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Resistivity

The resistance of a conductor depends on several factors. The physical shape and the type of material are factors that affect resistance. Two conductors with the same physical shape but made of two different materials have different resistances. The resistivity of the material is the physical quantity that determines the resistance of the object.

The resistance of a wire is directly proportional to the length and inversely proportional to the cross-sectional area. This is similar to the water flow in a pipe. The longer the pipe, the more the resistance to the flow rate. But the greater the cross-sectional area of the pipe, the greater the flow rate. The constant of proportionality that relates the resistance to the length and the cross sectional area is the resistivity.

Temperature is another factor that determines the resistance of the material. But in this exercise, the factors that will be considered are the shape and the resistivity of the material.

STUDENT OUTCOMES

Through this experiment, students will learn:

-the factors that determine the resistance of the wire

-how to determine the resistivity of the material

-difference between resistance and resistivity

MATERIALS

Tablet PC Computer Laptop / Rheostat
Logger Pro / Board with wire spools
Vernier Current Probe / Power Supply
Vernier Differential Voltage Probe / Wires

PRELIMINARY QUESTIONS:

1.What are the factors affecting the resistance of an electrical conductor?

2. If the length of a wire is doubled and the diameter is halved, how is the resistance affected? Explain.

3. Why is resistivity a material property? What are the units of resistivity?

PROCEDURE:

1. Connect the Current Probe to Channel 1 and the Differential Voltage Probe to Channel 2 of the computer interface.

2.Open the file “25 Ohms Law” in the Physics with Computers folder. A graph of potential vs. current will be displayed. The meter displays potential and current readings.

3.Connect together the two voltage leads (red and black) of the Voltage Probe. Click, and then click to zero both sensors. This sets the zero for both probes with no current flowing and with no voltage applied.

4.With the power supply turned off, connect the circuit as shown in the figure below. Take care that the positive lead from the power supply and the red terminal from the Current & Voltage Probe are connected properly. Note: Attach the red connectors electrically closer to the positive side of the power supply.

4.Set the rheostat at maximum resistance and have the instructor check the circuit.

5. Turn the control on the DC power supply to 3V and then turn on the power supply.

6.Adjust the rheostat until the current probe reads 0.5 A.

7.Record the current probe and voltage probe readings on the table. Open the switch as soon as the readings have been recorded.

8. Record the length and gauge number of the wire. The wire size is indicated by a gauge number which corresponds to the diameter measurement.

9. Using the same wire, repeat steps 6 – 7 for a different current probe reading.

10. Return the rheostat to the maximum resistance and repeat procedures for the other wire spools.

ANALYSIS:

1. Using Ohm’s Law, compute the resistance of each spool of wire.

2.Look up the corresponding diameter of your wire from a gauge number table. Calculate the cross sectional area of each wire.

3.Compare the resistance of the wires with their respective cross sectional areas. Is there a proportional relationship between the two quantities? If so, state the relationship into a mathematical equation. (Use K as your constant of proportionality.)

4.Compare the resistance of the wires with their lengths. Is there a proportional relationship between the two quantities? If so, state the relationship into a mathematical equation. (Use K as your constant of proportionality.)

5. Combine the two mathematical equations obtained in numbers 3 and 4. Write down the equation that shows the relationship between the resistance, the cross sectional area and the length. The proportionality constant is known as the resistivity.

6.Using the equation that you got in number 5, compute the resistivity of the wires for each trial and compute the average.

7.Compare the average resistivity for wires made of the same material but different lengths. Does the resistivity change with length? Explain.

8. Compare the average resistivity for wires made of the same material but different cross sectional areas. Does the resistivity change with area? Explain.

DATA TABLE:

Wire / Type of material / Voltage ( ) / Current ( ) / R =v/I ( ) / Length ( ) / Gauge / Area ( ) / Resistivity ( )
1
2
3
4
5

9.Look up the accepted resistivity values for the wires used in the exercise. Compare the experimental resistivities with the accepted values by computing the percent error.

10. Are your experimental values accurate? Explain.