ES 3: Introduction to Electrical Systems
Laboratory 1: DC Measurements
I.
GOALS:
In this lab you will learn how to measure DC voltages, DC currents, and electrical
resistance. You will create an Excel spreadsheet to graph data and use the “trend line”
feature to find the best fit line to experimental data. We will investigate the statistical
variation of resistance values and use Excel to quantify this variation.
Many sensors use DC resistance to translate a physical measurement (for example,
temperature) into an electrical signal. You will investigate light sensors (photoresistors),
temperature sensors (thermistors), and angular position sensors (potentiometers).
Finally, we will learn that wire has a small but measurable resistance. An audio speaker
is one application in which the resistance of wire is important. You will measure the
resistance of very thin magnet wire, and then determine the correct length of wire
needed to produce standard 8Ω and 16Ω speaker voice coils.
II.
PRE-LAB QUESTIONS:
Before coming to lab, you must complete the Pre-Lab exercises. The Pre-Lab work is
due at the beginning of the lab period.
First, read the entire lab manual for Laboratory #1. It is important that you understand
the instruments and measurement methods before coming to lab so that you can
complete the experiments efficiently.
After reading this manual, answer the following questions:
1. What is the color code used to denote a 47,000Ω (±10%) resistor?
2. An air conditioner requires 12 amperes (rms) of current. A non-engineer decides
to connect the a/c to an electrical outlet in another room using a 50-meter long
extension cord. The extension cord is made using AWG-16 wire (see Section V).
What is the total resistance of the extension cord (all 100 meters)? What is the
power dissipated within the extension cord when the a/c is running? Remember:
P=I2R.
ES 3 Laboratory #1
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III.
EXPERIMENTS:
Before starting to measure DC voltages, you need to get familiar with DC voltage
sources. In this lab, you will use the Regulated DC Power Supply, Model 3010, by
R.S.R. Electronics that is shown in Figure 1.
Figure 1. The DC power supply
This power supply contains three independent voltage sources. The leftmost voltage
source produces +5 volts. This voltage appears across the red connector (+5V 3A) and
the black connector (COMMON). The current from this source depends on the
resistance of the device being powered, but the maximum current is electronically limited
to be less than 3 amperes.
The power supply also contains two adjustable DC voltage sources. One source
produces positive voltages (+1.5 to +15V, red banana plug) and the other source
produces negative voltages (-1.5 to -15V, yellow banana plug). The output voltage of
each source can be adjusted with one of the two knobs. The current depends on the
resistance and the voltage setting, but the current may not exceed ±1 ampere.
The schematic diagram of the 3010 power supply (Figure 2) shows the three ideal
voltage sources. The COMMON terminals of the variable voltage sources are
connected together. Note that the symbol for an ideal voltage source that can be varied
includes a diagonal arrow.
Model 3010 Power Supply
1.5 to 15 volts
1 A (max)
-1.5 to -15 volts
1 A (max)
+
-
+
-
+
-
5 volts
3 A (max)
Figure 2. The schematic of the DC power supply.
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A. Measurement of DC Voltage
A voltmeter measures the difference in voltage between two nodes in a circuit. In this
lab you will use a digital multimeter (Figure 3). This instrument contains several different
meters in a single instrument: voltmeter, ammeter, ohmmeter, and a frequency counter.
Figure 3. The multimeter (voltmeter, ammeter, ohmmeter, and frequency counter)
V . Insert red and black test
To measure DC voltages, press the button labeled
wires into the “V Ω Hz” and “COM” jacks on the front panel of the voltmeter. Attach the
test wires to the +5V and COMMON terminals of the power supply. Now, you may
need to select the correct RANGE for the voltage measurement. Press the RANGE
button for 20; this means that the largest voltage that you can measure is 20 volts.
(Note that pressing 2 would not work because you are measuring 5V!). The “V Ω Hz”
input is always considered to be the positive input: a positive voltage reading means
that the node voltage read by the “V Ω Hz” input is greater than the node voltage read by
the “COM” input. The meter should tell you that the voltage is 5.0 volts; if you switch the
two input wires, the meter reads -5 volts. To avoid confusion, most people use red
wires and red connectors to indicate positive DC voltages. Black is often used to
designate COMMON or negative voltage.
IMPORTANT TIP: To make the most accurate measurement, you should always select
the lowest possible RANGE. To demonstrate this principle, hit the 200 button and
observe that the measurement is less accurate. (Now return the RANGE to 20!).
