ECE 2A Lab #1
Lab 1
Voltage, Current,
and Resistance
Overview
In this lab you will learn to about two basic lab tools - the Digital Multimeter (DMM) and the
DC power supply – and to use these tools to investigate simple resistive circuits and devices.
In particular you will examine the non-idealities of current (ammeter) and voltage (voltmeter)
measurements, and then use the DMMs to characterize series and parallel resistor
combinations, voltage dividers, and the current-voltage relationship of some simple nonlinear
devices like light bulbs and motors. You will also examine a simple variable-resistance
device called a potentiometer, and (for extra credit) a photocell.
Table of Contents
Background Information
Resistors
Solderless Breadboards
Digital Multimeters
Further Reading
Pre-lab Preparation
Before Coming to the Lab
Required Equipment
Parts List
In-Lab Procedure
1.1
Power Supply and Voltmeter
1.2
Resistance Measurements
Ammeter and Voltmeter Internal Resistance
Continuity Testing
1.3
Series and Parallel Resistor Combinations
1.4
Voltage Dividers and Potentiometers
1.5
Current-Voltage Characteristics
Extra Credit: Photocell
1
2
2
4
5
6
7
7
7
7
8
8
9
10
10
11
12
14
15
© Bob York
2
Voltage, Current, and Resistance
Background Information
Resistors
There are a number of different types of resistors depending on the application. All obey
Ohm’s law with a specified resistance, of course, but the electrical behavior can also vary in
terms of power handling or current handling, temperature dependence of the resistance,
size/shape, and manufacturing tolerances. All factors must be considered in circuit design.
In ECE 2 we use so-called “through-hole” components which have long metal leads.
Figure 1-1 shows four common families of through-hole resistors. The carbon-film resistors
are the most ubiquitous by far, and dirt cheap: in large quantities, these resistors are priced in
fractions of a US cent (e.g. $0.004 per resistor in quantities of 1,000). They are so cheap that
the primary cost of using them in a product nowadays is associated with the insertion time in
the robotic assembly and not the cost of the part itself (the robotic “labor” cost is usually
about 1-2 cents per part).
Carbon Film
• ±5%, ±10%
• Cheap
• General purpose
Metal Oxide
Metal Film
Wirewound
• Higher Power
• Precision ±1%
• High Performance
• High Power,
High Current
Figure 1-1 – Here we show a few of the most common types of “through-hole” resistors. In
ECE 2 we will use the cheap carbon-film type almost exclusively.
Probability Density
Carbon-film resistors are made by
0.25
depositing a thin carbon film on a small
±5%
ceramic cylinder, and then etching the
0.20
film into a narrow helical pattern. It is
0.15
difficult to precisely control the
thickness and conductivity of the carbon
0.10
film so there are always some random
±10%
manufacturing errors. The statistical
0.05
distribution of resistor values is
characterized
by
the
specified
0.00
“tolerance”. Although manufacturers do
-10
-5
0
5
10
not usually share the details of their
% Deviation from Nominal
processes it is generally assumed that
Figure 1-2 – Probability density function describing
the resistor values can be described by a resistor statistics, assume a 3 tolerance.
Gaussian (normal) distribution with a
standard deviation  such that the tolerance is around 3 . This effectively means that
99.7% of the resistors will fall within the specified tolerance range, clustered near the
nominal value. Figure 1-2 shows the probability-density functions computed for two
commonly-encountered tolerances, ±5% and ±10%.
© Bob York
3
Background Information
When companies make electrical components they try to avoid testing each part
individually; that would take too much time and would add significantly to the cost of each
component. Instead the engineers work to characterize the process statistics very well, and
then can test a few sample parts periodically to insure that components remain within the
acceptable range of values.
That brings us to component values. There are a HUGE range of values to cover:
resistances can be anywhere from tiny fractions of an ohm to tens of mega-ohms
(mega=million). The resistor values that are selected for production are based on a system
that is tied closely to the expected manufacturing tolerances. The basic idea is to select
discrete values that cover as much of the full range of resistance as possible without having
the statistical distributions overlap too much. Consider two successive values of resistance,
r1 and r2 . If the component tolerance is defined as t , then the largest possible value of r1
would be r1 (1  t ) . Similarly the smallest possible value of r2 would be r2 (1  t ) . Equating
those limiting values give a ratio of successive resistor values as:
r1 1  t

(1.1)
r0 1  t
For example, if the tolerance is 20% ( t  0.2 ), then (1.1) gives a ratio of consecutive
resistances of 1.5. Figure 1-3 illustrates a set of six values in the range of 1-10 that are
commonly used to describe components with this tolerance, and you can verify that the ratio
of successive values is indeed close to 1.5 in each case.
