Experimental Characterization of an Unknown Conducting Material

This lab is designed to align with AAOT science outcome #1: Gather, comprehend, and communicate scientific and technical information in order to explore ideas, models, and solutions and generate further questions.

Materials

• digital device with spreadsheet program
• digital device with internet access

ObjectiveS

1. Explain how a multimeter can be used to measure voltage and current.
2. Analyze voltage and current data to determine if an unknown conductive material follows Ohm’s Law.
3. Explain the function and operating principles of a wound-wire rheostat.
4. Explain how a multimeter can be used to measure resistance.
5. Apply a uniform current resistance model to experimental resistance data to extract the resistivity of an unknown conducting material.
6. Examine the assumptions built into the uniform current model.

Methods

Experimental Methods

The following video demonstrates the experimental setup and the collection of all necessary data for this lab.

Analysis Methods

Ohm’s Law Test

First we will determine if the wire in the rheostat is made of an Ohmic material (follows Ohm’s Law).

1) Write Ohm’s Law in the form where voltage is isolated on the left:

2) According to Ohm’s Law, what type of function should relate voltage and current? (proportional, linear, quadratic, etc.)?

3) Use the data provided in the video to plot the voltage on the vertical axis and current on the horizontal axis. Title your graph and label the axes, including units.

4) Fit the expected type of function to the data and record the fit function and R² value here:

5) Does the material appear to be Ohmic? Explain how your data and fit equation lead to your conclusion.

6) Typically we plot the independent variable on the horizontal axis and dependent variable on the vertical axis. We controlled the voltage, so that was our independent variable, and we measured the resulting current, so that was our dependent variable. However, we switched our plot axes so that the slope of would correspond directly to a particular physical quantity (instead of the inverse of that quantity). What quantity does the slope of your fit function represent? Explain.

7) What is the resistance of the rheostat at the particular position used for this Ohm’s Law test. (Be sure to include units!)

Resistance Modeling

We will use the common conductor resistance model that assumes the conductor is:

• Ohmic (follow’s Ohm’s Law)
• Uniform (the cross section is the same size and shape throughout)
• Homogeneous (the electrical properties are constant throughout, for example is it not made of layers of different material)
• Isotropic (the electrical properties are the same in all directions, for example down the axis of the wire or along the radius)

The result of this model is an expression for resistance that depends only on conductor length ($L$), cross sectional area ($A$), and material resistivity $\rho$.

$R = \rho\frac{L}{A}$

8) As a by product, the Ohm’s Law experiment has already provided you with one value for the resistance at a particular rheostat position. The video provides you with that position value and an additional four measurements of resistance at different positions. Create a spreadsheet to record the resistance and position data, including the value from the Ohm’s Law test.

9) As described in the video, we need to convert the measured rheostat position to an actual wire length if we want to model the resistance. As seen in the video, there are 10 turns for each centimeter of rheostat position. The circumference of the turns can be found from the measured turn diameter of 5.34 cm. Create a conversion factor between rheostat position in cm and actual wire length in meters. Show you work. [Hint: Apply unit analysis techniques!]

10) Use your conversion factor and the formula features of the spreadsheet to efficiently add a column to your spreadsheet that calculates the wire length in meters.

11) Plot the measured resistance vs. the wire length in meters (resistance on vertical axis). Title your graph and label the axes, including units.

12) Looking back at the resistance model, what type of function should fit the resistance vs. length data (proportional, linear, quadratic, etc.)? Explain.

13) Apply the type of fit predicted by the resistance model and record the fit equation and R² values here:

14) The resistance model predicts zero resistance when the wire length is zero, but your fit function does not (it has a non-zero y-intercept). Why would there be a non-zero resistance when the rheostat wire length was zero?

15) Based on your fit function, what is the total resistance of the wires used to connect the rheostat to the multimeter? (What is the resistance when the length of rheostat wire is zero?)

16) Looking back at the resistance model equation, and recognizing that we plotted resistance on the y-axis and length on the x-axis, we can see that the slope of the fit function should represent a specific combination of wire properties. Rewrite the equation below, but replacing the question mark with the symbol for the correct wire property.

$slope = \frac{\rho}{?}$

17) Use the actual value of your slope in the previous equation to solve for the resistivity of the wire. Show your work, including units.

Conclusions

18) Does the data indicate that the material is Ohmic and  and can also be modeled using the simple linear resistance model? Explain.

19) Look at this table of resistivity values or this one to determine the wire material. Explain your choice. (Be careful with units!)

FURTHER QUESTIONS

20) Now that you have identified the material, do some research on that material in order to learn and then explain below why it was chosen for use in the rheostat.