Use the voltmeter to adjust the two variable voltage sources to +6 volts and -12
volts (within ±0.1 volt). Record these two voltages. Now measure the voltage produced
by both voltage sources in series. (Measure from the RED to the YELLOW connector).
Record this voltage and explain your result using Kirchhoff’s voltage law.
B. Measurement of DC Current
The measurement of an electric current is performed using an ammeter and is quite
different than the measurement of voltage. When we speak of current, we are referring
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to the flow of charge through a circuit element. This means that we must place the
ammeter in series with that circuit element. Usually placing an ammeter in a circuit
involves breaking a connection and inserting the meter, as shown below:
resistor
resistor
I=?
+
-
Open
and
insert
ammeter
+
-
A
ammeter
Figure 4. To measure current (left), it is necessary to open-circuit the branch to be measured and
insert an ammeter (right)
To use the multimeter as a DC ammeter, press the Function button marked
RED test lead must be inserted into either
A
. The
(1) the jack marked “mA” for low current measurements, or
(2) the jack marked “10A” for high current measurements.
In this lab, all of our currents are less than 1 ampere, so use the “mA” input. The other
ammeter connection is the black COM jack, just like the voltmeter. Next, select an
appropriate range, choosing the smallest range possible to maximize the accuracy of
your measurement.
Positive and negative currents: Current that enters the “mA” jack flows out the “COM”
jack and provides a positive reading on the meter. If the current flows from “COM” to the
“mA” jack, then the meter displays a negative current.
Turn the DC power supply OFF. Create the circuit shown on the right hand side of
Figure 4. The ammeter has a fuse to protect against accidental overloads. If you blow
the fuse, you will be substantially delayed in completing the lab! Ask one of the TAs to
check your circuit before turning the DC power supply ON to avoid this delay. Then
proceed to the following questions:
Measure the current that flows through a 1kΩ resistor (Figure 5) when the resistor is
connected to a voltage source of 5V. Use the 5V output of the 3010 power supply.
Refer to the circuit diagram above for guidance when you set up the circuit. Record the
following data: The measured voltage produced by the power supply and the measured
current that flows through the 1kΩ resistor. Verify that this result obeys Ohm’s Law:
V=IR
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Figure 5. A 1000Ω resistor, ±5% (code: brown-black-red-gold1)
How is current measured by an ammeter? Actually, it is not difficult. A simple digital
ammeter consists of a small resistor (Rs) and a digital voltmeter in parallel. As current (I)
flows through the small resistor (Rs), the voltage that forms across Rs is measured by the
voltmeter (see the figure below). The current is displayed as I = V / RS.
An ammeter in a simple circuit
+
-
The actual measurement uses a resistor and a voltmeter
A
+
-
RS
V
ammeter
Figure 6. A digital ammeter measures the voltage that forms across a small resistance RS to
determine the current that flows through the meter.
If your ammeter is set to the 20mA range, then Rs = 10Ω. If a current of 5 mA is flowing
through the resistor, then the voltage measured across RS is I *RS = 50 mV. The meter
then divides the measured voltage by Rs = 10Ω, and displays 5 mA.
If you accidentally attempted to measure 10 amperes of current using the “mA” input of
the ammeter with the RANGE set to 20, what would be the power dissipated in RS? If RS
is designed to withstand 1 W of power dissipation, what would happen to RS in the
accidental situation above? Note: Most current meters have a fuse to protect the
ammeter from such large currents.
1
See the Supplementary Information at the end of this lab manual for instructions on reading resistor color
codes.
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C.
Measurement of DC Resistance
According to Ohm’s Law, we can determine the resistance of a circuit element if we
know the voltage across the element and the current through the element: R = V/I.
Use the DC power supply, a 1kΩ resistor, and the multimeter to measure the actual
resistance of the 1kΩ (±5%) resistor. The circuit diagram for this measurement is
shown in Figure 7. Record the voltage measured across the resistor, the current flowing
through the resistor, and calculate its actual resistance. Please don’t forget to include
units in your lab report (V, mA, kΩ).
