A parallel-plate capacitor is to be connected across 1 kV. The dielectric has K = 6π and dielectric strength 10⁷ V/m. For safety, the electric field must not exceed 10% of the dielectric strength. If the required capacitance is 50 pF, find the minimum plate area in mm². Use ε₀ = [1/(36π)]×10⁻⁹ SI.
Physics · Capacitor
JEE Advanced

Question

A parallel-plate capacitor is to be connected across 1 kV. The dielectric has K = 6π and dielectric strength 10⁷ V/m. For safety, the electric field must not exceed 10% of the dielectric strength. If the required capacitance is 50 pF, find the minimum plate area in mm². Use ε₀ = [1/(36π)]×10⁻⁹ SI.

Physics · Capacitor

G1 Physics · Accepted Answer

Use Q = CV, U = ½CV² and C = εA/d; reduce the capacitor network by series/parallel combination and apply charge conservation where a node is isolated. Substituting the given values gives 300.