1.0
1.5
2.2
3.3
4.7
6.8
10
Figure 1-3 – Illustration showing values appropriate to a ±20% tolerance (E6),
with expected normal distributions shown around each nominal value.
You will see that the ratio isn’t exactly 1.5 for every pair of adjacent values. One reason is
that we want the pattern of numbers to repeat for each successive decade of values (e.g.
10,15,22,33…..100,150,220,330….etc.). In order for the pattern to repeat after N discrete
values, the ratio x must satisfy
x N  10
 x  101/ N
(1.2)
So for N  6 the ideal ratio would be x  1.468 . But there are also some rounding errors that
come into play, so the set of numbers in Figure 1-3 represent a reasonable compromise.
It’s not hard to figure how many values are needed to cover the range 1-10 for a different
tolerance. For ±10% we need N  12 ; for ±5% we need N  24 , and so on. This has led the
EIA (Electronics Industry Association) to standardize a set of values designated as E6, E12,
E24, etc. The first three are shown in Table 1-1.
Table 1-1 – Standard EIA Decade Values for E6, E12, E24
E6
E12
1.0
1.0
1.5
1.2
1.5
2.2
1.8
2.2
3.3
2.7
3.3
4.7
3.9
4.7
6.8
5.6
6.8
8.2
E24 1.0 1.1 1.2 1.3 1.5 1.6 1.8 2.0 2.2 2.4 2.7 3.0 3.3 3.6 3.9 4.3 4.7 5.1 5.6 6.2 6.8 7.5 8.2 9.1
4
Voltage, Current, and Resistance
A tighter tolerance typically costs more so there is a tradeoff between precision and cost.
As a future circuit designer it will be up to you to determine the sensitivity of your circuit in
order to choose the appropriate tolerance. In certain types of frequency-selective filter
circuits, for example, precision ±1% metal-film components are often required. In the
circuits we will use in ECE 2, ±10% tolerances will be fine so you should familiarize yourself
with the values available in this range (E12).
Another practical issue is how to READ component values. Ideally the value would just
be printed on the side of the device, but most through-hole resistors use a multi-band color
code, described in Table 1-2. It is simple but takes a little getting used to, and you will only
figure it out with practice. Some common examples are shown on the right.
Table 1-2 – Resistor color-code and examples
Color
Black
Brown
Red
Orange
Yellow
Green
Blue
Violet
Gray
White
1st Stripe
(1st digit)
0
1
2
3
4
5
6
7
8
9
2nd Stripe
(2nd digit)
0
1
2
3
4
5
6
7
8
9
3rd Stripe
(Multiplier)
1
10
102
103
104
105
106
107
108
109
A final practical issue: the carbon-film resistors come in
different SIZES depending on power-handling.
An
illustration of the relative sizes is shown in Figure 1-4. When
a current flows in a resistor some electrical energy is
dissipated, and this manifests itself as a rise in temperature
(heat). Ordinarily the resistors are mounted in a PC board or
breadboard where the only mechanism for getting rid of that
heat is convection to the surrounding air. Convection heat
transfer is enhanced by increasing the surface area, so resistors
that must handle higher powers have a larger surface area. For
very high power the resistors may have an integral metal
heatsink with fins for extra surface area. In ECE 2, the
resistors are almost always ¼ Watt resistors.
Examples of Common Values:
Brown-Black-Red
10×102 = 1kΩ
Yellow-Purple-Red
47×102 = 4.7kΩ
Brown-Black-Orange
10×103 = 10kΩ
Orange-Orange-Orange
33×103 = 33kΩ
Brown-Black-Yellow
10×104 = 100kΩ
Red-Red-Yellow
22×104 = 220kΩ
Aluminum
fins
Figure 1-4 – Size for power!
Solderless Breadboards
The most common method of experimenting with through-hole or “leaded” components like
resistors is using a solderless “breadboard” to simplify electrical connections. These get their
name from the early days of radio when it was common to build vacuum tube circuit
prototypes on a wooden surface. Today's breadboards are a grid of insulating plastic atop a
© Bob York
5
Background Information
pattern of conducting metal strips. Figure 1-5 shows the top view of a typical breadboard
used in ECE2, and a close-up of the pattern of connection points.
