A parallel plate capacitor with plate area A and plate separation d is filled with a dielectric material of dielectric constant K=4. The thickness of…

A parallel plate capacitor with plate area $\displaystyle A$ and plate separation $\displaystyle d$ is filled with a dielectric material of dielectric constant $\displaystyle K=4$. The thickness of the dielectric material is $\displaystyle x$, where $\displaystyle x<d$. Let $\displaystyle \mathrm{C}_1$ and $\displaystyle \mathrm{C}_2$ be the capacitance of the system for $\displaystyle x=\frac{1}{3} d$ and $\displaystyle x=\frac{2 d}{3}$, respectively. If $\displaystyle \mathrm{C}_1=2 \mu \mathrm{~F}$ the value of $\displaystyle \mathrm{C}_2$ is $\displaystyle \_\_\_\_$ $\displaystyle \mu \mathrm{F}$