LPC Physics 2
Resistance and Resistivity
©
2003 Las Positas College, Physics Department Staff
Resistance and Resistivity
Purpose:
To measure the resistance of resistors by several methods and learn the use of the digital multimeter
(DMM) and the micrometer, and to estimate accuracies of these instruments.
Equipment:
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Micrometer
2 Chromel (Nichrome) wires of different diameter, both approximately 0.95 m
long
3 Resistors, 100Ω – 1000Ω
2 DMMs
DIGI 35 A Power Supply
Patch Cords, Alligator Clips
Multimeter Accuracy List (include in lab write-up)
CRC Handbook
Color Code for Resistors
Meter Stick
Theory:
The resistance of an electrical conductor depends on several factors. Consider a wire
conductor. The resistance, of course, depends on the type of conductor material, and also
on (a) the length, (b) the cross-sectional area, and (c) the temperature of the wire. As
might be expected, the resistance of a wire conductor is directly proportional to its length
l and inversely proportional to its cross-sectional area, A:
R∝
l
A
Eq. 1
For example, a 4-m length of wire has twice as much resistance as a 2-m length of the
same wire. Also, the larger the cross-sectional area, the greater the current flow (less
resistance) for a given voltage. These geometrical conditions are analogous to those for
liquid flow in a pipe. The longer the pipe, the more resistance to flow; but the larger the
cross-sectional area, the smaller the resistance to flow.
The material property of resistance is characterized by the resistivity, ρ, and for a
given temperature,
R=
ρl
A
Eq. 2
The resistivity is independent of the shape of the conductor, and rearranging Eq. 2,
ρ=
RA
l
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Eq. 3
LPC Physics 2
Resistance and Resistivity
©
2003 Las Positas College, Physics Department Staff
From the equation, resistivity can be seen to have the units Ω-m or Ω-cm. Common
metal conductors have resistivities on the order of 10-6 Ω-cm. Another name sometimes
used for resistivity is specific resistance, indicating that it is specific for a given material.
To determine the resistivities of some materials, a circuit arrangement as
illustrated in Figure 2 will be used. The ammeter A measures the current I in a length of
wire and the voltmeter V registers the voltage drop across the conductor. Then, the
resistance of the wire, by Ohm’s law, is R = V I .
Measuring the length of the wire, l, and its cross-sectional area, A, the resistivity
of the conductor can be calculated from Eq. 3.
Experiment and Analysis:
(DMM)
V
Part A:
R (resistor)
A (DMM)
DIGI power supply
Figure 1
Measuring Resistance by Ohm’s Law
1. Using the color code, determine the resistance and tolerance of each resistor and record.
2. Measure the resistance of each resistor with the DMM and record.
3. Connect each resistor in turn to the power supply using 5.0 V to give a measurable current in mA
(see sketch above).
4. Using the DMM as an ammeter and the VOM as a voltmeter, measure the current and voltage.
5. Calculate the resistance and record.
6. Compare each resistance you have measured with the color coded (nominal) resistance and
tolerance, by calculating the percent difference. Is each measure of resistance with the coded
tolerance?
7. Which of the 3 methods do you believe yields the most accurate value of resistance? Why?
8. Which of the three methods has the least uncertainty? Show how you arrived at your conclusion.1
1
The theory section of this lab was shamelessly borrowed from: Jerry D. Wilson. Physics Laboratory
Experiments, 2nd Edition. Lexington MA: D.C. Heath and Company, 1986. Experiment 31.
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LPC Physics 2
Resistance and Resistivity
©
2003 Las Positas College, Physics Department Staff
Part B:
(DMM)
V
R (wire conductor)
A (DMM)
DIGI power supply
Figure 2
Measuring the Resistance of Various Wire Conductors
1. Measure the length of one chromel (nichrome) wire to 0.001m with the meter stick and the diameter
to 0.01mm with the micrometer. What is the B&S gauge?
2. Tape the wire to a meter stick, leaving spaces where leads may be clipped.
3. Measure the resistance of each wire for at least 10 lengths along the wire.
4. Using Excel, Graphical Analysis, or another graph-making program, make a plot of R vs. L with
clearly labeled axes. Using Eq. 1, determine how to find the resistivity of the wire from the slope of
your plot. Then determine the resistivity. Be sure to include your plot in your lab report.
L
R = ρ(A ) .
Eq. 4
5. Determine your experimental errors. Within the limits of accuracy, is your value of the resistivity
equal to that given in the handbook? If not, why not?
6. Repeat the process for the other chromel wire.
Results:
Write at least one paragraph describing the following:
• what you expected to learn about the lab (i.e. what was the reason for conducting the
experiment?)
• your results, and what you learned from them
• Think of at least one other experiment might you perform to verify these results
• Think of at least one new question or problem that could be answered with the
physics you have learned in this laboratory, or be extrapolated from the ideas in this
laboratory.
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LPC Physics 2
Resistance and Resistivity
©
2003 Las Positas College, Physics Department Staff
Clean-Up:
Before you can leave the classroom, you must clean up your equipment, and have your
instructor sign below. If you do not turn in this page with your instructor’s signature with
your lab report, you will receive a 5% point reduction on your lab grade. How you divide
clean-up duties between lab members is up to you.
Clean-up involves:
• Completely dismantling the experimental setup
• Removing tape from anything you put tape on
• Drying-off any wet equipment
• Putting away equipment in proper boxes (if applicable)
• Returning equipment to proper cabinets, or to the cart at the front of the room
• Throwing away pieces of string, paper, and other detritus (i.e. your water bottles)
• Shutting down the computer
• Anything else that needs to be done to return the room to its pristine, pre lab form.
I certify that the equipment used by ________________________ has been cleaned up.
(student’s name)
______________________________ , _______________.
(instructor’s name)
(date)
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LPC Physics 2
Resistance and Resistivity
©
2003 Las Positas College, Physics Department Staff
Resistors:
R: color code
1
2
3
R: DMM
R: Ohm’s Law
tol: color code
tol: % uncertainty
Nichrome Wires:
No. 1
Total Length of Wire: ______________
B&S Gauge: _____________
Length
Diameter of Wire: ______________
Resistance
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LPC Physics 2
Resistance and Resistivity
©
2003 Las Positas College, Physics Department Staff
No. 2
Total Length of Wire: ________________
B&S Gauge: ______________
Length
Diameter of Wire: ______________
Resistance
No. 1
No. 2
Resistivity as measured from slope of graph:
__________
___________
Uncertainty in slope:
__________
___________
Resistivity from CRC Handbook:
__________
___________
Percent difference in meas. vs. theory:
__________
___________
Agreement between values:
__________
___________
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