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 11000 V. You think of using the sides of a tall plastic drinking glass as a dielectric (with a dielectric constant 6.5 and dielectric strength 11 kV/mm), lining the inside and outside curved surfaces with aluminum foil to act as the plates. The glass is 14 cm tall with an inner radius of 2.71 cm and an outer radius of 2.89 cm. (a) What are the capacitance and(b) breakdown potential of this capacitor?

Explanation / Answer

C   =   2 pi epsilon * k * h / loge(b/a)

C   =   2 * pi * 8.85 * 10-12 * 4.7 * 0.14 / loge (2.89 / 2.71)

= 5.69* 10-10   F

= 0.569 nF

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V   =   dielectricstrength * separation

V   =   14* 106 (V/m)   *   (b - a)

=   14* 106 * ( 0.0289 - 0.0271)

=   2.52 * 104   V

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