A parallel plate capacitor is to be designed with a voltage rating 1kV, using a maeterial of dielectric constant 3 and dielectric strength about `10^(7) Vm^(-1)`, (Dielectric strength is the maximum electric field a material can tolerate without breakdown, i.e, without starting to conduct electricity 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 50pF?

Explanation

`V=10^(3)V, epsi_(r)=3, " "E_(de)=10^(7)Vm^(-1)," "E=(10)/(100) xx 10^(7) =10^(6)Vm^(-1)`
`A=? C=50pF =50 xx 10^(-12)F`
`E=V/d, therefore d=V/E=(10^(3))/(10^(6))=10^(-3)m`
`C=(epsi_(0)epsi_(r)A)/(d)`
`A=(C.d)/(epsi_(0) epsi_(r))= (50 xx 10^(-12) xx 10^(-3))/(8.85 xx 10^(-12) xx 3)=1.9 xx 10^(-3) m^(2)=19 xx 10^(-4) m^(2)=19cm^(2)`