Power/Ground terminals
Rails
(lines denote internal connection)
Groove
isolates
holes on
either side
Each group of 5 horizontal
holes are electrically
connected internally
by a metal clip
Figure 1-5 – Solderless breadboard used in ECE 2
Component leads and wires are inserted into the holes to make contact with conducting
metal strips inside. On either side of the long channels or grooves, each perpendicular group
of five holes are electrically connected. There are also long groups of connected holes called
“rails” running the length of the breadboard, marked by colored lines. These are normally
used for power and ground connections. Breadboards come in a variety of sizes and shapes
but most have the same basic pattern of holes and rails.
Digital Multimeters
The digital multimeter (DMM) is a versatile measurement tool for electrical circuits. It is
capable of multiple types of measurements, including at least the three in Table 1-3:
Table 1-3 – Basic Multimeter Measurements
Function
Symbol
Voltmeter
V
Ammeter
A
Ohmeter
Ω
Description
Measures voltage between terminals, ideally with zero
current draw (infinite resistance)
Measured current flowing through the meter, ideally with
zero voltage drop (zero resistance)
Calculates resistance between terminals by applying a
known current and measuring the terminal voltage
At first glance the use of the DMM seems trivial: just hook it up and read the data, right?
But like all measurement instruments a real DMM is not perfect, and a clear understanding of
those non-idealities is essentially in order to use it properly.
6
Voltage, Current, and Resistance
Consider the voltmeter function: we want to measure the voltage between two points in
some circuit, but we don’t want to the act of measuring to change the circuit in any way.
That means the voltmeter should not draw any current away from the circuit under test; it
should appear to the circuit as an infinite resistance. But a real voltmeter must draw some
current in order to make the measurement. So real voltmeters will always affect the circuit to
a certain extent; they always have a finite resistance. This could be an issue if we are probing
circuits with tiny currents or extremely large resistances.
Similarly the ammeter is designed to measure the current flowing in some part of a circuit.
To do that we break the circuit at some point and insert the so that the current will passes
THROUGH the ammeter. To minimize the impact on the circuit the ammeter should not
introduce any additional voltage drops, which means it should appear like a perfect shortcircuit (zero resistance) to the circuit. But real ammeters necessarily have a non-zero
resistance, because the resulting voltage drop across
the internal resistance is used to calculate the
current. When measuring small currents a rather
large internal resistance may be necessary to create a
measureable voltage drop.
In most DMMs there are three terminals: one
common terminal, one for voltage or resistance
measurements, and one for current measurements.
The user then manually attaches the leads to the
appropriate terminal, and manually selects the
appropriate measurement function. Some meters
also require you to manually select the measurement
range, whereas others are “autoranging” and choose
the range for you. The circuit behavior of the DMM
(how much current it draws, or equivalently its
internal resistance) usually depends on the
Figure 1-6 – Handheld DMM
measurement range.
A common and often destructive mistake by beginners is to configure the DMM for use as
an ammeter (zero internal resistance) and then attach the test leads across a carrying
component or voltage source. The ammeter then shorts the circuit and a large current may
flow through the DMM, causing an internal fuse to blow. The fuse will then have to be
replaced before any further measurements can be made. In the little hand-held DMMs like
that in Figure 1-6, the enclosure must be taken apart to replace the fuse.
Lastly, note that most multimeters can be used for both AC and DC measurements. In the
AC measurement mode where the currents and voltages are presumed to vary sinusoidally
with time, the instrument compute an RMS (root-mean-square) value for the waveform, NOT
the peak voltage or current.
Further Reading
Read the relevant sections of the Equipment Tutorial posted on the class website to
familiarize yourself with the details of the specific DMM and power supply in the ECE 2 lab.
Some useful/relevant Wikipedia Links:
http://en.wikipedia.org/wiki/Resistor and also http://en.wikibooks.org/wiki/Electronics/Resistors
http://en.wikipedia.org/wiki/Breadboard
http://en.wikipedia.org/wiki/Multimeter
© Bob York
Pre-lab Preparation
7
Pre-lab Preparation
Before Coming to the Lab
□
Read the “Equipment Tutorial” on the course website to familiarize yourself with the
bench power supply and DMM.
□
Read through the details of the lab experiment to familiarize yourself with the
components and testing sequence.
