Question

In a parallel plate capacitor set up, the plate area of capacitor is $2m^2$ and the plates are separated by $1m$. If the space between the plates are filled with a dielectric material of thickness $0.5m$ and area $2m^2$ (see fig.) the capacitance of the set-up will be ____ ${\epsilon }_0$.
(Dielectric constant of the material $=3.2$)
(Round off to the Nearest Integer)

Answer 1

Answer: 3

$C=\frac{{\epsilon }_{0}A}{\frac{d}{2K}+\frac{d}{2}}=\frac{2{\epsilon }_{0}A}{\frac{d}{K}+d}$
$=\frac{2\times 2{\epsilon }_0}{\frac{1}{3.2}+1}=\frac{4\times 3.2}{4.2}{\epsilon }_0$
$=3.04{\epsilon }_0$