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Thin film resistance

Electric current is passing through the steel thin film with two electrodes attached.

Problem type:
Plane problem of DC conduction.

Given:
h = 6 mm, g = 20 mm, d = 1 mm - thickness of the film
Electrical conductivity of the steel: γ = 10·106 Sm/m,
Voltage drop ΔU = 0.02 V.

Task:
Calculate the resistance of the steel film and compare with the analytical result.

Solution:
Current through the surface (I) is calculated in QuickField and then the resistance may be found using the Ohm's law:
R = ΔU / I

Analytical solution*:
R = (g/h + 0.469) / (γ·d).

Result:
QuickField: R = 0.02/52.6 = 3.80·10-4 Ohm.
Analytical solution: R = (0.020/0.006+0.469) / (10·106 · 0.001) = 3.80·10-4 Ohm.

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*Conformal Mapping: Methods and Applications, Roland Schinzinger, Patricio A. A. Laura, 1991, Elsevier Science Publishers, B.V., p. 224. ISBN 0-486-43236-X (pbk).