is filled with four dielectric materials having 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

A

$$k=\frac{2}{3}(k_1+k_2+k_3)+2k_4$$

B

$$\frac{2}{k}=\frac{3}{k_1+k_2+k_3}+\frac{1}{k_4}$$

C

$$\frac{1}{k}=\frac{1}{k_1}+\frac{1}{k_2}+\frac{1}{k_3}+\frac{3}{2k_4}$$

D

$$k=k_1+k_2+k_3+3k_4$$