□
One person from each lab group should obtain a parts kit from the ECE Shop.
□
Fill in the color-codes in Table 1-4 usign the information in the background section.
□
Calculate the “Theory w/Nominal Values” column in Table 1-5
Required Equipment
■ Provided in lab: Bench power supply, Bench DMM, Decade Resistor Box
■ Student equipment: Hand-held DMM, Solderless breadboard, and jumper wire kit
Parts List
Qty
Description
1
4
4
1.5
1.5
3
1
1
1
1
1
1
1
1
Handheld DMM
Banana plug (red) with set screw
Banana plug (black) with set screw
18AWG wire (per foot), Black, 16x30 stranded
18AWG wire (per foot), Red 16x30 stranded
1.0 k -Ohm 1/4 Watt resistor
2.0 k -Ohm 1/4 Watt resistor
3.0 k -Ohm 1/4 Watt resistor
4.7 k -Ohm 1/4 Watt resistor
10 k-Ohm 1/4 Watt resistor
10k trimpot (Bourns 3/8" thumbwheel type)
3V @ 45mA DC motor
6V lamp with PC pins (T1 3/4 bi-pin)
CdS photocell
8
Voltage, Current, and Resistance
In-Lab Procedure
Read the instructions carefully. If you skim through the text too quickly you may miss
something important.
□
Each critical step begins with a check box like the one at the left. When you complete a
step, check the associated box.
Be sure to document all steps and results in your notebook for inclusion in your lab report.
1.1 Power Supply and Voltmeter
We’ll start by using the bench DMM to probe the output voltage of the bench power supply.
This step is easy and should not take much time:
□
First set the bench DMM to measure DC Volts on the 20V full-scale range. Using one of
your cables, connect the V/Ω terminal of the DMM to the +18V output of the power
supply, and with a second cable connect the COM terminals together. These connections
are shown schematically in Figure 1-7. A common convention in microelectronics is to
use black wires for the ground or “common” lead,
but of course the color of the cable doesn’t really
Power
matter much here.1
DMM
Supply
□ Turn on the DMM and the power supply. Be sure
V
Vout
the “METER” switch on the power supply is set
to correctly display the output of the +18V
terminal, and be sure to note which scale is
appropriate for this setting. Then adjust the power
COM
supply to get a reading of +7.0V on the DMM.
Figure 1-7 – Voltmeter test.
To which full-scale range must the DMM be set if
the display only shows one digit past the decimal? (i.e. 7.0 and not 7.00 or 7.000) What
is the lowest range that can be used to measure 7V? How does the DMM display an outof-range measurement?
When properly calibrated, DMMs are usually more accurate than the cheap indicators on the
power supplies, so in case there is a disagreement between what the power-supply says and
what the DMM says we will usually trust the DMM!
□
Repeat the steps above to set the +20V output on the power-supply to +10.0V. Be sure
the “METER” switch on the power supply is set to correctly display the output of the
+20V terminal. Repeat again to set the -20V output to -5.0V, and then double check that
the three output terminals on the power supply are still at their desired values:
o
+18V terminal: should be set to +7.0V,
o
+20V terminal: should be set to +10.0V
o -20V terminal: should be set to -5.0V.
In each case above we have defined the voltages at the various output terminals with respect
to the common terminal on the power supply.
1
It’s a different story with the AC electrical wiring you find in buildings like your home. In that
case, white is always the “neutral” lead, black is the “hot” lead, and green is usually used for ground.
© Bob York
Resistance Measurements
9
Let’s now use the DMM to make measurements with respect to other reference points:
□
Using the DMM, record the following measurements between power-supply terminals:
o
+18V terminal with respect to the +20V terminal
o
+18V terminal with respect to the -20V terminal
o
+20V terminal with respect to the -20V terminal
o COM terminal with respect to the +18V terminal
Clearly the voltage recorded by the DMM is critically dependent on the reference point.
You may have noticed that in addition to the COM terminal on the power supply there is
also a “ground” terminal. The ground terminal is electrically connected to the physical Earth
through the AC distribution system in the building, usually via a large copper pipe driven into
the ground outside the building somewhere. In some electrical instruments the “ground”
terminal is electrically connected to a metal case or enclosure to avoid hazardous shocks if
there is a wiring fault in the instrument. But it is important to note that COM and ground are
not the same. This is because power supplies are designed so that they can supply power to a
variety of loads, some of which may not be referenced to ground (so-called “floating” loads).
