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ME 101
Measurement Demonstration (MD 2)
Linear Systems and Simple Resistance Measurements
Objective: To learn about linear systems and linear transducers from an engineering standpoint and to
conduct measurements on a simple example: a resistive circuit.
Technical Outcomes:
Upon completion of this experiment, the student will be able to:
− Understand the concept of a linear system and determine linearity
− Understand the concept of resistance and conductance
− Conduct simple experiments with the power supply (PS) and digital multimeter (DMM)
− Become acquainted with breadboards and build simple resistive series and parallel circuits
using the solderless breadboard
− Experimentally measure resistance, voltage and current
Equipment:
The following is a list of equipment used in the experiment:
− Tektronix TX3 handheld digital multimeter (DMM)
− Tektronix PS280 Triple output Direct Current (DC) power supply
− Breadboard
− Assorted resistors
− Jumper Kit
Glossary of Basic Physical Quantities Used in this Experiment
In this experiment, you will be asked to measure voltage, current, and resistance in an electric circuit. It
is very important to define these quantities before describing the experiment in detail.
Charge (Q) – Charge is the property that certain particles have which produce either forces of attraction
or repulsion between the particles. Charge has polarity (+/-) and is measured in Coulombs. A single
electron has a charge of -1.6 × 10-19 Coulombs. The symbol for charge is Q.
Current (I) - Electrical current is simply the flow or rate of change of charge with respect to time. If the
rate of change of charge is constant, then direct current (DC) results. Current has direction indicated by an
arrow and is measured in amperes which is simply a Coulomb/second.
Voltage (V) – Voltage is simply the measure of potential energy available to move or drive a current from
one point to another. Voltage has polarity as indicated by a plus (+) and minus (-) sign and it is measured
in Volts which is simply joules/Coulomb and is represented by the symbol, V. Typical voltage sources
are batteries and power supplies.
Circuit – A connection of basic circuit components which has at least one complete path through which
electrons can flow from the negative (-) terminal of a voltage source to the positive terminal.
Circuit Element - A basic component of a circuit. Examples include resistors, capacitors, voltage
sources, diodes, and inductors.
Resistance (R) - Resistance is a measure of how much a circuit element opposes the flow of electric
current. Resistance is measured in Ohms and is represented by the symbol, R.
Measurement Demonstration (MD2) - Instructions & Homework.doc
Measurement Demonstration (MD2) Introduction:
A favorite analogy is the comparision of engineers to carpenters. A master carpenter can design and
fashion extraordinary pieces of fine furniture but is powerless to do so without a set of tools. With a
limited set of rudimentary tools, the carpenter can probably practice his/her trade, but the final quality and
amount of time required to complete a project will certainly be impaired.
Similarly, an engineer can design systems and devices to resolve many complex problems. But, like the
carpenter, an engineer’s productivity is severely hampered without mastery of the critical tools of the
trade. In lieu of a saw, hammer, and file an engineer uses math, science and computers to craft solutions.
Perhaps the most important tool an engineer has is the ability to conduct experiments. In fact, the
Accreditation Board for Engineering and Technology (ABET) demands that every graduate of an
accredited program have “an ability to design and conduct experiments, as well as to analyze and interpret
data.”
The purpose of the measurement labs in ME 101 is to do precisely that. Although this experiment has
already been designed, the student will have to analyze and interpret the resulting data. Additionally, this
experiment will give a glimpse into laboratory experimentation as it pertains to all fields of engineering
and to impart certain basic competencies needed in future curricula and as an engineering professional.
This laboratory is divided into two parts. The first part is to acquaint you with the use of the basic
equipment in this experiment and the second part is devoted to conducting actual experiments on linear
systems and simple resistive networks.
Equipment used in Experiment 2
In this experiment, you will learn how to use the Tektronix TX3 handheld digital multimeter (DMM), the
Tektronix PS280 Triple output Direct Current (DC) power supply, and how to construct simple circuits
using a solderless breadboard.
Tektronix TX3 DMM
A handheld Digital Multimeter (DMM) is very much like a calculator for the engineer in the field. With a
DMM, an engineer can quickly measure voltage (both DC and AC), current, resistance, capacitance,
frequency, and circuit continuity. One might make the mistake of thinking a DMM is only useful to
Electrical and Computer Engineers. Yet, with the addition of special transducers available for most
DMMs, the engineer can also measure temperature, pressure, force and other “non-electrical engineering”
entities. In this experiment, the DMM will be used to measure resistance, voltage, and current.
