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  4. A parallel plate capacitor with air between the plates has a capacitance of 10 pF. The capacitance, if the distance between the plates is reduced by half and the space between them is filled with a substance of dielectric constant 4 is

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Q. A parallel plate capacitor with air between the plates has a capacitance of $10\, pF$. The capacitance, if the distance between the plates is reduced by half and the space between them is filled with a substance of dielectric constant $4$ is

Electrostatic Potential and Capacitance

Solution:

Here, $C_{1}=\frac{\varepsilon_{0}A}{d}=10\,PF \ldots\left(i\right)$
and $C_{2}=k\frac{\varepsilon_{0}A}{d 2}=\frac{4\times2\varepsilon_{0}A}{d} \left(\because k=4\right)$
$=8\times10 \left(using \left(i\right)\right)$
$=80\,PF$