Ohm's Law
In this lab we will make detailed measurements on a resistor to see if it obeys
Ohm's law. We will also check the rules for combining resistors in series and
parallel.
I. Theory
Ohm's law describes the behavior of a resistor in the thermal range where the voltage across
the resistor is proportional to the current flowing through the resistor. Ohm's law is usually
expressed as
Ohm's Law
V  IR ,
where V is the potential difference across the resistor (measured in volts), I is the current through
the resistor (measured in amperes), and R is the resistance of the resistor (measured in ohms).
The full implication of the law is that the ratio of V to I remains constant as the current and
voltage change. This would mean that a plot of V as a function of I would be a straight line.
It can be shown (and probably has been, in the lecture part of the course) that resistors
combined in parallel and in series behave as a single equivalent resistor, of value
RS  R1  R2 ,
Resistors in Series
or
1
1
1
 
,
Resistors in Parallel
RP R1 R2
II. Experimental Procedure
A. Setting up a basic circuit.
Remove a resistor from the protoboard, and using the
ohmmeter function of your multimeter measure its resistance, as
shown in figure 1. Repeat this for each resistor on the board.
Record your results in your lab notebook. The nominal
resistance values are R1 = 470 , R2 = 1,000 , and R3 = 3,000
. The resistors have a precision rating of 5%.
Q1. Is your measured value R for each resistor within the
expected limits?
R

Figure 1. Measuring a resistor
with an ohm-meter.
Draw a circuit diagram similar to figure 2a in your lab book, showing the 1 k resistor
connected to the power supply. Then connect the circuit. Turn on your power supply and set it to
about 10 V. (The meter on the power supply gives an approximate value, but should not be used
for accurate measurements.) For details on how to connect circuits using the protoboard, see
Appendix B. We will be using this same connection board in two other experiments in this lab.
Ohm - 1
A
Now draw a circuit
diagram in your lab book
showing how to connect the
R
R
R
V
voltmeter so as to accurately
measure the voltage across the
resistor. (See figure 2b.) Turn
(a)
(b)
(c)
the multimeter to the "V” DC Figure 2. (a) Resistor circuit. (b) Placement of volt-meter. (c)
voltage scale, and connect the Placement of ammeter.
circuit. Record the voltage in
your lab notebook. If it doesn’t seem reasonable, have your instructor check your connections.
Turn the power supply off, to minimize the risk of blowing the fuse in the ammeter. We will
now connect the ammeter in series with the resistor. First draw a circuit diagram in your lab
book showing how to do this, based on figure 2c. Turn the multimeter to the "400 mA" setting,
and connect up the circuit. Note that in order to connect the ammeter, you will need to "break"
the circuit at the resistor and connect the ammeter into the circuit so that the current flows
through it. Check your circuit carefully, turn on the power supply and record the current. If the
result seems unreasonable, have your instructor check your connections.
Use Ohm’s law and your measured values of the voltage across the resistor and the current
through the resistor to calculate its resistance Rcalc.
Q2. Calculate the % discrepancy between Rcalc and R. Does this seem reasonable?
B. Detailed Measurements on a Single Resistor.
Let's see if the 470  resistor obeys Ohm's law. You will
be putting known voltages across the resistor and then
measuring the current. You will plot the results to get the
value of the resistor.
A
R
V
Draw a circuit diagram in your lab book showing how to
connect the power supply, resistor, voltmeter and ammeter so
Figure 3. Circuit for detailed
as to obtain simultaneous measurements of voltage across the
measurements on one resistor.
resistor and current through the resistor. (See figure 3.) Set
up a table in Excel to record your voltage and current measurements, following the sample data
table shown in figure 4. Put 2.0 volts across the resistor and measure the current; record your
values PRECISELY. Now take about 8 data points over the range 0 to 16V. As the voltage rises,
check to see if the resistor is
point
I
V
P
overheating.
Plot voltage (y-axis) vs. current (xaxis) in Excel. Use Excel’s linest
method to get the slope of this graph
and the error. Use the slope to
determine the resistance of your
resistor (including the error). For
(amps)
1 0.00215
2 0.0044
3
4
(volts) (watts)
1.132
2.352
Figure 4. Sample Excel spreadsheet to test Ohm's law.
Ohm - 2
refresher about how to do this, see the first lab. Write down your experimental result (value and
error) for the resistance determined this way, Rslope, in the standard way.
Q3. Does the value of the resistor R (as determined using the ohmmeter) fall in your
experimentally determined range?
Using the spreadsheet, calculate the maximum power dissipated by your resistor (P = I2R =
IV = V2/R). The resistor is rated for 0.5 watts of power (i.e. the resistor can dissipate up to 0.5
watts of power before it is damaged).
Q4.
Did you exceed the power rating, and did it do any damage?
Q5.
Did the resistor get hot? Why or why not?
C. Resistors in Series:
RS  R1  R2  R3
Let's see if three resistors connected in series obey Ohm's
law. Draw a circuit diagram in your lab book, showing the
three resistors in series with the ohm meter. (See figure 5.)
Calculate the theoretically expected value Rcalc of the series
resistance, using the values R for the individual resistors that
you measured earlier.
R1
Now connect up the circuit and measure the series
resistance RS with the ohm-meter.
R3
Q6.
Compare RS with Rcalc. Is this result reasonable?
D. Resistors in Parallel:

