Electrical Resistance
and Ohm’s Law
UM Physics Demo Lab 07/2013
Pre-Lab Question
For a given potential difference (voltage), does the current in a circuit increase or
decrease as the resistance of a circuit increases?
EXPLORATION
Materials
1 green multimeter (with leads)
1 battery board
1 alligator lead card
1 resistor
1 calculator
1 clear plastic ruler
1. Direct Measurement of Resistance
Take the resistor and measure its resistance with the multimeter set to Ω. The Greek
letter omega (Ω) is the symbol for Ohms, the unit of resistance.
You measure resistance across a resistor, just as you measure voltage, but using
the Ω scale on the multimeter.
Resistance of Resistor: __________________
2. Voltage Versus Current for a Resistor
Build a series circuit with 4 cells in series (a 6V battery), a switch, and the resistor
that you just measured connected with alligator leads. Measure the voltage and
current of the circuit with different applied voltages.
Make it easy on yourself: Measure the voltage first. Connect the multimeter
across the resistor, and change the applied voltage from the battery by moving one
alligator lead to include fewer and fewer cells in the circuit. Record your findings in
the table on the following page.
Second, complete the current measurements. This time, interrupt the circuit with
the multimeter and measure in mA. Again change the applied voltage from the
batteries by moving one alligator lead for each measurement. Record your findings in
the table below.
Number of
Cells
Potential (Volts)
Current (mA)
Current (A)
4
3
2
1
0
Plot a graph with the values for voltage and current you found. Plot the potential in
volts on the vertical axis and the current in Amperes (Note: you measured current in
milliamperes) on the horizontal axis.
Potential
(Volts)
Current (Amperes)
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What is the shape of the graph? What is the relationship between voltage, current,
and resistance?
What quantity derived from your graph characterizes the
resistance of the resistor? (Hint: one Ohm of resistance is one Volt per Ampere:
1Ω = (1V)/A ).
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3. Voltage Versus Current for a Light Bulb
Remove the resistor from the circuit and replace it with a light bulb. Do not
measure the resistance with the multimeter. Repeat your measurements of
voltage and current with different numbers of cells.
Number of
Cells
Potential (Volts)
Current (mA)
Current (A)
4
3
2
1
0
Plot a graph with the values for the voltages and currents you measured for the light
bulb.
Potential
(Volts)
Current (Amperes)
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Find the resistance of the light bulb from the data you measured.
Measure the resistance of the light bulb with the multimeter: __________________
Compare the plot for the light bulb with the graph for your resistor
measurements.
Do the graphs have the same shape?
Does the resistance
measured from the graph for the light bulb agree with the multimeter measurement
of the light bulb’s resistance? What effect might account for the light bulb’s
behavior?
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Everyday Applications
Simple resistors are used in many everyday appliances:
 Heating elements in ovens and on ranges
 Heat lamps
 Toaster ovens
 Tea kettles
APPLICATION
Materials
1 green multimeter (with leads)
1 battery board
1 alligator lead card
1 carbon pencil
1. Starting with the Single-Strip Shading Regions on the Ohms Law Resistor Sheet,
shade in the 0.2 and 0.6 inch regions with a carbon pencil. Press firmly with the pencil
to get a thick layer of carbon on the sheet.


Measure the resistance of 0.2 inch region.
Predict the resistance of the 0.6 inch region. That region will have three times
as much carbon because it is three times as high as the first region. Will the
region have the same, higher, or lower resistance? Discuss with your group and
explain your prediction. Measure the resistance.
To measure the resistance of the region set the multimeter to ohms (Ω). Lay one
probe along one end of the region horizontally (more surface area means better
reading), and the other probe on the other end of the region horizontally.
Region
Predicted
Resistance
(Ω)
0.2 inch
NA
Measured
Resistance
(Ω)
Explanation of Prediction
NA
0.6 inch
Does this measurement agree with your predictions? Explain how the height of the
shaded region affects resistance.
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2. Now use the Parallel Paths Shading Regions section of the Resistor Sheet.
Shade in the two large boxes on the left and right.

Then shade in one of the parallel paths which can be thought of as an individual
connecting resistor. First predict what the resistance will be, then measure the
resistance by placing the probes in either of the large boxes on the end.
Remember where you place the probes and measure from the same place each
time for consistency. Record the resistance of 1 path alone below.

