A parallel plate capacitor is to be designed, using a dielectric of dielectric constant $5$, so as to have a dielectric strength of $10^9\;Vm^{-1}$ . If the voltage rating of the capacitor is $12\;kV$, the minimum area of each plate required to have a capacitance of $80\;pF$ is
NEET 2017, Medium
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$V=E d$
$\therefore d=\frac{V}{E}$
$C=\frac{K \varepsilon_0 A}{d}$
$\therefore A=\frac{C d}{K \varepsilon_0}$
$=\frac{C V}{K E \varepsilon_0}$
$=\frac{80 \times 10^{-12} \times 12 \times 10^3}{5 \times 10^9 \times 8.85 \times 10^{-12}}$
$=21.69 \times 10^{-6}$
$=21.7 \times 10^{-6} \;m ^2$
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