A picture of the Tektronix TX3 DMM is shown in Figure 2. There are three main areas of operation of
the DMM: the terminal connections, the rotary dial, and the soft (menu) buttons. The DMM uses probes
or leads (red and black wires) to connect to a circuit and measure different quantities. These leads insert
into different terminals of the DMM depending upon the quantity you wish to measure. Similarly, the
rotary dial and menu buttons must be configured differently for measuring current, voltage, or resistance.
The following lists the procedures for configuring the DMM correctly:
To measure DC Voltage drop across a circuit element with the DMM:
2
−
−
−
−
−
Insert the red probe into the rightmost red DMM terminal marked V¬°C (V for Volts)
Insert the black probe into the middle black DMM terminal marked COM
Turn the rotary dial to the V position
Press the second menu key from the left until DC appears on the LCD Display
Touch the other end of the red/black probes to either side of the circuit element and the
display will show the DC voltage drop across this circuit element.
NOTE: Inserting the probes across a circuit element like this is called a parallel connection. Two circuit
elements in parallel always have the same voltage across them. In this case, the DMM is in parallel with
the circuit element and hence the voltage measured by the DMM is the voltage across the circuit element.
Figure 1 shows how to use the DMM to measure voltage.
1.234 V
+
V=?
Red Probe
DC
HOLD
RANGE
V
M/M/A
A
OFF
Circuit
Element
1MS
V=
1.234 Volts
ME
A
COM
V
5A
Figure 1 – Using the DMM to measure the
1000V
element.
3
o
C
Black Probe
voltage across a circuit
LCD Display
(Measuring 120.03
Volts at 60 Hertz
on Auto range)
Menu Button #2
(Measuring AC Volts)
Function Dial
(Set to Measure Volts)
3 Probe Connection Terminals
A = Amperage
COM = Common
V = Voltage
Figure 2 - A Picture of the Tektronix TX3 Digital Multimeter (courtesy of Tektronix).
To measure DC current through a circuit element with the DMM:
4
−
−
−
−
−
Insert the red probe into the leftmost red DMM terminal marked A (A for Amperes)
Insert the black probe into the middle black DMM terminal marked COM
Turn the rotary dial to the A position
Press the second menu key from the left until DC appears on the LCD Display
Disconnect one end of the circuit element from the circuit then touch the black probe to the
end of the circuit element just disconnected. Next, touch the red probe to the circuit at the
point where the element was disconnected. Note that the DMM is now being used to
reconnect the circuit element to the circuit and the display will show the DC current
(amperage) flowing through this circuit element.
NOTE: Inserting the probes to re-connect a circuit element into the circuit like this is called a series
connection. Two circuit elements in series always have the same current flowing through them. In this
case, the DMM is in series with the circuit element since the same current runs through the DMM and the
circuit element. Thus, the current measured through the DMM is the same current through the circuit
element. Figure 3 depicts how to use the DMM to measure current.
Current = ?
Circuit
Element
5
To measure the current flowing
through a circuit element,
disconnect one end of the circuit
element from the circuit then
insert the DMM in series as
shown in Figure 3.
1.234 A
Black Probe
DC
RANGE
HOLD
A
M/M/A
Current =
Δ
OFF
1MS
1.234 Amps
MEM
A
V
COM
5A
o
C
1000V
Red Probe
Figure 3 – Using the DMM to measure current flowing through a circuit element
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To measure resistance using the DMM:
−
−
−
−
Insert the red probe into the rightmost red DMM terminal marked V¬°C (V for volts)
Insert the black probe into the middle black DMM terminal marked COM
Turn the rotary dial to the Ω/
position
Touch the other end of the red/black probes to the points in the circuit across which the
resistance is to be measured. The LCD the display will show the value of the resistance in
Ohms across these two points in the circuit.
NOTE: The value you read using the above method will not necessarily be the value of the resistance of
the circuit element connected across the two points of measurement. If the circuit is active or if other
elements are connect across the same points, the value measured will not be the resistance of the circuit
element. To determine the value of the resistance of a particular circuit element, the element must be
completely removed from the circuit in question prior to measurement. Figure 4 shows how to use the
DMM to measure the resistance of a circuit element.