The COM terminal is the point of reference for the output terminals in ALL situations, so that
any current flowing from one of the output terminals should return to the power supply via
the COM terminal.
There are times when it makes sense to electrically connect COM and ground, in which
case we will add a little jumper wire between the terminals. In fact there may already be a
jumper installed on your bench supply; it is usually considered good practice to keep that
jumper wire there unless you have a specific reason not to use it.
□
If there is a jumper wire connecting COM and ground, remove it and measure all of the
the voltages at the output terminals with respect to this ground terminal. The add the
jumper wire and repeat the measurement.
The key takeaway from this section is that voltage is always measured as a difference in
potential between two points, and that the choice of reference point is critical.
1.2 Resistance Measurements
Now let’s explore the DMM as an Ohmeter for resistance measurements. For convenience we
will use the bench decade box as an adjustable resistor in
this step. Again these measurements are quite simple,
but we want to pay close attention to the characteristics
Bench
of the meters themselves:
DMM
R
Ω
□ Configure the DMM for resistance measurement by
pressing the “Ω” button. Select the 20k range.
Connect the V/Ω terminal of the DMM to a red
terminal on the decade resistor box, and the COM
COM
terminal of the DMM to a black terminal. The
Figure 1-8 – Ohmmeter setup.
connections are shown schematically in Figure 1-8.
□
Set R to 5kΩ. Record the actual value of R as
measured by the DMM. Adjust the range setting on the DMM to understand its effect on
the measurement resolution and record this in your notebook.
10
Voltage, Current, and Resistance
Ammeter and Voltmeter Internal Resistance
□
Now add your small handheld DMM to the
circuit as shown in Figure 1-9. Configure
the handheld DMM as a voltmeter by
selecting one of the DC Volt ranges with
the rotary switch. Does the resistance
measurement change when the voltmeter is
added? What can you conclude about the
internal resistance of the voltmeter?
Your hand-held DMM should indicate the
presence of a small voltage across the resistor.
In order to sense the value of the resistance the
ohmmeter must pass a small current through it!
Bench
DMM
Handheld
DMM
R
Ω
V
COM
Figure 1-9 – Voltmeter across the resistor
under test (parallel resistance).
□
Make a table in your lab notebook and record the measured resistance and the voltage
across the resistor for R=1k, 2k, 5k, and 10k, using the 20k measurement range on the
benchtop DMM. Using Ohm’s law with the measured resistance and voltage values,
calculate current that must be flowing in the resistor each time. Repeat using the 200K
measurement range on the ohmmeter. What is the average current supplied by the
ohmmeter for each measurement ranges?
□
Remove the handheld DMM from the circuit
and reconfigure it as an ammeter by selecting
the DCA 200μA range. With the bench
ohmmeter on the 20kΩ scale and R at 5k, add
the ammeter into the circuit as in Figure 1-10.
Is the measured current close to the current you
calculated in the previous step? What is the
measured resistance now? What must the series
resistance of the ammeter be for this setting?
□
Handheld DMM
Bench
DMM
A
Ω
R
COM
Set R to 0 so that only the resistance of the Figure 1-10 – Break circuit and add
ammeter is being measured.
Change the ammeter (series resistance).
ammeter to the 2mA scale.
Record the
ammeter resistance for each scale, and then move the lead from the ammeter’s V/Ω/mA
input to the 10A input and record its resistance.
□
Remove the handheld ammeter and reattach the test lead on the handheld DMM back to
the VΩmA input and put it in ohmmeter mode. This is a good precaution after making
current measurements!
A key takeaway here is that the meters will always perturb the electrical state of the system to
some extent, and we must always consider the possible influence of the meter itself on the
measurement.
Continuity Testing
A continuity test is done to confirm that things are electrically connecting in the manner we
want. We can use the ohmmeter to explore continuity in a circuit in the following way: if
two points are electrically connected (by a wire, for example) then the measured resistance
will be very low. If the two points are NOT connected, the measured resistance should be
very large (ideally infinite). It may sound trivial, but continuity testing is a very important
© Bob York
11
Series and Parallel Resistor Combinations
tool in debugging malfunctioning circuits: in ECE 2, the most common reason for a
malfunctioning circuit is a simple wiring error!
