Question

Two parallel plates of area A are separated by two different dielectric. The net capacitance is

• A. $\frac{{\epsilon }_{0}A}{d}$
• B. $\frac{7}{20}\frac{{\epsilon }_{0}A}{d}$
• C. $\frac{20}{7}\frac{{\epsilon }_{0}A}{d}$
• D. $\frac{2{\epsilon }_{0}A}{d}$

Answer 1

Answer: (C)

This is a series combination because there is separation charges and in parallel combination area changes
$\frac{1}{C_{eq}}=\frac{1}{C_1}+\frac{1}{C_2}$
$\Rightarrow \frac{1}{C_{eq}}$
$=\frac{d_1}{K_1{\epsilon }_{0}A}+\frac{d_2}{K_2{\epsilon }_{0}A}$
$\therefore \frac{1}{C_{eq}}=\frac{d}{2{\epsilon }_{0}A}\left[\frac{1}{2}+\frac{1}{5}\right]$
$\therefore \frac{1}{C_{eq}}=\frac{d}{2{\epsilon }_{0}A}\left(\frac{5+2}{10}\right)$
$\Rightarrow \frac{1}{C_{eq}}$ $=\frac{7d}{20{\epsilon }_{0}A}$
$C_{eq}=\frac{20{\epsilon }_{0}A}{7d}$