1.234 Ω
Red Probe
DC
Ω =?
RANGE
Ω
HOLD
A
M/M/A
Ω=
1.234
Ohms
OFF
1MS
MEM
A
Circuit
Element
COM
5A
V
o
C
1000V
Figure 4 – Using the DMM to measure resistance of a circuit element.
Power Supply
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Black Probe
This experiment will also incorporate the Tektronix PS280 triple output DC power supply. Direct
Current or DC simply means that the voltage (or current) eminating from the supply is a constant and
does not vary with time. This is different from the power available from a wall outlet which varies
sinusoidally with time. The PS280 contains a total of 3 different power supplies: two 0-30 Volt variable
supplies and one fixed 5 Volt supply. See Figure 5 for a picture of the PS280 and its functions.
Internal Voltmeter Displays
Current Limiter Knobs (2)
Voltage Adjust Knobs (2)
+/-/GND Output Terminals
(two 30 Volt variable, one 5
Volt fixed)
Power On/Off Button
Figure 5 – Picture of front of Tektronix PS280 Power Supply (courtesy of Tektronix).
Basic Circuit Elements
A circuit is a interconnection of elementary circuit elements that contains at least one closed-path for
current to flow. For this lab, we will deal with just two simple circuits and two simple current elements,
an independent voltage source (represented by the PS280 power supply) and a resistor. An independent
voltage source is depicted in Figure 6 and is characterized by supplying a constant voltage regardless of
the amount of current passing through it. Also, note that plus and minus signs are used to indicate the
polarity of the voltage. In the example, the independent voltage source has a voltage of 1.234 volts with
plus polarity indicated at the top.
The diagram for a resistor is also shown in Figure 6. The resistors we will use in this experiment are
made of carbon and are used to oppose the flow of current in a circuit. There are many other types of
circuit elements, diodes, capacitors, inductors, transistors, current sources, etc. The independent voltage
source and resistor will more than suffice for this first experiment.
8
+
_
567 Ohms
1.234 Volts
Symbol for Independent Voltage Source
Symbol for Resistor
Figure 6 – Basic Circuit Symbols for an independent voltage source and a resistor.
Solderless Breadboard
A solderless breadboard will be used in this experiment to rapidly build circuits. The breadboard is made
of white plastic with many holes on the top and a metal plate on the bottom. Running down the length of
the breadboard is a trough or channel which is used for inserting analog and digital dual-inline package
DIP chips. We wont be using DIP chips in this experiment, but it is important to know how the holes are
electrically connected to correctly construct a circuit.
If we could peel the plastic cover from the bread board, under each row of five holes we would reveal a
number of five fingered metal clips looking like this:
Metal clip underneath breadboard electrically connects this set of 5 holes
Breadboard channel electrically isolates the two rows of 5 holes
Figure 7 – Internal construction of a breadboard.
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Thus, any wires or circuit elements connected in this row of five holes are electrically connected together.
The channel electrically isolates a single row (i.e., there is no internal connection across the channel).
On the outside of the breadboard, there are four columns of holes with long metal clips electrically
connecting each of the holes in a single column together. Thus, from an electrical standpoint, the
breadboard looks like:
Row of 5 holes
is electrically
connected as
are the other
simliar rows of
5 holes.
However, each
row of 5 holes
is electrically
isolated from
each other row
of 5 (including
the opposite
row across the
channel).
This column of
holes is
electrically
connected as
are the other 3
simliar
columns on the
outside of the
breadboard.
However, the 4
columns are
electrically
isolated from
each other
Figure 8 - Schematic of a Breadboard Layout
Spend a few minutes at this juncture to familiarize yourself with the concepts of circuits and circuit
elements as well as the function of the DMM, the power supply, and the breadboard.
