Introduction to
Engineering
Experimentation
Murat Tanyel
Robert Quinn
Drexel University
McGraw-Hill, Inc.
College Custom Series
New York St. Louis San Francisco Auckland Bogotá
Caracas Lisbon London Madrid Mexico Milan Montreal
New Delhi Paris Son Juan Singapore Sydney Tokyo Toronto
McGraw-Hill's College Custom Series consists of products that are produced from camera-ready copy. Peer review,
class testing, and accuracy are primarily the responsibility of the author(s).
vii
PREFACE
This laboratory manual has been developed over the span of the experimental phase of E4 program
(Enhanced Educational Experience for Engineers) at Drexel University.
Many people have contributed to the development of this manual and the Engineering Design, Test
and Simulation Laboratory arid we wish to acknowledge them here. Mr. Wayne Hill of the
Electrical and Computer Engineering department deserves special recognition for his outstanding
work as the lab manager and as the person that `will make it happen'. Professor Ernest Barge of the
Electrical and Computer Engineering department, who worked during the initial offering of the
program is responsible for writing the original versions of many of the experiments. Dr. Ed Gerber
(Electrical and Computer Engineering department) has written some of the original versions of
these experiments and continues to contribute to the sophomore Engineering Lab. Dr. Chuck
Weinberger of the Chemical Engineering department provided the original versions of the
Calorimetry, Thermal Conductivity and Convective Heat Transfer experiments. Dr. Tom Moore
from Electrical and Computer Engineering department contributed the Electric Network Theorems
and AC Impedance experiments.
The help of Dr. John DiNardo of the Physics and Atmospheric Sciences department, both in the
delivery of the course and in the editing of the material is appreciated. Mr. Scott Bezick and Mr.
Joe Wetstein from the Electrical and Computer Engineering department as well as Russell
Anderson of the Chemical Engineering department have rendered invaluable help both in the
delivery and revision of some of the experiments. The initial compilation of the experiments by Ms.
Sandy Ricciardi Godsey of the Center for Curriculum Development was valuable assistance in
further development. The contributions of four of our students, Tim Coffman, Rebekah Rupp, Mike
Goslin and Mary House, are greatly appreciated.
Mr' Stuart Harper, who has served as lab technician, deserves special recognition for his technical
skills, dedication and enthusiasm.
M. Tanyel
R. G. Quinn
BASIC MEASUREMENT CONCEPTS AND PRACTICES
LENGTH AND MASS
Executive Summary
All scientific and engineering knowledge about the physical world and its governing principles has
been gained by observation and experimentation. In science and technology, the process of
understanding and progress has involved comparing theory with observation and measurement of
physical phenomena and/or engineering artifacts. The numbers used to describe physical phenomena
and properties are called physical quantities. In order to be consistent each physical quantity must be
expressed in some accepted units whose values are referred to some accepted standards. In any
measurement of a physical quantity, there is always some experimental error. There are a variety of
methods used to identify, control, and/or minimize these errors. This experiment will provide an
opportunity to measure two basic physical quantities, length and mass, and develop skill in using a
variety of instruments designed for this purpose. It will also provide an opportunity to learn and apply
concepts, practices and procedures fundamental to all types of scientific and engineering
experimentation.
Educational Objectives
•
Learn how to determine the accuracy and precision of instruments.
•
Learn to calibrate and use a spring, electronic and trip balance to measure mass.
•
Learn how to properly acquire and record data.
•
Learn how to analyze data to identify and / or minimize error.
•
Learn how to select an optimum method of measurement for a given application.
Background Information
Measurements are made by comparison to a reference or standard quantity. These reference quantities
are defined by units. For example, the second is a unit of time. The two common systems of
measurement are the SI and British (which is used only in US and Britain). The metric (SI) systems
relates all units by multiples of 10. The prefixes and specific reIationships are given in the UNITS
section. Whether SI or British units are used, dimensional consistency must be maintained. That is to
say, the terms must have compatible units. For example, it makes no sense to add meters and feet.
Likewise, the sum of kilogram and seconds has no meaning.
