Question

In the figure, capacitor is filled with dielectrics. Find the resultant capacitance.

Answer 1

$C_{eq}=\frac{C_1{C}_3}{C_1+C_3}+\frac{C_2{C}_3}{C_2+C_3}$

$\frac{{ϵ}_{o}A}{d}\{\left[\frac{\frac{1/2}{1/2}\times \frac{1/2}{1}}{1+\frac{1}{2}}\right]+\left[\frac{1\times 1/2}{1+1/2}\right]\}$

$=\frac{{ϵ}_{o}A}{d}(\frac{1}{3}+\frac{1}{3})$

$C_{eq}=\frac{2{ϵ}_{o}A}{3d}$