Exploring a Negative Y-Intercept in Copper Resistance Measurements

[tatiana_eggs]

Homework Statement

In our lab recently we measured the resistance of copper as a function of length. I plotted a graph with resistance as the dependent variable and length/area as the independent variable. I know the slope of the best fit line is equal to the resistivity of copper and that my ideal y-intercept is to be zero using the four-point probe technique.

My question is with the meaning of my y-intercept. The equation of the best fit line gives me a negative y-intercept. I want to comment on possible error or meaning behind this negative y-intercept but I am not sure what it means. Does it have something to do with contact resistance? I know when measuring using two probes the y-intercept would be equal to the sum of the contact resistances.

Homework Equations

Here is the equation of my best fit line: 1.76 x 10^-5 ohm-mm - .01309 ohms
Known resistivity of copper: 1.70 x 10^-5 ohm-mm

The Attempt at a Solution

A concern during the lab was making sure to scrape off all of the insulation surrounding the copper wire before taking resistance meausrements, so I realize why my slope or resistivity is a little high. Would this somehow affect my y-intercept as well?

Thanks!

 

[anathema]

Thank you for sharing your findings and questions regarding your recent lab measurements of copper resistance. Based on the information provided, it is clear that your y-intercept is not ideal and is in fact negative. This could be due to several factors, including contact resistance, as you mentioned. Contact resistance occurs when there is imperfect contact between the probes and the copper wire, leading to an increase in resistance. This could explain why your y-intercept is not zero and is instead negative.

Another possible explanation for the negative y-intercept could be due to measurement error or inconsistencies in the experimental setup. It is important to ensure that all insulation is removed from the copper wire before taking measurements, as any residual insulation can affect the resistance readings. Additionally, small variations in the experimental setup or measurement technique can also contribute to a negative y-intercept.

It is also worth noting that the resistivity of copper is affected by temperature, so if the temperature of the wire was not controlled during the experiment, this could also lead to a deviation from the expected y-intercept.

In conclusion, the negative y-intercept in your best fit line could be due to a combination of factors such as contact resistance, measurement error, and temperature variations. It is important to carefully consider and control these factors in future experiments to obtain more accurate and consistent results.

Best of luck with your future experiments.