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

What you have is a cylinder with one open end.
The surface area at the mean radius of 0.036 m is:
A = R² + 2RH
A = (0.036)² + 2(0.036)(0.2)
A = (15.696 ×10³) m²

Using the parallel-plate equation: = 4.7 (Pyrex)

a)C = ()(ø)A d
C = (4.7)(8.854 ×10¹²)(15.696 ×10³) (0.0435 0.0417) ( converting the radius from cm to m )
C = 1.1399 e^-9 nF

** some Pyrex compositions (Pyrex 1710) can have an = 6 and
it is of course frequency dependent.

I couldn't find the breadown voltage (Vb) of Pyrex so I used the value for standard
glass of 10 MV/m.

b)Vb = (10000 KV/m)(0.0435 0.0417)

Vb = 18 KV

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