A parallel-plate capacitor of area A, plate
separation d and capacitance C is filled with four
dielectric materials having dielectric constants k1,
k2, k3 and k4 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 :-

(1)``\frac 2k``= ``\frac{3}{k_1 + k_2 + k_3}`` + ``\frac{1}{k_4}``
(2)``\frac 1k``= ``\frac{1}{k_1}`` + ``\frac{1}{k_2}`` + ``\frac{1}{k_3}`` + ``\frac{3}{2k_4}``
(3)`` k = k_1 + k_2 + k_3 + 3k_4``
(4) `` k =\frac 23`` ``( k_1 + k_2 + k_3 )+ 2k_4``