Question

A parallel plate capacitor has plate area $100m^2$ and plate separation of $10m$. The space between the plates is filled up to a thickness 5 $m$ with a material of dielectric constant of $10.$ The resultant capacitance of the system is 'x' $pF$. The value of ${\epsilon }_0=8.85\times 10^{-12}F.m^{-1}$.The value of ' $x$ ' to the nearest integer is ______.

Answer 1

Answer: 161

$A=100m^2$
Using $C=\frac{k{\in }_{0}A}{d}$
$C_1=\frac{10{\in }_0(100)}{5}$
$=200{\in }_0$
$C_2=\frac{{ϵ}_0(100)}{5}=20{\in }_0$
$C_1\&C_2$ are in series so $C_{\text{eqv. }}=\frac{C_1{C}_2}{C_1+C_2}$
$=\frac{4000{\in }_0}{220}$
$=160.9\times 10^{-12}\simeq 161pF$