Measured Surface Resistivity Much Higher than Theoretical Value (Why?)

AI Thread Summary
The measured surface resistivity of a carbon-filled conductive paper was significantly higher than the theoretical value, with results around 10,000 Ω/☐ compared to the expected 5,000 Ω/☐. This discrepancy raised questions about measurement procedures and the accuracy of the theoretical model used. Participants emphasized the importance of the experimental setup and potential factors affecting resistivity, such as electron flow and surface characteristics. Clarification on the definition of "theoretical" resistivity and the model used for calculations was also sought. The discussion highlights the need for careful analysis and consideration of measurement techniques in experimental physics.
LulaBell
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I recently conducted a physics lab to measure the surface resistivity of a conductive sheet of a paper with a carbon filler. The theoretical Rs is approx. 5,000 Ω/☐ for this paper and yet we have calculated two Rs values:

Rs when Varying Length and holding Width = 10100 +/- 83.07 Ω/☐
Rs when Varying Width and holding Length = 11220 +/- 63.02 Ω/☐

To me, this discrepancy is very large, and I can't seem to explain why it could even occur, although we are not the only ones measuring this almost double Rs, it seems consistent around 10,000 Ω/☐ across the entire lab and yet I can't figure out why that is. Does it have something to do with the flow of electrons being blocked? Perhaps we did not connect something right although I struggle to see how that would be consistent with other groups.

Any help is very appreciated.
 
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So what measurement procedures did you use? How does your setup method compare to how the paper is typically used in practice?
 
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Likes Lord Jestocost
Yes the procedures that you followed are important. Also, what do you mean by "theoretical" resistivity? Do you know the model that has been used to calculate it? There might be a factor of 2 in the calculation (and the measurement) that was made to determine it vis-à-vis the way you conducted and analyzed your measurement. Remember that a sheet of paper has two surfaces.
 
Do you have any additional details that may be useful @LulaBell ?

Or were you able to resolve the discrepancy?
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
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