Download Resistivity

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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
Logger Pro
Vernier Current Probe
Vernier Differential Voltage Probe
Rheostat
Board with wire spools
Power Supply
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.
ammeter
4.
Set the rheostat at maximum resistance and have the instructor
check the circuit.
5.
Turn the control on the DC power supply to 3 V 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.