Physics Active Learning (PAL)

Name:______Lab Section: ______Group Number: ______

Lab Partners: ______Grade:______

Physics 203 Lab 3 Resistivity of Play-Doh Pre-Lab

After reading the laboratory’s introduction and procedure, answer the following questions.

1. Design and then briefly describe an experiment that would produce a plot with a best-fit line slope equal to the resistivity of the material. Hint: Consider what would be plotted on the axes to produce this plot. Then think about what measurements could be made and what device could be used to measure these quantities.

2. Given that the internal resistance of the voltmeter is 1M, the resistance of each lead is 2 , and the current through each lead and the meter itself is .01 mA, find the percent difference between the voltage reading of the voltmeter with the leads and the voltage reading without the leads (assuming such a measurement could be made).

3. Name:______Lab Section: ______Group Number: ______

Lab Partners: ______Grade:______Physics 203 Lab 3 Resistivity of Play-Doh

Introduction

Many conducting wires can be described by Ohm's Law, which states that the voltage V across the ends of a wire is proportional to the current I passing through that wire. The constant of proportionality is the resistance, R:

Experiments show that R depends not only on the material used to make the wire but also on the diameter and length of the wire. Comparing wires made of the same material but having different dimensions, one finds that the electrical resistivity, (2)

is the same for all wires made of the same material. (A is the area of the cross-section of the wire and L is its length.) Therefore, the electrical resistivity, , is a physical property of a particular material.

In this experiment, you will explore the physics behind Equation 2 by forming wires of various properties, measuring the resistance of each wire, and computing the resistivity of the material. You will make the wires from a proprietary malleable material marketed under the name Play- Doh™.

One straightforward way to measure the resistance of a test wire would be to hook it up across the inputs of a digital ohmmeter, which passes a current through the wire and measures the resulting voltage difference between the ends. Note that the current may be passing through several connecting wires in addition to the test wire; the resistances of these connecting wires would then contribute to the voltage measured. In fact, connecting wires creates resistance also - the contact resistance - that arises from imperfect electrical contact and is difficult to account for. Thus, the resistance reading on the ohmmeter would be due to the test wire of interest plus the connecting wires plus the contact resistance. This is not a good measure of the resistance of the test wire. Figure 1. Experimental setup for four-lead measurement.

To eliminate these problems, in this experiment you will measure resistance by using a four-lead technique, depicted in Figure 1. In this technique, the current passes through one set of wires, while the voltage is measured with a different set of wires. Since essentially no current is passing through the wires used for the voltage measurement, the resistance of the connecting wires and the contact resistance between wires will not contribute to the measured voltage difference. You will control the current with the power supply and measure the resulting voltage difference across two points on the test wire.

Experimental Procedure

WARNING: Do not touch the brass plugs when the power supply is on. Turn the power supply off when adjusting the Play-Doh, setting up the next trial, etc.

Always keep the cover on the can when not in immediate use, to keep the Play-Doh from drying out.

Use Play-Doh of one color to make a wire 5 to 15 cm long and 4 to 8 mm in diameter. We will call this “wire A.”

The wire probably does not have the same diameter throughout its entire length, and the cross- section of the wire probably is not perfectly circular. Therefore, use the Vernier calipers to measure the diameter of the wire at three different locations. At each location, measure the diameter with two perpendicular orientations of the calipers. Use a spreadsheet to compute the average and standard deviation of these 6 measurements.

Examine the supplied connecting wires, two of which have standard banana plug connections at one end and brass rods at the other. These will carry the current into the test wire. Place a blob of Play-Doh (same color as the test wire) on each of the brass rods, to help make a secure connection with the test wire.

Two other wires have skinny, pointed probes at one end; these are the voltage probes. Drape the test wire across these voltage probes and secure the test wire to the blobs which connect to the current-carrying wires. Connect the remainder of the circuit depicted in Figure 1.

The digital multimeter that is used as an ammeter should be set to measure DC current, and the multimeter used as a voltmeter should be set to measure DC voltage. For best accuracy, all measurements should be taken on the lowest multimeter setting that does not give an overload reading.

Turn on the power supply and the digital multimeters. Turn the control knob on the power supply to set the current to about 0.5 mA, and record the current and voltage readings. Increase the current in increments of about 0.5 mA, taking readings at each step. Take 10 sets of readings. Take the readings quickly so the Play-Doh does not dry out before you are finished. It is possible the readings will drift. That's ok. Simply make sure you read both current and voltage at the same time.

When you are done with these measurements, disconnect the circuit and measure the distance between the voltage probes (the distance between the dents on the test wire). Don't stretch the wire (Play-Doh).

1) What quantities should you plot on the x- and y-axes, so that you can determine the resistance from the slope of your best-fit line?

2) Make this plot and determine the resistance of your test wire.

3) From this resistance and the dimensions of the wire, determine the resistivity of the Play-Doh material.

4) Disconnect the power source from the setup, turn the multimeter to the Ohms setting, and make a direct measurement of the resistance of the Play-Doh wire.

5) Suppose you want to make another wire (wire B) of the same length as wire A and from the same material, but you want a higher resistance. How should you change the diameter of the wire? 6) Do you expect the resistivity of wire B to be greater than, less than, or approximately equal to the resistivity of wire A?

Make another wire (wire B) of the same color as wire A according to your answer to question #4. Repeat the measurements and calculations outlined above to determine the resistance and resistivity of this new test wire.

7) Was the resistance of wire B higher than that of wire A, as you predicted in question #4? Discuss any discrepancy.

8) Was the resistivity of wire B greater than, less than, or approximately equal to the resistivity of wire A made from the same material? Does this agree with your answer to question #5? Discuss any discrepancy.

Soon you will use another color of Play-Doh to make a wire (wire C) with approximately the same length and diameter as wire A.

9) Do you expect the resistance of wire C to be greater than, less than, or approximately equal to the resistance of wire A?

10) Do you expect the resistivity of wire C to be greater than, less than, or approximately equal to the resistivity of wire A? Now make wire C with approximately the same length and diameter as wire A. Repeat the measurements and calculations to determine the resistance and resistivity of wire C.

11) Is the resistance of wire C greater than, less than, or approximately equal to the resistance of wire A? Does this agree with your answer to question #8? Discuss any discrepancy.

12) Is the resistivity of wire C greater than, less than, or approximately equal to the resistivity of wire A? Does this agree with your answer to question #9? Discuss any discrepancy.

13) Comment on your graphs. Do the data for each wire fall on a straight line? Do the Play-doh wires follow Ohm’s law?

14) Comment on the results of the resistivity calculations. Does the resistivity appear to depend on the color of the Play-Doh? Can you think of reasons why it might depend on color? Physics 203 Lab 3 Resistivity of Play-Doh Post-Lab

1. Given that the resistivity of copper wire is 1.69 x 10-8 m, find the resistance of a 6 m long wire with a diameter of 1.628 mm (#14 gauge, typical for wiring in the walls of buildings).

2. Would you expect the direct measurement of the resistance to be higher? Why? Given the direct measurement you made in 6) above, does the 4-wire method provide a more accurate measurement of the resistance? Find the % discrepancy between the values to support your answer.

3. Thinking about the resistance of nerves in the body, what relative dimensions (length and diameter) would you expect to find for nerves that travel from your brain to your lips versus nerves that travel from your brain to your feet? Explain your answer.