#$2-$ Inhomogeneous Capacitors $(10$ pts$)$

An inhomogeneous parallel$-$plate capacitor is shown to the right. The terminals are placed at the top and bottom of the plates. Recall the resistance of a single homogeneous parallel$-$plate capacitor:

$C=\frac{lo{n}_{r}lo{n}_{o}S}{h}$

Where $S$ is the surface area cross$-$section, $lo{n}_r$ is the relative material permittivity and $lo{n}_o$ is the free$-$space permittivity.

The dimensions are $w_1=w_2=2\mathrm{.}7cm,l=4cm,h=1\mathrm{.}54cm,lo{n}_{r1}=18,lo{n}_{r2}=10.$ Perform the following:

$($a$)$ Draw the corresponding circuit schematic of homogeneous capacitors that comprise the inhomogeneous capacitor.

$($b$)$ Calculate the corresponding capacitance for each homogeneous capacitor.

$($c$)$ Calculate the overall capacitance.

Recall that the permittivity of free space is given by $lo{n}_o=8\mathrm{.}854{10}^{-12}\frac{F}{m}.$