R2
Figure 5. Resistors connected
1
1
1


RP R1 R2
in series for measurement with an
ohm-meter.
Here you will check the law for parallel addition of resistors Figure 5. Measuring the series
by connecting the resistors in various parallel (and series-parallel) combination
combinations,
to seeresistors
if
of three
with
prediction and measurement agree. Record all measurements and an
do ammeter.
all calculations in your lab
book.
1. Two resistors in parallel.
Choose two of your three
resistors, and calculate a prediction
for the parallel resistance that they
should give. Then connect them to
the ohm-meter in parallel, as shown in
figure 6g, and measure their parallel
resistance. Calculate the percent
discrepancy between Rcalc and Rmeas.
Q7.
Is this result reasonable?
2. Three resistors in parallel.
Calculate the expected equivalent

R1

R2
R1
R2
(g)
R3
(h)

R1
R2
R3
(i)
Figure 6. (g) Two resistors in parallel. (h) Three resistors in
parallel. (i) Series-parallel combination.
Ohm - 3
resistance for all three resistors connected in parallel, as shown in figure 6h. Draw the circuit,
hook them up and measure the resistance. Calculate the percent discrepancy.
Q8.
Is this result reasonable?
3. Series-parallel combination.
Now try the combination in figure 6i. As before, draw the circuit; predict the equivalent
resistance; wire it up; and measure the equivalent resistance. Calculate the percent discrepancy.
Q9.
What is your general feeling for the accuracy of the measurements of resistance made in
this lab? Which of the methods used (ratio of V to I, slope of graph, ohm meter) is more
accurate?
E. The resistor cube challenge problem. Ask your lab instructor if you should do this.
III. Equipment
Resistors: 470  3,000  resistors (0.5 W power rating)
PB-6 Global Specialties protoboard
2 - Digital multimeters (Metex M-3850)
Power supply (HY3003D-3)
Banana-plug hookup wires: 4 short, 2 long
Mini-grabbers - 1 red, 1 black
Resistor cube for demonstration, if available (10 k on a side)
IV. Appendix A: Resistor Color Code
a b c
d
One of the
important
components in
an electric
circuit is the
Figure A1. A color-coded resistor.
resistor. The
most common
kind is made from a thin carbon film. You should have some at
your table. Their resistance can vary from less than one ohm to
20 million ohms or so. Each one is marked with the value of its
resistance, using the resistor color code. (See Table A-I for the
code.)
There are four colored bands on a resistor. The first three colors
represent numbers: a, b, and c. The value of the resistance in
ohms is then given by the number:
R  ab x10c ohms
For example, if a=6, b=8, and c=3, R = 68 x 103 ohms. The
fourth band indicates the precision with which the resistance is
known.
Ohm - 4
TABLE A-I.
RESISTOR COLOR
CODE
color number
black 0
brown 1
red
2
orange 3
yellow 4
green 5
blue 6
violet 7
gray 8
white 9
silver 10% precision
gold 5% precision
NOTE: you may be supplied with high-precision resistors, which have five bands, with the extra
band used to give another significant figure to the resistance value.
Appendix B. Wiring using the Prototyping Board
The circuits studied in this lab will use the Global Specialties PB-6 Prototyping Board (or
protoboard for short). This board is shown schematically in figure B-1. (The spacing between
holes is somewhat exaggerated on the figure for clarity.) Wires and the ends of resistors,
capacitors and other components are meant to be inserted into the holes in the protoboard. These
holes are interconnected in a certain way to create continuous wiring between the components.
Specifically:
 In the central sections, holes are connected across the width of the board in groups of 5.
 In the sections on the edge of the board, holes are connected in long strips going the full
length of the board.
D
E
F
A
B

G
C
Figure B-1. Interconnection of protoboard plug locations. Points A and B are electrically
connected, while points A and C are not; and points D, E and F are electrically
connected, but none of them connect to point G.
Ohm - 5