A parallel-plate capacitor of area A, plate separation d and capacitance C is filled with four dielectric materials having dielectric constants k_1,…

A parallel-plate capacitor of area $\displaystyle A$, plate separation $\displaystyle d$ and capacitance $\displaystyle C$ is filled with four dielectric materials having dielectric constants $\displaystyle k_1, k_2, k_3$ and $\displaystyle k_4$ as shown in the figure below. If a single dielectric material is to be used to have the same capacitance $\displaystyle C$ in this capacitor, then its dielectric constant $\displaystyle k$ is given by