If you are having difficulty making the proper connections, you can refer to the
photographs in the Supplementary Materials section. Try to hook-up the circuit without
looking at the photo first. This is good practice, and in the future the lab manual won’t
provide photographs!
resistor
Power Supply
1.5- 15 volts
1 A (max)
+
-
V
voltmeter
A
ammeter
Figure 7. Schematic for the Measurement of the DC Resistance of a Resistor using a Voltmeter
and an Ammeter
Often a single measurement may suffer from errors, so it is a recommended engineering
practice to make multiple measurements. Using the circuit above (Fig. 7), measure the
current that flows through the 1kΩ resistor for at least five (5) different voltages. Spread
out the measurements between voltages 1.5 volts to 15 volts.
Using the lab computer, start the spreadsheet software called Excel. Enter the data into
the spreadsheet in two columns, one for the measured voltage and one for the
measured current, as shown in Figure 8.
Next, make a graph of the data by selecting Insert>>Chart… from the top menu bar.
Choose “XY(Scatter)” as the Chart Type and hit Next.
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Figure 8. Excel spreadsheet with voltage and current measurements.
Next, select the data that you wish to plot by clicking and dragging the mouse to form a
box around the data as shown in Figure 9.
Figure 9. Graphing data requires the selection of the data cells.
Finally, click Next> and then add a title and label the axes of the plot (including units).
Click Finish to add the plot to your spreadsheet.
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Figure 10. Adding a title and labels to the axes (including units!)
The experimental measurements should fall in a straight line. To find the equation for
this line, you can add a “trend line” by choosing Chart>>Add trendline… from the top
menu bar. Choose a Linear trendline as seen in Figure 11.
Figure 11. Adding a “best fit” trendline to your data. Technically, this is called linear regression.
Finally, add the equation to the graph by clicking on the Options tab (Fig. 11) and using
the checkbox for Display equation on chart (Fig. 12).
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Figure 12. Displaying the equation for the trendline on the chart.
Include the spreadsheet and a description of the experiment in your lab report. You can
save the entire spreadsheet, or you can take a screen shot (hit the Prnt Scrn key), then
paste the screen shot into a Word file (ctrl-v). Send this file to yourself by email or save
it to your memory stick.
The Ohmmeter
You may have thought that the last circuit was unnecessarily complicated. You are
correct! All of the necessary circuitry is already included in the digital multimeter: a DC
voltage source and an ammeter. You can quickly measure the DC resistance of a circuit
element by connecting the element to the “V Ω Hz” jack and the “COM” jack. Switch the
FUNCTION button to Ω and select the proper RANGE (i.e., the smallest possible range).
In this configuration, the multimeter applies a DC voltage to the circuit element and
measures the current that flows through the element. From this data the DC resistance
(R=V/I) is found and displayed.
Use the ohmmeter to find the resistance of the same 1kΩ resistor used in your previous
measurement. Compare this result with your measurement of resistance using I and V.
Why do the two methods produce slightly different results? Hint: Think about RS.
It is impossible to manufacture resistors that are identical. Therefore, there is always
some variation of the actual resistance value among a random sampling of resistors.
The last color band on the resistor indicates the uncertainty in the resistance (silver Æ
±10%, gold Ʊ5%). This lab uses ±5% resistors, so every 1kΩ resistor should have an
actual resistance between 950Ω and 1050Ω.
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D. Sensors
1. Thermistor
A thermistor is temperature-sensitive resistor. Many thermistors are made by
connecting wires to a small piece of silicon. Silicon is a semiconductor, meaning that its
electrical resistance is somewhere between an insulator (like glass) and a metal.
Semiconductors have far fewer free charges (electrons) than metals, which is why a
semiconductor does not conduct current as freely as metal. As the temperature of a
semiconductor increases, however, the heat causes electrons to break free of the silicon
atoms. The larger number of free electrons allows the semiconductor to conduct
electricity more freely. In other words, the resistance decreases as temperature
increases.
The NTC-102 thermistor (Figure 13) has a temperature-dependent resistance of
R(T) = 1000Ω + K*(T - 25oC)
…where the temperature coefficient is K = -43 Ω/oC, and T is the temperature in Celsius.
Figure 13. NTC-102 Thermistor
Measure the resistance of the thermistor at room temperature, RRT. Next, pinch the
thermistor between your fingers to increase its temperature and measure Rwarm. (Try to
avoid touching the bare wires; your fingers will reduce the measured resistance!)
Record these data for your lab report, and calculate the temperatures of the room and
your fingers using the equation for R(T).
