Inverse relationship between radius and resistance

[Navras]

Homework Statement

We did an experiment using resistance putty and a multimeter. We changed the radius of the putty but kept the length the same. We recorded the resistances at different radius'. I know that physics theory says that resistance is inversely proportional to cross-sectional area of wire. For example, if the radius doubles, the cross sectional area increases four times and the resistance decreases by four times.

Homework Equations

radius (m) resistance (Ω)
0.0015 601
0.003 270
0.0075 72.4
0.0115 50
0.015 43

The Attempt at a Solution

However my results don't follow the theory at all. the resistance decreases by closer to 2 or 3 times when the radius doubles.

I'm kind of stumped by this. Thanks for any help or pointers in the right direction :)

 

[cepheid]

Every experimental result has an error. What is the uncertainty in your measurement of the radius? How precisely were you able to control the length? What do you think the error in this was? Are these errors able to account for the discrepancy?

P.S. the plural of radius is radii

 

[Chestermiller]

Homework Statement

We did an experiment using resistance putty and a multimeter. We changed the radius of the putty but kept the length the same. We recorded the resistances at different radius'. I know that physics theory says that resistance is inversely proportional to cross-sectional area of wire. For example, if the radius doubles, the cross sectional area increases four times and the resistance decreases by four times.

Homework Equations

radius (m) resistance (Ω)
0.0015 601
0.003 270
0.0075 72.4
0.0115 50
0.015 43

The Attempt at a Solution

However my results don't follow the theory at all. the resistance decreases by closer to 2 or 3 times when the radius doubles.

I'm kind of stumped by this. Thanks for any help or pointers in the right direction :)

I did a curve fit to the data (using a graphics package), and the resistance decreased with the radius to the ~ 1.2 power. This is much lower sensitivity than to the 2.0 power. So Navras' question still stands: What is the reason for the lower sensitivity?

 

[cepheid]

I did a curve fit to the data (using a graphics package), and the resistance decreased with the radius to the ~ 1.2 power. This is much lower sensitivity than to the 2.0 power. So Navras' question still stands: What is the reason for the lower sensitivity?

How should I know? I was just trying to get him to take experimental error into account, and to determine whether or not it could account for the discrepancy. If it can't, then I don't know what to say other than that our assumptions about the properties of the system must not have been in line with the actual properties.

 

[Nickie]

Thank you for sharing your experiment and results. It is important to keep in mind that while physics theory can provide a general understanding of how certain variables may affect each other, real-world experiments may not always perfectly align with these theoretical predictions. In your case, the inverse relationship between radius and resistance is a well-known concept, but it is also influenced by other factors such as the material and composition of the putty, as well as the precision and accuracy of your measurements.

It is possible that the resistance putty used in your experiment may have some irregularities or variations in its composition, leading to slightly different results from what is expected based on theory. Additionally, the accuracy of your measurements may also play a role in the discrepancies you observed.

To further investigate this, you could try repeating the experiment with different types of resistance putty or using a different measuring device to see if your results remain consistent. It may also be helpful to consult with your instructor or other experts in the field to discuss possible explanations for your findings.

Overall, it is important to approach scientific experiments with an open and critical mindset, and to recognize that there may be factors beyond theoretical predictions that can influence the results. Your experiment has provided valuable data that can contribute to a better understanding of the relationship between radius and resistance, and further exploration and analysis can help shed light on any discrepancies.