A parallel plate capacitor is to be designed with a voltage rating 1 KV using a material of dielectrical constant 3 and dielectric strength about `10^(7) Vm^(-1)`. [Dielectric strength is the maximum electric field a material can tolerate without break down, i.e, without starting to conduct electrically through partial ionisation. For safety, we should like the field never to exceed say `10%` of the dielectric strength]. What minimum area of the plates is required to have a capacitance of 50 pF ?

Explanation

`Elt10^8 rArr 10^3/dlt10^6`
`dgt10^(-3)m rArr C=(kepsilon_0A)/d`
`d=(kepsilon_0A)/Cgt10^(-3)`
`Agt(10^(-3)xxC)/(kepsilon_0)rArr Agt (10^(-3)xx50xx10^(-12))/((6pi)xx1/(36xx10^(-9))=300 mm^2`