2. Photoresistor
A photoresistor is a resistor that is sensitive to light. Photoresistors work in a manner
that is similar to a thermistor. Light enters a transparent window and falls on a thin layer
of semiconductor (cadmium sulfide, CdS) that has a serpentine shape (Fig. 14). The
photons striking the semiconductor release free electrons and increase the electrical
conduction through the device. That is, more light will produce more electrons, and this
decreases the resistance of the photoresistor.
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Measure the resistance of a photoresistor when it is exposed to normal room light.
Repeat the measurement in darkness (you may cup your hands around the sensor, but
don’t touch the wires or you will also measure the resistance of your body!)
Include this data in your lab report. Then write a description of how this device might be
used to automatically control streetlights by sensing day and night.
Figure 14. A photoresistor (also called a photocell)
3. Potentiometer
A potentiometer can be used as a rotational position sensor. A small metal wiper is
connected to the shaft of the potentiometer. As the shaft rotates, the position where the
wiper contacts a semicircular resistor changes (Fig. 15). This changes the resistance
between the nodes A and W, as well as between nodes B and W.
A
B
Figure 15. A sketch and a photograph of a potentiometer. (Sketch source: www.markallen.com)
Measure the resistance between terminals A and B. Then measure and record the
resistance between terminals A-W and B-W every 90o as you rotate the shaft of the
potentiometer in the clockwise direction. In your lab report write an explanation of how
this device works based on your observations and describe how one might use a
potentiometer to electrically determine the position of the gas pedal of an automobile.
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E. Audio Speakers
An audio speaker produces sound by displacing air with a rigid cone (see Figure 16).
The cone is connected to a coil of wire called a “voice coil”. This coil is placed between
the north and south poles of a permanent magnet. If current flows in the coil, the current
creates a magnetic field that either attracts or repels the voice coil from the permanent
magnets. If the current is varying in time such that the waveform represents music, the
speaker then reproduces that music.
basket
basket
pole
piece
cone
voice
coil
N S
dust
cap
pole
piece
S
N S
speaker cone
magnet
http://en.wikipedia.org/wiki/Loudspeaker
Figure 16. Front and side views of an audio speaker.
Later in ES-3 you will build your own speaker, including the voice coil. One important
design parameter for a voice coil is its DC resistance. Typically, the DC resistance of a
voice coil is 4, 8 or 16Ω.
In class, we usually assume that wires have zero resistance, that is, wires are perfect
short circuits. In reality, all wires have a small, nonzero resistance. You will design the
voice coil of your speaker to have one of these standard resistances (4, 8, 16Ω).
The resistance of a wire can be determined from
R = ρ(L/πr2)
…where L is the length of the wire, r is the radius of the wire, and ρ is a property of the
metal wire called resistivity. Copper has one of the lowest resistivities of all metals, and
it is a common metal used for wires -- including the microscopic wires within an
integrated circuit or chip.
From the equation above, you should notice that long wires have greater resistance.
Very thin wires (small radius, r) also have a high resistance. If you look around your
room, you will notice that appliances that require a large amount of power (that is, a high
current) also have thick, short power cords. This minimizes the resistance of the wires
that connect the appliance to the wall outlet, and it prevents the wires from overheating
due to large power dissipation: Pwire = I2Rwire.
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You should have two 1-meter long pieces of thin magnet wire labeled A and B. Measure
the resistance of these wires (take care to subtract the measured resistance of the red
and black test wires!). Record the resistance values and then use the tabulated data in
Section V to determine the wire gauge (AWG) of each 1-meter sample. Include these
calculations and results in your lab report.
Using the ohmmeter, measure the resistance of the small audio speaker provided.
Again, remember to subtract the resistance of the test wires by shorting the tips of the
test wires together! Include these measurements in your lab report.
Question: The voice coil inside an audio speaker is a long piece of wire wound around a
cylindrical form. If we wanted to make a 16Ω speaker using AWG-30 wire, what length
of wire is needed?
Question: If you were required to limit the length of wire in the voice coil to less than 5
meters, which gauge wire should you use to produce an 8Ω voice coil?
IV.
LAB REPORT:
All required data, questions, and written comments can be found within the framed text
blocks. In your report, tabulate or plot all of the requested data and answer the
questions in a manner that flows naturally.
Lab Report Guidelines are listed on the website.
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V.
