Lab 5: Ohm's Law

5 Ohm’s Law
In addition to reading this assignment, you may need to refer to Appendix A on
uncertainties and Appendix B on linear regressions.
Introduction
Ohm’s Law
The current flowing through an Ohmic device is directly proportional to the potential
difference ∆V between its terminals,
∆V = iR (1)
The constant of proportionality R is called the resistance of the device. This relationship is
knownasOhm’s Law. Youwillinvestigatethedependence ofcurrent onpotentialdifference
in resistors and light bulbs. Your job will be to determine whether or not these devices are
Ohmic and if so to determine their resistances.
R
1
R
2
R eq
R 1 R 2
R eq
Series
Parallel
(a)
(b)
Figure 1: A pair of resistors connected (a) in series and (b) in parallel.
Equivalent Resistance
A pair of resistors can be connected either in series or in parallel as shown in Figure 1.
Note that two wires emerge from each pair. The equivalent resistance R eq of a pair of
resistors is the resistance between these two wires. The equivalent resistance of two or more
resistors connected in series is given by
R eq = R 1 +R 2 +R 3 +... (2)
and that of two or more resistors connected in parallel is given by
1
R eq
= 1 R 1
+ 1 R 2
+ 1 R 3
+... (3)
You will test Eqs. 2 and 3 empirically by measuring the current drawn by series and parallel
pairs of resistors subject to a known potential difference.

Resistor Color Codes
Most resistors you will encounter are marked with a set of bands, according to a standard
color code, which you can use to determine their resistances. There are ten colors corresponding
to numerical digits 0-9 (See the table below.), and gold and silver bands indicating
5% and 10% accuracy in the coded resistance, respectively. Starting at the far end of the resistor
from the gold/silver band, the first two bands are the first two digits in the resistance.
The third band gives the power of ten by which you multiply the first two digits to obtain
the resistance.
color black brown red orange yellow green blue violet gray white
digit 0 1 2 3 4 5 6 7 8 9
multiplier 1 10 100 1k 10k 100k 1M 10M 100M 1000M
R = [band1][band2]×10 [band3] ± 5%(gold) (4)
± 10%(silver)
For example, Blue Yellow Red Gold gives R = 64 ×10 2 Ω = 64×100 Ω = 6400 Ω with a
tolerance of 5%, or ±320 Ω.
Experiment
You have been supplied with three resistors, a light bulb, a power supply, several wires
for connecting them, and a digital multimeter (DMM) for measuring potential differences
(voltages), currents, and resistances.
Warnings
1. Before turning on the power supply or connecting it to a circuit, make sure that the
switch for the voltage range is in the 0-8 V position, and that the Voltage Increase dial
is turned all the way down (the counter-clockwise direction). Then slowly increase the
voltage as needed. Do not put more than 3 V across a light bulb!
2. When using the DMM as an ammeter (i.e. to measure current) ...
(a) make sure the red lead is plugged into the port on the DMM labeled for measuring
current. Start with the one for large currents (10 A or 20 A), and move to the
more sensitive port(s) if you find that you need better precision.
(b) always be certain to connect it in series with the device through which you are trying
to measure the current. Never connect an ammeter in parallel with anything,
or you will blow its fuse!
3. When using the DMM as a voltmeter or ohmmeter, make sure the red lead is plugged
into the voltage port, and make sure to connect it in parallel with the device(s) of
interest. (Connecting a voltmeter or Ohmmeter in series with something doesn’t make
any sense, but it also doesn’t blow any fuses.)

A
E R V
E
R
(b)
(c)
Figure 2: (a) A simple circuit consisting of a voltage source connected in series with a
resistor. (b) The same circuit with a voltmeter to measure the potential difference between
its terminals. (c) The same circuit with an ammeter to measure the current.
Resistance
1. Set up the circuit shown in Figure 2a with one of your resistors.
2. Record the resistance and uncertainty indicated by the color code on the resistor.
3. Set the emf of the power supply to a value in the range 0 < E < 3 V.
4. Plug the red lead of the DMM into the voltage port, and connect the DMM in parallel
with the resistor as shown in Figure 2b. Turn the knob on the DMM to a suitable
voltage scale, and record the voltage across the resistor.
5. Plug the red lead of the DMM into the current port, and connect the DMM in series
with the resistor as shown in Figure 2c. Remember never to connect an ammeter in
parallel with anything! Turn the knob on the DMM to a suitable current scale, and
record the current through the resistor.
6. Repeat steps 3-5 for four other source emfs in the range 0 < E < 3 V.
7. Repeat the whole process (steps 3-6) with the light bulb instead of a resistor. In
choosing your source emfs be sure that all of your source emfs are below 3 V and
that you cover, with at least three measurements, the low-voltage range in which the
filament does not glow.
8. Use the DMM to measure the resistances of the resistor and light bulb you used. Ask
for help if you need it.
Equivalent Resistance
1. Set up the circuit shown in Figure 3a.
2. Set the source emf to about 1 V.
3. Use the DMM to measure the voltages V 1 and V 2 across each of the resistors and the
voltage V across the pair.
4. UsetheDMMtomeasurethecurrentthroughtheresistors. Remember never to connect
an ammeter in parallel with anything!

Figure 3: A voltage source connected in series with (a) two resistors connected in series and
(b) two resistors connected in parallel.
5. Set up the circuit shown in Figure 3b.
6. Keep the source emf at about 1 V.
7. Use the DMM to measure the voltage across the resistors.
8. Use the DMM to measure the currents i 1 and i 2 flowing through each of the resistors
and the current i flowing into the pair. Remember never to connect an ammeter in
parallel with anything!
9. Use the DMM to measure the resistances of the resistors.
Analysis
Resistance
1. Put your voltage and current data into a spreadsheet, and plot V vs i for the resistor
and the light bulb.
2. Are your data compatible with a linear model If so, use the LINEST function to find
the slope of a linear fit to the data and its uncertainty (see Appendix A).
Equivalent Resistance
1. Use your voltage and current measurements (i and V) and Ohm’s law (Eq. 1) to
determine the equivalent resistances of the series and parallel pairs of resistors.
2. Use the resistances you measured with the DMM and Eqs. 2 and 3 to calculate the
predicted equivalent resistances of your series and parallel pairs of resistors.
3. Is there an obvious relationship between your measured V 1 , V 2 , and V in the series
circuit How about between i 1 , i 2 , and i in the parallel circuit
Questions
1. For the resistor you studied in detail, give the resistance indicated by the color codes,
the resistance you measured with the DMM, and the resistance you extracted from

your V vs. i graph with uncertainties. Are they consistent with each other within
uncertainty
2. Is the light bulb you studied an Ohmic device Give reasoning based on your data.
3. Compare your measurement of the resistance of the light bulb with your graph of V
vs. i. What might be going on here
4. What relationships, if any, did you find between V 1 , V 2 , and V in the series circuit and
between i 1 , i 2 , and i in the parallel circuit
5. Do the equivalent resistances you determined from your voltage and current measurements
agree with the predictions of Eqs. 2 and 3 within uncertainty Include your
results in your response.