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# Thin film resistance

QuickField simulation example

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

Problem Type
Plane problem of DC conduction.

Geometry
h = 6 mm, g = 20 mm, d = 1 mm - thickness of the film

Given
Electrical conductivity of the steel σ = 10 MS/m,
Voltage drop ΔU = 0.02 V.

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) / (σ·d).

Result
QuickField: R = 0.02/52.6 = 3.80·10-4 Ohm.
Analytical solution: R = (0.020/0.006+0.469) / (10'000'000 · 0.001) = 3.80·10-4 Ohm. Reference: * Roland Schinzinger, Patricio A. A. Laura Conformal Mapping: Methods and Applications, 1991, Elsevier Science Publishers, B.V., p. 224. ISBN 0-486-43236-X (pbk). 