Question

You are asked to construct a capacitor having a capacitance near 1  nF and a breakdown voltage in excess of 10000  V . You think of using the sides of a tall Pyrex drinking glass as a dielectric, lining the inside and outside curved surfaces with aluminum foil to act as the plates. The glass is 15  cm tall with an inner radius of 3.6  cm and an outer radius of 3.8  cm . Use 4.7 for the dielectric constant of Pyrex, and use 13.0  MV/m for the dielectric strength of Pyrex.

Part A

What is the capacitance of this capacitor?(pF)

Part B

What is the breakdown potential of this capacitor? (units kV)

Answer 1

here,

inner radius , ri = 3.6 cm

ri = 0.036 m

outer radius , ro = 3.8 cm

ro = 0.038 m

length of glass , L = 15 cm

L = 0.15 m

dielectric constant of Pyrex , K = 4.7

part A)

the capacitance , C = 2 * pi * K * E0 * L /(ln(r0/ri))

C = 2 * pi * 4.7 * 8.854 *10^-12 * 0.15 /(ln(3.8/3.6))

C = 708.86 * 10^-12 F

C = 708.86 pF

the capacitance of this capacitor is 708.86 pF

part B)

dielectric strength , Ds = 13 MV/m

the breakdown potential of this capacitor , V = Ds * (ro-ri)

V = 13 * 10^6 * (0.038-0.036)

V = 26 * 10^3 V

V = 26 KV

the breakdown potential of this capacitor is 26 KV