□
□
Move the red test lead back to the
Using the ohmmeter and some jumper
wires, check for continuity between
the sockets in and around a sample row
in your breadboard to confirm the
connections
described
in
the
background section. For example,
using the row and column designations
shown in Figure 1-11, draw lines
through the sockets which are
connected in row 6, for example. Is
their any continuity between rows 5
and 6, or 6 and 7, or across the gap
between columns e and f?
Figure 1-11 – Section of a solderless breadboard.
Similarly confirm continuity between the ends of one the red and blue bus-bar strips.
1.3 Series and Parallel Resistor Combinations
Now find the small ¼ Watt resistors in your parts kit. We will first measure the resistances of
these components and then explore the resistance of simple combinations of them
□
Create a table in your notebook like Table 1-4, and for each resistor value in the table,
find the corresponding component in your parts kit and record the color-code in the
appropriate place. The use your ohmmeter to measure the actual resistance and determine
the % error in comparison to the nominal value (to save time you can do the calculations
later, outside of lab). It is convenient to mount the resistors on the breadboard and use
the pointed probes of your handheld meter for this measurement.
Table 1-4 – Summary of Measurements on Individual Resistors
Nominal
Color Code (e.g. red-orange-brown)
Measured [Ω]
% Error
1kΩ
1kΩ
1kΩ
2kΩ
3kΩ
4.7kΩ
10kΩ
□
Next, create a table like Table 1-5 in your notebook. For each row, interconnect the
selected resistors on your breadboard in the desired configuration and measure the net
resistance between the terminals (open-circles in each figure) with the ohmeter. Then
compare your measured data.
12
Voltage, Current, and Resistance
Table 1-5 – Summary of Measurements on Resistors Combinations
Resistor
Configuration
R1
R1
R2
Theoretical
Net
Resistance
R1  R2
R1
1
R2
1
1

R1 R2
R2
R3
R1
1
1
1
1


R1 R2 R3
R2
R3
R1
R2
R3
R1  R2  R3
1
1
1

R1  R2 R3
Nominal
Values
Theory w/
Nominal
Values
Theory
w/Actual
Values
Measured
Resistance
R1=1kΩ
R2=1kΩ
R1=2kΩ
R2=3kΩ
R1=1kΩ
R2=1kΩ
R1=4.7kΩ
R2=10kΩ
R1=1kΩ
R2=1kΩ
R3=1kΩ
R1=1kΩ
R2=1kΩ
R3=1kΩ
R1=1kΩ
R2=1kΩ
R3=2kΩ
1.4 Voltage Dividers and Potentiometers
In lecture we have discussed (or will soon) the fact that the voltage supplied to a circuit by a
battery or power supply will divide among the circuit components in proportion to the
relative resistances of the components.
□
□
Verify that the +20V output of the
power supply is still set at +10V and
make the connections shown in Figure
1-12, where the two resistors are
mounted
on
your
solderless
breadboard.
Begin
with
R1  R2  1k .
R1
Power
Supply
+10V
DMM
1 kΩ
R2
Vout
V
With the DMM set to measure DC
Figure 1-12 – Simple voltage divider.
volts, measure the voltage across R2 .
Here the voltage is indicated by the
variable, Vout , and the polarity of the variable is defined with + and – signs. For DMM
measurements the – corresponds to the reference node where the COM terminal is to be
© Bob York
13
Voltage Dividers and Potentiometers
connected. Enter this result in your notebook using a table like that in Table 1-6, where
the theoretical expectation in this case is given by
R2
(1.3)
Vout  10 V
R1  R2
□
Repeat for the remaining resistor
values in Table 1-6, keeping R1 fixed
at 1kΩ in each case.
Table 1-6 – Voltage Divider Measurements
R2
Vout (Theory)
Vout (Meas.)
1kΩ
The voltage divider circuit thus
provides a simple way reduce an applied
2kΩ
voltage by a desired amount, but it would
3kΩ
be nice if we could adjust the output
4.7kΩ
voltage more easily and continuously. The
potentiometer (“pot” for short) allows us
10kΩ
to do this. A potentiometer is a resistor
with a third terminal called the “wiper”.
The wiper rubs along the length of the resistor material internally, creating a self-contained
adjustable voltage divider network. Figure 1-13a illustrates one particular type of
potentiometer (a “thumbwheel” type), and Figure 1-13b shows ones very simple voltagedivider configuration using a potentiometer configuration. These kinds of circuits are often
used in audio volume controls to adjust the level of the audio signal before it is fed into a preamp or power amp.