Concept of Linear Engineering Systems and Resistance
Engineering systems are omnipresent in every field of engineering. Examples of engineering systems
include an aircraft and flight control system, an automated coal conveyor, a GPS controlled grain
harvester, a vibration suppression device for bridges, an oil refinery, an active suspension for an
automobile, a computer or data network, or even a computer program. A system could have very few
components (e.g., the circuit we will build) or many millions (e.g., the Pentium 4 chip). Whether simple
or complex, engineers spend a great deal of their time and effort analyzing and designing systems. Often
times, an engineer cannot see “inside” a given system and knowledge of this system must be determined
by making external measurements. Such systems are often referred to as “black boxes” meaning that the
internal workings of the system are hidden from direct examination. Almost all electronic and compurer
systems are “black boxes” in that unless we designed the system or have a complete schematic, only
certain input and output points or nodes are accessible to us. Anyone who has ever looked at a computer
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motherboard knows that the vast majority of this system structure is shrouded behind charcoal grey
electronic chips.
Black box systems as well as many other engineering systems are characterized by external inputs and
output variables or signals. An input to a system is simply a signal or variable which causes the system to
react in some way. Examples of inputs include a voltage to an electric motor (electrical), the profile of a
road to an automobile suspension (mechanical), or the position of a valve on an input pipe for a water
treatment plant (civil). Changing these variables causes the system to react.
An output of a system is simply a signal or variable which is externally measureable by an engineer and
characterizes the performance of the system. Examples of outputs include the speed of our electric motor,
the displacement of our automobile chasis, the level of pollutants in the final tank of our water treatment
plant.
Engineering systems can be classified into many different categories: continuous versus discrete, digital
versus analog, time varying versus time-invariant, dertiministic versus stochastic. Perhaps the most
frequently used classification of a system is whether it is linear or nonlinear. The most elementary
definition of a linear system is that the principle of superposition holds. Superposition simply means if
you apply the sum of two different inputs to a linear system, then the output produced will be the sum of
the outputs produced by each of the two inputs, individually. Thus, if you double a given input to a linear
system the output will double, as well.
In this ME 101 experiment, we will build two very simple linear systems comprised of resistors and
independent voltage sources. Other engineering examples of simple linear systems include springs
(governed by Hooke’s law) and accelerometers (convert acceleration into voltage). Both of these system
we will study at at later time in ME 101. In fact, the two resistive electrical circuits we will construct
have analogous or “dual” mechanical circuits comprised of simple dashpots or viscous dampers!
Resistance and Ohm’s Law
In the previous section, the circuit symbol for a resistor was given and as well as an explanation that a
resistor is generally made of carbon and serves to oppose current flow in a circuit. The higher the
resistance, the more voltage that is needed to force the same amount of current to flow. The equation that
governs the relationship between current, voltage, and resistance is called Ohm’s law in honor of Georg
Simon Ohm, the german physicist who is credited for first discovering it. Quite simply stated, Ohm’s law
says that voltage equals current times resistance or V = I x R. Obviously, the unit on resistance must be
Volts/Ampere, which is true. However, a volt/ampere is also called an ohm and symbolized with a capital
omega, Ω. Since voltage has polarity and current has direction, ohm’s law is only valid if the current
direction enters the resistor at the positive (plus) side as shown below:
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I (Amperes)
+
R (Ohms)
V (volts)
_
Ohm’s Law: V = I ⋅ R
If this convention (called the passive sign convention) is not true, Ohm’s law is off by a minus sign.
Two other concepts we will employ in this first experiment are the concept of series and parallel. Circuit
elements are said to be in series when the same current flows through them. If the same voltage exists
across two or more circuit elements, they are said to be in parallel (see below for illustration)
Circuit Elements in Series
(same current flows through each)
+
+
+
_
_
_
Circuit Elements in Parallel
(same voltage appears across each)
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ME 101
Measurement Demonstration (MD 2)
Linear Systems and Simple Resistance Measurements
Lab 2 - In Lab Experimental Procedures:
Name:______________________________
Section:____________Team:____________
Resistors in Series
1. Your lab teaching assistant (TA) will give you three resistors: R1, R2, and R3 . Use the DMM to
measure the resisistance (in ohms) of each. Record the values Don’t forget units.:
R1 = ___________
R2 = ___________
R3 = ___________
(Brown-Black-Red-Gold color bars)
(Red-Black-Red-Gold color bars)
(Brown-Black-Orange-Gold color bars)
2. Using the jumper kit and solderless breadboard, connect the following series circuit. Use one of
the two 0-30 volt outputs set to 2.0 volts on the PS280 power supply as the independent voltage
source.
