Question

A composite parallel plate capacitor is made up of two different dielectric materials with different thickness $(t_1$ and $t_2)$ as shown in figure. The two different dielectric material are separated by a conducting foil $F$. The voltage of the conducting foil is _______$V$

Answer 1

Answer: 60

Capacitance of each capacitor
$C_1=\frac{A3{\in }_0}{\frac{1}{2}}=6A{\in }_0$
$C_2=A4{\in }_0=4A{\in }_0$
Equivalent capacitance
$C_{eq}=\frac{C_1{C}_2}{C_1+C_2}\Rightarrow \frac{24}{10}A{\in }_0$
$q_{net}=C_{eq}(\Delta V)\Rightarrow 240A{\in }_0$
$\Delta V_2=\frac{240A{ϵ}_0}{4A{ϵ}_0}=60V$
$(\Delta V_2=$ Potential drop across $C_2)$
$V_{\text{foil }}=60V$