Resistivity calculation from two-probe resistance measurement of sheet

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SUMMARY

The discussion focuses on the calculation of resistivity from two-probe resistance measurements of a sheet, emphasizing the importance of incorporating a correction factor related to the contact area. It highlights that the perimeter of each contact area significantly influences the resistance measurement, particularly when using point contacts, which theoretically yield infinite resistance. An exact solution is achievable by modeling the contact areas as elliptical, allowing for the use of nested elliptical equipotentials to determine potential distribution. The logarithmic relationship between distances to the centers of the contact areas is crucial for accurate resistivity calculations.

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  • Understanding of two-probe resistance measurement techniques
  • Familiarity with resistivity and its calculation methods
  • Knowledge of elliptical geometry and equipotential surfaces
  • Basic principles of electrical potential and resistance
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  • Research the impact of contact area shape on resistance measurements
  • Study the mathematical modeling of elliptical equipotentials
  • Explore advanced techniques for correcting resistance measurements in materials
  • Investigate the theoretical implications of point contacts in electrical resistance
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Physicists, electrical engineers, and materials scientists interested in accurate resistivity measurements and the theoretical foundations of resistance in conductive materials.

no_einstein
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New user has been reminded to please always show their work on schoolwork problems.
Homework Statement
You make a two-probe resistance measurement (probe spacing S) of an infinite sheet (thickness t) of a high-resistance material. How do you calculate the resistivity of the material?
Relevant Equations
R = ohm, rho = ohm*m
I'm really not sure. Obviously I can get the units right with Resistance * thickness, but I assume there's a correction factor here that I can't find anywhere?
 
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I studied this once out of my own interest. I concluded that as stated in post #1 it makes no sense. What you also need to know is the perimeter of each contact area. With point contacts the theoretical resistance is infinite.
If we take those areas to be elliptical, we can have an exact solution with nested elliptical equipotentials around each contact ellipse. The 'central ellipse', i.e. where the one family transmutes into the other, is the perpendicular bisector of the two contact areas. The potential at any point is proportional to the logarithm of the ratio of distances to the 'centres', i.e. where the two families of ellipses would shrink to zero.
 
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