Question

The paper dielectric in a paper-and-foil capacitor is 0.0800 mm thick. Its dielectric constant is 2.50, and its dielectric strength is 50.0 MV/m. Assume that the geometry is that of a parallel-plate capacitor, with the metal foil serving as the plates. (a) What area of each plate is required for a 0.200 wF capacitor? (b) If the electric field in the paper is not to exceed one-half the dielectric strength, what is the maximum potential difference that can be applied across the capacitor?

Answer 1

a) 0.723 m²

b) 2000V

Step-by-step explanation:

Given that

Thickness of the capacitor, d = 0.08*10^-3 m

Dielectric constant of the capacitor, k = 2.5

Dielectric strength of the capacitor, E = 50*10^6

Capacitance of the capacitor, C = 0.2*10^-6

Permittivity of free space, E• = 8.85*10^-12

a)

The area, A is given by the formula

A = (C * d) / (k * E•)

A = (0.2*10^-6 * 0.08*10^-3) / (2.5 * 8.85*10^-12)

A = 1.6*10^-11 / 2.213*10^-11

A = 0.723 m²

b)

Potencial difference, V is given by the formula

V = E * d

V = 1/2 * 50*10^6 * 0.08*10^-3

V = 1/2 * 4000

V = 2000 V