Alan Gleue, physics teacher at Lawrence High School in Lawrence, Kansas, called our tech support line with a challenge. He wanted to be able to use Vernier sensors to investigate resistivity in copper wire. The issue troubling Alan – how to measure small changes in voltage with enough precision to be able to see the relationship between wire length, cross-sectional area, and resistance.
At the Vernier end of the call was our own Rick Sorensen. Rick is one of the co-authors of our physics lab books, Physics with Vernier. Rick recommended Alan use the Vernier Instrumentation Amplifier to measure the voltage drop across short lengths of wire. The Instrumentation Amplifier is basically a multi-range voltage probe with range settings: 0-20 mV, 0-200 mV, 0-1 V, ± 20 mV, ± 200 mV, and ± 1V. Using an Instrumentation Amplifier, along with a Current Probe and a Vernier Circuit Board, Alan was able to do his measurements.
Resistance vs. Length
Obtain various lengths of the same gauge copper wire (we used 0.2, 0.4, 0.6, 0.8 and 1.0 meter lengths of 22-gauge wire). Set up a series circuit using a 3-V DC power supply, a Current Probe (ammeter), a 10 Ω resistor, and one length of the copper wire. Connect the Instrumentation Amplifier in parallel with the copper wire. Set up Logger Pro to measure the voltage using the 0-20 mV range of the Instrumentation Amplifier. (Note: The Instrumentation Amplifier does not auto ID. You will need to manually choose this sensor from the list in Logger Pro.) Add a calculated column to automatically calculate the resistance based on the voltage and current readings for the circuit. Select the Events with Entry data collection mode and have the event be defined as the wire length. Modify the graph to display Resistance vs. Length. With the circuit open, zero the sensors. (Note: Zeroing a voltage sensor requires the leads to be shorted together. In this activity, connecting the leads to the sample copper wire effectively does this.)
Start the data collection. Close the circuit and take a measurement of the resistance of the first piece of wire. When prompted, enter the length of the wire. Open the circuit and replace the wire with one having a different length. Repeat taking measurements until you have resistance data for each of your lengths of wire.
Model the data using a linear fit to determine the relationship between resistance and length of the wire.
Resistance vs. Area
The next step would be to investigate the relationship between resistance and cross sectional area. To do this, repeat the above experiment using 10-cm lengths of various gauge copper wire.
Download the Logger Pro experiment file for your own investigations!
Download resistivity.zip (5 KB zipped file)