Question

A parallel plate capacitor of capacitance $100pF$ is to be constructed by using paper sheets of $1mm$ thickness as dielectric. If the dielectric constant of paper is $4$, the number of circular metal foils of diameter $2cm$ each required for the purpose is

• A. 40
• B. 20
• C. 30
• D. 10

Answer 1

Answer: (D)

The arrangement of $n$ metal plates separated by dielectric acts as parallel combination of $(n-1)$ capacitors.
Therefore, $C=\frac{(n-1)K{\epsilon }_{0}A}{d}$
Here, $C=100pF$
$=100\times 10^{-12}F$
$K=4,{\epsilon }_0=8.85\times 10^{-12}{C}^2/N{m}^2$
$A=\pi r^2=3.14\times {\left(1\times 10^{-2}\right)}^2$
$d=1mm=1\times 10^{-3}$
$(n-1)\times 4\times 8.85\times 10^{-12}$
$\therefore 100\times 10^{-12}=\frac{\times 3.14\times {\left(1\times 10^{-2}\right)}^2}{1\times 10^{-3}}$
or$n=\frac{1111.156}{111.156}$
$=9.99$
$\approx 10$