You are asked to construct a capacitor having a capacitance near 1 nF and a brea

Question

You are asked to construct a capacitor having a capacitance near 1 nF and a breakdown potential in excess of 12000 V. You think of using the sides of a tall plastic drinking glass as a dielectric (with a dielectric constant 3.8 and dielectric strength 14 kV/mm), lining the inside and outside curved surfaces with aluminum foil to act as the plates. The glass is 20 cm tall with an inner radius of 4.17 cm and an outer radius of 4.35 cm. (a) What are the capacitance and (b) breakdown potential of this capacitor?

Explanation / Answer

(a) What you have is a cylinder with one open end.

Mean radius: R = (4.17 + 4.35) / 2 = 4.26 cm = 0.0426 m

The surface area at the mean radius of 0.0426 m is:

A = R^2 + 2RH
= (0.0426)² + 2(0.0426)(0.2) = (3.519*10^-3) m^2

Dielectric constant: = 3.8 and   ø = 8.854*10^-12

The capacitance for this situation:

C = ()(ø)A / d

= (3.8)(8.854*10^-12)(3.519*10^-3) / (0.0435 0.0417)

= 0.206 *10^-9 F  = 0.206 nF

(b) Dielectric constant = 14 kV / mm = 14*10^3 kV / m

So, the breakdown potential of this capacitor:

V = (14*10^3)(0.0435 0.0417) = 25.2 kV

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