All measurements have error and a consequent uncertainty. Errors are classified as systematic or
random. Systematic errors are usually categorized as instrumental, personal, or external. An
instrumental error is due to faults or limitations of the measuring device. This includes improper
calibration as well as broken devices. Personal errors vary from one observer to the next and indicate
any bias the observer may have. External error is introduced by the environment in which
measurements are taken.
2 Basic Measurement Concepts & Practices: Length & Mass
Hysteresis is another phenomenon that may contribute to error. An instrument is said to have hysteresis
when it shows a different reading for the same measured quantity depending on whether the quantity is
approached from above or below.
Some of the systematic errors may be corrected using a calibration curve. A plot of the instrument reading
against the standard being measured is called a calibration curve. The calibration curve for an ideal
instrument would start at the origin and would have a slope of 1. Fig. 1 depicts calibration curves for an
ideal instrument, a nonideal instrument and an instrument with hysteresis.
Basic Measurement Concepts 8 Practices: Length & Mass 3
All errors affect the results in varying degrees. As measurements are used to compute other
physical quantities, the errors are carried throughout in the computation. This compounding of
error as it is carried at each consecutive step is called propagation of error. A few examples of
these basic ideas are given below.
Example 2: Accuracy
The accuracy of a measurement is its deviation from the actual value of the quantity being
measured. If, for example, a certain balance measures a 250 g standard weight as 260 g, its
accuracy is only 4%. Similarly, the accuracy of an instrument is the deviation of its reading from a
known input. Accuracy of an instrument is usually expressed as a percentage of its full scale
reading. If a voltmeter with a 25 kV range has an accuracy of 1 %, its reading over this range
would be accurate within ±250 V.
Example 3: Precision
The precision of an instrument has to do with the repeatability of its readings. If the balance from
the previous example gives five different readings (260 g, 257.5 g, 262.5 g, 257.5 g and 262.5 g) for
the same standard weight of 250 g, then its precision would be t2.5 g since the individual
measurements deviate from the average (260 g) by 2.5 g.
4 Basic Measurement Concepts & Practices: Length & Mass
It is clearly seen that a small error in the original measurement is magnified in further calculations.
Finally, the we would like to review two related concepts: least count and sensitivity. Least count
is the smallest increment of the measurement unit that can be detected with the instrument.
Sensitivity is the ratio of the linear movement of the pointer on an analog instrument to the change
in measurement.
In approaching a given experimental problem, various criteria can determine which method of
measurement is optimum or "best". For example, high priority may be given to the errors a method
will introduce and the effect of such errors on the end result. Clearly an uncertainty of t 1 tsp. salt in
a large pot of "grub" for an Army mess hall is not as significant as t 1 tsp. salt in an individual
serving. In another application an engineer might have to give primary consideration to the
practicality of each method. An engineer working in the field will find it inconvenient to carry an
analytic balance. A less precise trip balance may be the best choice for reasons of convenience
alone. Therefore, the purpose of each measurement must be clearly defined. In this experiment, our
purpose is to learn about experimentation and we will explore different devices and concepts. For
our purposes, all equipment will be assumed to be equally practical.
Problem Statement
Given: Test specimens having different shapes, sizes and masses (washers and ball bearings).
Test instruments for measuring length and mass.
Find: The physical dimensions and masses requested.
Problem Formulation
In each sample lot there will be eight specimens' Each will be measured for spatial dimensions using
a vernier caliper, micrometer, and ruler, and for mass using either a spring, an electronic and / or a
trip balance. Ideally the specimens in each given lot are exactly the same. Your experimental
observations may determine otherwise.
In this experiment errors could include poor alignment of the caliper or improper operation of the
trip balance' Personal errors arise from changes in perspective, angle of sight or even the lighting in
the room. The electronic balance may be effected by the ventilation system, thus creating an external
error.
Procedure
Try to finish each part as quickly as you can. There may be fewer stations equipped with trip and
electronic balances than the total number of stations. If these stations are being used, simply do
another part of the experiment. Record the time taken for doing each procedure.
