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Note: Items in red are measurements that must be made as you do the experiment.

Introduction

You will use a digital multimeter to determine the resistances of several wires (and wire combinations) having different lengths and diameters and made from different materials (copper, nickel, and aluminum).  You will use Equation 1 to calculate the resistivity of each one, for comparison against your measured values.   Eq. 1

Checking the Connections:

No one should change the connections, but sometimes they change them anyway. Just in case, be sure the connections are as follows: One wire from the power supply goes to the ammeter. The wire out of the ammeter and the second wire from the power supply go to the terminals on the right side of the board. Thus, the ammeter and the four wires on the board are all in series with the power supply. This means that the current registered by the ammeter is the current going through each of the four wires.

The voltmeter is connected to two probes that are not yet used.

Checking Ohm's Law:

Select any one of the four wires. Connect the two leads of the voltmeter to the terminals at the ends of the wire. The effective length of the wire will be length between the two terminals. Adjust the "Current" knob on the power supply to provide a variable current source for the wire.  Plot the voltage as a function of current on the graph in  Figure 1. (Depending on the wire you select, you may find it convenient adjust the scale on the y-axis by a factor of 10, but if you do, don't forget to take that into account when you calculate the slope!)  Calculate the resistance of this wire by finding the slope of what looks like the best-fit line through the data points. Remember the line should pass through the origin (Why?)  Note that the slope will be in units of  mV/mA=Ω (Ohms). Select the wire you used:  Pull down and select: Copper A Copper B Nickel Aluminum Your value of resistance from the graph:    Ω (Ohms) Note that as long as the graph is linear, you could determine the resistance by applying Ohm's Law to a single measurement. Set the current to 100 mA and calculate the resistance based on the voltage measured for this current. Your value of R from this measurement:   Ω (Ohms)

Figure 1

Resistivity of the Wire:

Use the micrometer to measure the diameter of your wire. Then calculate the cross sectional area of the wire. From this, the wire length, and your graphical measurement of resistance, determine the resistivity of the wire. Be sure to keep everything in SI units. Wire diameter: m   (You may use the forms 1.2E-3 or .0012) Wire area:       m2   Wire length:       m Resistivity:         Ωm (Ohm-m) The following are accepted values of resistivity: Material Reistivity in Ωm (Ohm-m) Copper 1.7 × 10-8 Nickel 6.8 × 10-8 Aluminum 2.8 × 10-8

Resistance as a Function of Length: From Eq. 1, the resistance of a wire should be directly proportional to its length. Predict the resistance of a 40 cm and of an 80 cm length of your wire based on the resistance of the entire length of the wire. Calculated resistance of 40 cm of the wire:    Ω (Ohms) Calculated resistance of 80 cm of the wire:    Ω (Ohms) Now measure the resistance of a 40 cm and of an 80 cm length of the wire using a single current setting : Measured resistance of 40 cm of the wire:    Ω (Ohms) Measured resistance of 80 cm of the wire:    Ω (Ohms)