R1
I
2V
+
-
+ V2 -
+ V1 -
R2
+ V3 R3
Once the circuit is in place, use the DMM to measure and record the quantities. Don’t forget
units.:
I
V
V1
V2
V3
Req
= ___________
= ___________
= ___________
= ___________
= ___________
= ___________
3. Change the voltage on the PS280 supply to 4.0 Volts and measure the current, I, again.
I4v = __________
Note Remainder of this Section is Homework:
Given what you now know about linear systems, does your answer seem reasonable?
Explain why?
1
4. It is possible to replace the three resistors you used with only one resistor that would give the
same current I that you measured in step 2 (see figure below). This resistance is called the
equivalent resistance.
R1
I
2V
I
+
-
R2
=
2V
+
-
Requivalent
R3
a) What is the value of the equivalent resistance Req? Show your work. (hint: use Ohm’s
Law).
Req
= _________
b) Now add the three resistor values you used in step 2.
Rsum = R1 + R2 + R3 = _________
c) Do you see the relationship between Req and Rsum? Come up with a general relationship
that you could use to combine resistors in series for any circuit.
Req =__________
5. Find the equivalent resistance of the following circuit if:
R1 = R2 = 100 Ohms and R3 = R4 = R5 = 1000 Ohms.
R1
R2
R3
R5
R4
Req = _________
2
6. Now consider a generic series circuit as a system with the input voltage of 1V from the power
supply and the output of the system being the current, I.
a) Is this a linear system (i.e., if you double your input, the output doubles)?
b) If yes, what current would you expect if we changed the input voltage from the power supply
to be 9 volts?
7. Sum the voltages V1, V2, and V3 together and compare your answer to V. Can you see a
relationship between the sum of voltage drops and the power supply voltage? What is that
relationship?
8. Consider the following black box system with input/output measurements taken by the DMM.
V (input voltage)
System
(linear?)
I (output current)
X input value
Y output value
10 volt
0.25 amperes
30 volts
0.75 amperes
1 volt
0.025 amperes
a) Is it linear? Show how you came to that conclusion.
b) What would the equivalent resistance be for this system?
Req = ________
c) Come up with a series circuit, with at least 2 resistors, that would behave like this system.
Draw the circuit and label all the required elements (voltage, current, and resistances).
3
Resistors in Parallel
1. Reconfigure the resistors on the breadboard so that the are now in parallel and reconnect the
PS280 power supply so that you form the following circuit:
I
+
+
-
1.0
Volt
I1
V
_
I2
R1
R2
I3
R3
Use the DMM to measure and record the quantities:
V = ___________
I1 = ___________
I2 = ___________
I3 = ___________
I = ___________
Req = ___________
Note Remainder of this Section is Homework:
2. Is the parallel circuit you built also a linear system? If yes, what value of the current I would
result if the input voltage were changed to 6.4 volts?
I6.4V = ________
3. It is possible to replace the three resistors you used with only one resistor that would give the
same current I that you measured in step 1 (see figure below). This resistance is called the
equivalent resistance.
I
1V
+
-
I
R1
R2
R3
=
1V
+
-
Requivalent
a) What is the value of the equivalent resistance Req? Show your work. (hint: use Ohm’s Law).
4
Req
= _________
b) The relationship between the equivalent resistance and resitance in parallel is as follow:
Req =
1
1
1
1
+
+
+ ...
R1 R 2 R3
Using your values of R1, R2, R3, and the calculated value or R eq in part a), show that this
relationship is correct.
4. What should be the equivalent resistance for the following parallel combination if R1=R2=
R3=R4=R5=400 ohms.
R1
R2
R3
R4
R5
Req = __________
5. Sum the currents I1, I2, and I3 together and compare your answer to I. Can you see a relationship
between the sum of current in the branches and the current coming out of the power supply?
What is that relationship?
5
Extra Credit
Now that you know how to reduce resistors in series and resistors in parallel, can you reduce the
following circuit into a single equivalent resistor using repeated applications of your series and
parallel rules if R1=R2=R3=R4=R5=100 ohms?
R2
R4
R1
R3
R5
You must show your work!
Do not work with other teams on this problem!
Req = ________
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