A parallel plate capacitor is to be designed with a voltage rating of 1 kV, using a material of dielectric constant 3 and dielectric strength of about 107Vm–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 50 pF?
Step 1 : Electric field inside capacitor For safety, the field intensity never exceeds 10% of the dielectric strength. Hence, electric field intensity, E=10% of 107 V/m =106 V/m Given V=1kV=1000V We know that, V=E×d ∴ Distance between the plates d=EV=1061000=10−3m Step 2: Capacitance Given, Capacitance C=50pF Also, C=dKAεo Dielectric constant of material, K=3 ∴ A=εoKCd=8.85×10−12×350×10−12×10−3≈19 cm2