R1
10 kΩ
+10V
+10V
1 kΩ
Vout
R2
10 kΩ
Vout
“Wiper”
(a)
(b)
(c)
Figure 1-13 – Potentiometer and its use in simple voltage-divider circuits.
Potentiometers are specified in terms of the total resistance between the outer terminals.
In your parts kit you should have a 10kΩ potentiometer. Figure 1-13c shows another
common configuration where the wiper is intentionally shorted to one of the other terminals.
This creates a two-terminal variable resistance.
□
Construct the circuit in Figure 1-13c on your breadboard. Monitor the output voltage
using the DMM as the thumbwheel is varied over its extremes.
14
Voltage, Current, and Resistance
There are many other types of potentiometers on the market, the one in our kit is just one
example. Some must be adjusted with a screwdriver and may allow for multiple turns for
better control over the resistance. Some have large rotating shafts that can be fitted with a
knob for instrument panels. Potentiometers are sometimes used to tweak a circuit after
production to compensate for other component errors; in this application they are sometimes
referred to as “trimpots”.
1.5 Current-Voltage Characteristics
Resistors are engineered to obey Ohm’s law over a wide range of voltages and currents. The
relationship between voltage and current is not always as simple in other devices, but
knowing this relationship is critical for circuit design. We will examine the I-V
characteristics of two simple devices: a
DMM
50Ω
small incandescent bulb, and a small
A
DC “toy” motor.
DMM
To determine the current-voltage
Power
(“I-V”) characteristics of a device, we
V
D.U.T.
Supply
apply a certain voltage and measure the
resulting current, or vice versa. Figure
1-14 illustrates the basic experimental
Figure 1-14 – Measuring I-V curves
setup. An adjustable DC power supply
provides the stimulus, and we use two
DMMs to monitor the current through the device and the voltage across it.
To protect both the device and ammeter from accidental excessive currents it is advisable
to include a small “current-limiting” resistor in series with the device as shown.
□
Set up the circuit shown in Figure 1-14 using the decade-box for the 50Ω current-limiting
resistor. Set the power-supply output to zero volts initially.
□
In your notebook, create a table for the voltage-current measurements. The first data
point is of course (0 V, 0 mA).
□
With the handheld DMM, measure the “cold” DC resistance of the lamp prior to putting
it in the circuit.
□
Now add the lamp to the circuit. Slowly raise the power supply voltage until the voltage
across the lamp increases by about 0.1V and record the current in [mA]. Repeat this until
you reach +0.5V across the bulb (five data points). Note that the voltage across the bulb
is what we want to record, not the power-supply voltage. Also, your voltage increments
do not need to be exactly 0.1V, just something close (within 10%)
Continuing from where you left off, raise the voltage in larger increments of 0.5V and
keep recording the currents in this fashion until you reach +6V (the recommended
voltage for this particular bulb).
You should now have enough data to make a nice plot in your lab report. Can you tell that
the data is not linear? Incandescent bulbs have a tiny resistive tungsten filament inside, but
when the filament gets really hot its resistance increases substantially, changing the slope of
the I-V curve.
□
□
Now replace the lamp with the toy DC motor and repeat the measurement to characterize
its I-V curve. The motor is a +3V device, so you will need to choose your voltage
increments differently. Note that at low voltages and currents the motor does nothing,
© Bob York
Current-Voltage Characteristics
15
and there is a particular threshold at which the motor begins to turn. To get an accurate
representation of the I-V behavior near this threshold you may need to use finer
increments.
In your lab report, make a nice plot of the I-V curves for the lamp and the motor, and contrast
with Ohm’s law. There is a short tutorial on the course website for making plots in Microsoft
Excel, but you can also use MATLAB, Mathematica, or any other program of your choice.
NO HAND-DRAWN PLOTS WILL BE ACCEPTED.
Extra Credit: Photocell
For students who finish early or want an extra challenge, there is a cadmium-sulfide (CdS)
photocell included in your parts kit (the data sheet is on the course web site). Characterize
the I-V curve for the photocell under bright light and dark conditions. Can you think of a
way to pair the lamp and photocell to make an electronically-variable resistor?
Congratulations!
You have now completed Lab 1
Note: keep all your electrical components! Over the course of the year you will
accumulate a number of parts and we will make use of parts from prior labs in order
to save you some money on lab kits.