SUPPLEMENTARY INFORMATION:
Photograph of the Circuit Used to Measure DC Resistance in Section III.C
1kΩ
resistor
voltage
probe
I
I
Figure V.1: Photograph of the circuit used to measure the voltage across a 1kΩ resistor and the
current through the resistor.
Reading Resistor Color Codes
The resistance is usually printed on a resistor using four bands of color. Each color represents a
digit from 0-9, or, in the case of silver and gold, a manufacturing tolerance.
The code is formatted in scientific notation. The first two bands represent the mantissa (with no
decimal point!) and the third band represents the power of ten in the exponent. In the example
below, a 26kΩ resistor is coded as 26x103 which uses the colors red-blue-orange.
Resistor Color Codes
Black 0
Brown 1
Red
2
Orange 3
Yellow 4
Green 5
Blue
6
Violet 7
Gray 8
White 9
Silver ±10%
Gold ±5%
Example: 26 kΩ ± 5% =
RED +
2
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BLUE
6
+
ORANGE +
x
103
GOLD
±5%
=
26kΩ ±5%
Page 14 of 18
Table I. Wire Gauge Chart
One kilometer of AWG 14 wire
(residential electrical wire)
has a resistance of 8.54Ω
Wire
Gauge
(AWG)
38
37
36
35
34
33
32
30
28
27
26
25
24
22
20
18
16
14
13
12
10
8
6
4
2
1
0
Diameter(mm) Area(mm2) Ω/km
0.10
0.11
0.13
0.14
0.16
0.18
0.20
0.25
0.33
0.36
0.41
0.45
0.51
0.64
0.81
1.02
1.29
1.63
1.80
2.05
2.59
3.25
4.115
5.189
6.543
7.348
8.252
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0.0078
0.0095
0.013
0.015
0.020
0.026
0.031
0.049
0.08
0.096
0.13
0.16
0.20
0.33
0.50
0.82
1.3
2.0
2.6
3.3
5.26
8.296
13.3
21.15
33.62
42.41
53.49
2190
1810
1300
1120
844
676
547
351
232
178
137
108
87.5
51.7
34.1
21.9
13.0
8.54
6.76
5.4
3.4
2.2
1.5
0.8
0.5
0.4
0.31
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Optional Lab Exercise (Statistical Variation of Resistance: Standard Deviation)
Using the ohmmeter (on the most accurate range), measure and record the resistance of
10 different 1kΩ resistors. Ask a neighboring lab group for their 10 resistance values.
Enter all 20 resistance values into an Excel spreadsheet, and then find the average
resistance and the standard deviation of the resistance, as shown below. Add these
data to your lab report and comment on whether the manufacturer has produced
sufficiently accurate resistors (+/-5%).
To find the average, click on a cell below the column of resistance data. Next choose
Insert>>Function…>>AVERAGE, and select the range of data to be averaged:
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To find the standard deviation of the data, click on the next cell below the AVERAGE,
then choose Insert>>Function…>STDEV and select the range of data:
The standard deviation indicates the range of resistance values. If RAVE is the average
resistance and σ is the standard deviation, then around 70% of the resistors2 should fall
between RAVE – σ and RAVE + σ. For the data in the example, RAVE = 985Ω and σ=9Ω.
So we can expect that there is a 70% chance that any randomly selected resistor will
have a resistance between 976 and 994Ω.
2
This assumes that the resistors follow a Normal or Gaussian distribution, sometimes called a Bell Curve.
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VI.
PARTS LIST:
Equipment
DC Power Supply
Digital Multimeter
Assorted test leads:
R.S.R. Inc. Model 3010
Tenma, Model 72-410A
Banana plug to alligator clip
Components
1 kΩ, ±5% resistors (10 per group if the Optional Experiment is selected, otherwise 1 per
group)
Thermistor, NTC-102 (Jameco Part No. 207482, NTC,K=-0.43±10%),
Potentiometer, 10kΩ (Jameco Part No. 29081, LINEAR TAPER,1/2W,10K OHM)
Cadmium Sulfide Photocell (Jameco Part No. 120310, 90mW,150V PEAK)
Small audio speaker (Jameco Part No. 31958 or 16Ω equivalent)
Magnet Wire: Two 1-meter lengths of assorted small gauge wire (thinner than AWG 30).
The wire should be labeled “A” and “B” so that the AWG is known to the TA.
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