Question

A parallel plate capacitor has plate area $40c{m}^2$ and plates separation $2mm$. The space between the plates is filled with a dielectric medium of a thickness $1mm$ and dielectric constant $5$ . The capacitance of the system is :

• A. $\frac{10}{3}{\epsilon }_{0}F$
• B. $\frac{3}{10}{\epsilon }_{0}F$
• C. $24{\epsilon }_{0}F$
• D. $10{\epsilon }_{0}F$

Answer 1

Answer: (A)

This can be seen as two capacitors in series combination so
$\frac{1}{C_{eq}}=\frac{1}{C_1}+\frac{1}{C_2}$
$=\frac{1}{\frac{K{\in }_{0}A}{t}}+\frac{1}{\frac{{\in }_{0}A}{d-t}}$
$=\frac{t}{K{\in }_{0}A}+\frac{d-t}{{ϵ}_{0}A}$
$=\frac{1\times 10^{-3}}{5{ϵ}_0\times 40\times 10^{-4}}+\frac{1\times 10^{-3}}{{ϵ}_{0}40\times 10^{-4}}$
$\frac{1}{C_{eq}}=\frac{1}{20{ϵ}_0}+\frac{1}{4{ϵ}_0}$
$C_{eq}=\frac{20\times 4{ϵ}_0}{24}=\frac{10{ϵ}_0}{3}F$