Predict and explain what the resistance of 2 paths will be. Continue to predict
and add paths until you’ve filled all 4.
Number of
Parallel Paths
Predicted
Resistance
Measured
Resistance
Explanation of Prediction
1
2
3
4
Explain how parallel paths affect the resistance.
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Now shade in the horizontal sections (1, 2, 3, and 4) of the Series Shading Regions
of the worksheet, but do not shade in the connecting paths marked with dashed lines.
3. Measure the resistance of each individual region.
Horizontal Region
Resistance (Ω)
1
2
3
4



Predict the resistance of paths 1 and 2 combined in series. Explain your
prediction. Measure and record.
Predict the resistance of paths 1, 2, and 3 combined in series. Explain your
prediction. Measure and record.
Predict the resistance of paths 1, 2, 3, and 4 combined in series. Explain your
prediction. Measure and record.
Remember, the resistance is measured across the longest length of the two regions
(e.g. for 2 series paths you should be measuring near where it’s labeled “1” and “2”).
Number of
Series Paths
Predicted
Resistance
(Ω)
Measured
Resistance
(Ω)
Explanation of Prediction
2
(1 and 2
combined)
3
(1, 2, and 3
combined)
4
(1, 2, 3, and 4
combined)
4. Discuss with your group and explain how series connections contribute to
resistance. How does this compare to parallel?
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Challenge Work
5. Explain how the mulitmeter measures the resistance when you connect the leads
across a resistor.
Summary:
1. A resistor for which the potential required to drive a current is proportional
to the current obeys Ohm’s Law: V = I R.
2. The resistance of an “Ohmic” resistor (one that obeys Ohm’s Law) is the
constant of proportionality between current and potential: R = V/I.
3. The units of resistance are volts per ampere (V/A) which are denoted as
Ohms (Ω) in honor of the physicist Ohm who made early studies of electrical
resistance.
4. The graph of potential versus current for a resistor which obeys Ohm’s Law
is a straight line and the slope of the line is the resistance of the resistor
(change in potential divided by change in current).
5. Ohm’s “Law” is not a law at all, it’s actually a definition. Many devices do not
exhibit a simple proportionality between current and voltage. Semiconductor
devices such as diodes and transistors are useful precisely because they are
nonlinear and do not obey Ohm’s “Law”. If Ohm’s Law were truly a law for
solid matter, we would still be using vacuum tubes to build electronics—
transistors would not be possible!
6. The equivalent resistance increases as resistors are added in series and is
obtained by adding the individual resistances: Req = R1 + R2 + R3 + …
7. The equivalent resistance decreases as resistors are added in parallel and
is calculated as: 1/ Req = 1/R1 +1/R2 + 1/R3 + …
8. At low temperatures some materials lose all electrical resistance and become
perfect conductors called superconductors. Superconductors can be used to
build very powerful electromagnets and to levitate objects magnetically by
exploiting the Meissner effect whereby a superconductor expels all
magnetic fields from its interior so that a magnet will sit suspended above the
surface of the superconductor supported by magnetic forces.
If
superconductivity can be achieved at room temperature, magnetic levitation of
trains will become truly practical as well as loss-free transmission of electrical
power over wires. To date the highest temperature superconductors operate
near the temperature of liquid nitrogen (77 degrees Kelvin, equivalent to 77
Celsius degrees above absolute zero).
Final Clean-up
Please disconnect all alligator leads and reattach them to the clip card. Discard the
Ohms Law resistor sheet you colored in with the pencil. Replace all equipment to the
carts.
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OHM’S LAW
ANALYSIS
Resistance is a measure of how much a circuit component resists the flow of current. A
component with high resistance will not allow as much current to pass for a given
voltage as would a low resistance component.
Ohmic Resistors
Resistors like the one you used in Step 2 are “ohmic”, that is, they obey Ohm’s Law:
V  IR
Ohm’s Law states that voltage across a resistor is equal to the current passing through
the resistor multiplied by the resistance of the resistor (V varies linearly with I, and
vice versa). This defines resistance as the ratio of current and potential. Ohm’s “Law”
is not a law at all— semiconductor electronic components such as diodes and
transistors are useful precisely because they do not exhibit a simple linear relationship
between current and voltage.
Non-Ohmic Resistors
All resistors, such as the light bulb filament, become non-Ohmic when sufficiently hot.
That is, their resistances changes (with temperature) and is not a single well defined
number. Your measurements should have shown that the bulb did not draw current in
strict proportionality with voltage. In the case of the light bulb, the resistance
increases as the light bulb heats up.
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Copyright 2006, The Regents of the University of Michigan, Ann Arbor, Michigan 48109
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