Physics Shenandoah Valley Governor’s School

Revised 20150224 1

Lab 25 Resistivity

Introduction: The resistance of a wire is not 0 as we conveniently make it in lecture, and it in fact changes as the temperature of the conductor changes. For this experiment we will consider the change in resistance due to the heating of the wires to be minimal. Given that condition, the resistance of a cylindrical wire can be shown to depend on three things: the length of the wire (l), the cross sectional area of the wire (A), and the material. The dependency of the wire resistance on the material, called resistivity, is symbolized by the Greek letter, ρ. The resistance, R is then

(Giambattista, 2007) In this laboratory exercise you will determine the resistivity of copper using Ohm’s Observation (V = IR), thus:

where V is the voltage across the resistance and I is the measured current. Note also that the resistivity of the wire can be found using the temperature coefficient:

where ρ0 is the resistivity at 20°C, and α is the temperature coefficient. NOTE: Wire size in the United States is customarily measured by gauges. This customary system is further complicated by the fact that each manufacturer had a slightly different system. The problem for the naïve user is that the gauge number goes DOWN as the cross sectional area goes UP. Small thin wires have a larger gauge than thick wires. The system makes superficial sense since the resistance is inversely proportional to the cross sectional area. This means that a large gauge wire (thin wire) has a higher resistance than a comparable length small gauge (thick) wire (but it is NOT a linear relationship!). The following table is provided for your convenience (Trinklein):

Gauge Diameter (B&S) (mm)

21 0.7230 22 0.6438 23 0.5733 24 0.5106 25 0.4547 26 0.4049 27 0.3606 28 0.3211

AlR ρ

=

IlVA

lAR

==ρ

( )0 1 Tρ ρ α= + ⋅Δ

Physics Shenandoah Valley Governor’s School

Revised 20150224 2

Finally, according to page 646 of your textbook, the accepted theoretical values for the resistivity (at 20°C) and temperature coefficient for copper are

ρ0 = 1.67 x 10-8 Ω·m α = 4.05 x 10-3 °C-1

Equipment: Wavetek Multimeter DM 27-XT (x2) (or DM 25-XT) Science Workshop 750 Interface running Data Studio Test leads (three red double banana plug and two black double banana plug) Resistivity spools Method: Set one DM 25-XT multimeter to Volts (setting 200 mV) and connect it across the first resistivity spool as shown. Set the other DM 25-XT multimeter to Amperes (setting 200 mA) and connect it to the Science Workshop interface and the resistor spool as shown. The black lead goes the ground symbol on the SW 750 interface box and the red lead goes to the Output (± 5 V / 300 mA). IT IS VERY IMPORTANT THAT THE VOLTMETER IS SET TO VOLTAGE. If the probes are set up for current then the fuse will blow. Connect the power supply to the resistor as shown:

The dashed lines represent the red lead in both diagrams

A

V

SW 750

R

Physics Shenandoah Valley Governor’s School

Revised 20150224 3

Start up Data Studio and click on the Voltage Out icon on the far right of the interface icon.

Select (by up arrow) DC voltage. Use the + and – buttons on the screen to change the voltage to 0 V. Change the range of the meter to 0.010 V using the left and right arrow buttons just beneath

the “DC Voltage” box on the screen. Change the DC voltage to 0.040V. Click the “Start” button. The voltage across the first resistor spool should read something on the order of 10.1 mV and the current should read approximately 18.1 mA. Make sure that there are three significant figures for both readings. If not, increase to the voltage by 0.010 V. Record the multimeter voltage and the multimeter current. Increase the voltage slightly (by 0.010 or 0.020 V) and record the voltage and current again. Continue for a total of sixteen trials. Do not

exceed 200 mV during the experiment. Construct an appropriate data table (with units and labels). Items that should be measured include the following:

1. Length of the wire in the spool 2. Cross sectional area of the wire in the spool 3. Voltage 4. Current 5. Experimental resistance of the spool 6. Experimental resistivity of the spool material 7. Accepted value of the resistivity of the spool material 8. Relative error

Physics Shenandoah Valley Governor’s School

Revised 20150224 4

Turn off data collection and unplug your leads. Move the voltmeter and ammeter probes so that the multimeters record the current and voltage across the second spool. Take ten to twelve measurements of the current and voltage for the second spool, making sure that there are three significant figures for each reading. Repeat the voltage and current measurements for the 3rd, 4th and 5th spools. Note that the 5th spool is an entirely new material: copper-nickel. As such, we will not have an “accepted” value to compare with our readings. Instead, after taking your measurements, report your discovered resistivity for copper-nickel as (average) ± (2*standard deviation). Uncertainty Analysis: Determine the expected uncertainty by determining the following uncertainties in measurement: Considering the voltmeter, what was the largest possible uncertainty for the smallest voltage that was measured? Example: the voltmeter measured 10.5 mV, 12.1 mV, 14.4 mV, 15.9 mV, and 18.0 mV. The smallest measured voltage was 10.5 mV and the uncertainty is ± 0.1 in the reading. The uncertainty due to the voltmeter is 0.1/10.5 = 0.00952 (or 1.0 %) Complete the following table:

Uncertainty Smallest Measurement (%) Voltage Current Length Diameter

Total We will make the simplifying assumption that the uncertainties in this experiment add and determine the expected uncertainty. Note that this is NOT the relative error. The expected uncertainty is a measure of how precise our experiment should be. Using the resistivity equation and the data from the first four spools, determine the average resistivity for copper. Using your theoretical value from the textbook, report the accepted value for the resistivity of copper and determine the experimental relative error.

Report all of this in an appropriate table.

AcceptedAcceptedObserved −

=Error Relative

Physics Shenandoah Valley Governor’s School

Revised 20150224 5

To be answered in a textbox on the Excel spreadsheet: Question 1: In light of this result, how many significant figures should be used to report the resistivity of copper? Question 2: Is the relative experimental error less than or greater than the expected uncertainty? Question 3: What sources of error could contribute to your percent error beyond measurement uncertainties? Question 4: What is your measured resistivity for the copper-nickel wire (spool 5)? Report your answer as [average] ± [2*standard deviation]. Question 5: Given your experimental data, which material would be more ideal to use in a circuit: copper or copper-nickel? Why? Write-up Make sure all lab partner names are listed on the Excel document in a text box. Answers to the questions should be entered in a text box on the worksheet.

The data and analysis will be written up by each lab group as a short lab report. The report will be completed in Excel and saved as follows:

Lab 25_userid1, userid2, userid3.xls

where “userid” is your SVGS login identity. The report is due in the appropriate Moodle folder one week from the completion of

the experiment. Be sure to check your lab for proper usage of significant figures, labels, and units. Be sure to make a back-up copy as necessary. Works Cited Giambattista, A., Richardson, B., &Richardson, R. (2007). College Physics, 2nd Ed. Boston,

MA: McGraw-Hill. 644-659. O’Neill, T. and Martin, C.