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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.

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.

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

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).

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).