1. Spring Balance: (Each station has one)
1.1 Hang the spring balance and then attach the weighing pan. Adjust the metal tab on top of the
balance to make sure pointer is zeroed.
1.2 Each washer weighs about 30 grams. The average weight of the washers in your package is
indicated on the specifications card that comes with the washers. Use this average weight as
your standard. Add 1 washer at a time into the pan and take the corresponding readings until the
balance is out of range (about 8 washers). After this, take the readings backwards, i.e. remove 1
washer each time from the pan and take the readings. (Remove the washers in the reverse order,
i.e., the last washer in should be the first one out. Also keep track of the order so that you may
reproduce your results later.)
1.3 Put all data into the EXCEL data sheet. Start from 0 grams, so that your data sheet looks like
Table 1.
1.4 Plot both add and remove columns versus standard weight column in EXCEL on one line graph
showing all the data points. Make the graph full screen so that you might see any hysteresis
effects.
3. Electronic balance
In this part, you will calibrate the weights on an electronic balance.
3.1 Starting with 10 grams, increase the mass in 10 gram increments until you reach 100 grams, using all
possible combinations from the standard weight box. Take the corresponding readings. Then decrease
in 10 gram increments and take readings again.
3.2 Put all data in another EXCEL data sheet similar to table 1. Plot both reading columns versus standard
weight column in EXCEL, make the graph full screen, are there any hysteresis effects? Why?
3.3 Weigh each washer you used in procedures 1 & 2 and record the weights in 1 column of data in your
spreadsheet.
4. Measuring lengths (For each station)
In this part, you are to measure dimensions of washers and ball bearings.
4.1 Obtain the Excel spreadsheet titled "Measurements-L&M" and copy it onto your disk. Rename it with
your last names. Open this file on your disk.
4.2 You will be given a package of 8 small washers and 8 balls. Measure the thickness, the inner and
outer diameters of each washer and the diameters of each ball. Record the data on the blank
spreadsheet which you just opened. Be sure to include the accuracy of each scale. Note the smallest
unit on each scale. Length measurements are done using the vernier caliper, micrometer and ruler.
4.3 Note that the mean, deviation and standard deviation of each measurement have been programmed
in for you. These will be used in your report.
LABORATORY REQUIREMENTS
Participants in this laboratory are required to complete the following computer assignments
and answer the questions distributed in the laboratory. Individual student grades will be
determined by performance in the laboratory as well as the quality and degree to which the
work meets these requirements.
Computer Assignment
1.
2.
3.
Print out your spreadsheets
(procedures 1-4). Print out any
graph that you were required to plot.
(50 pts)
Determine (by actually counting) the number of occurrences of each
deviation value for all 4 sets of length data you obtained in
procedure # Q. To do this, first determine the number of times each
value in the "dev." column occurs, and then make two columns: one
with each deviation value and next to it the corresponding number of
occurrences. Scatter plot this information with deviation value as
the independent variable and number of occurrences as the dependent
variable. Do this for all 4 sets of data separately. Print them out.
(10 pts)
Plothistograms that compare all the length data. Each
histogram should have 3 intervals. For each length category
(i.e.,thickness, inner diameter, etc.) divide the range of the
lengthinto 3 intervals and manually count how many
measurements fall in each interval. In one column, fill in the
mid-value of the interval, in the next column fill
in the
number of measurement in these intervals. Then plot the second
columnagainst the first column (i.e., with the mid-value of
the interval as the independent variable) as a bar chart.
(20 pts)
BASIC MEASUREMENT CONCEPTS AND PRACTICES
DC VOLTAGE AND CURRENT
Executive Summary
Greeks discovered that if one rubbed a resin called amber with a piece of fur, the amber would
attract lightweight particles. Since the Greek word for amber is elektron, this process ultimately
became known as electrification and was perhaps the first example of electrical engineering. A very
large number of important electrical phenomena and engineering applications are based on the
movement and/or control of electrons. Virtually all modern experimental methods depend on
electronic devices in one way or another. Therefore it is important to be able to measure moving or
accumulated electric charges and their effects (current and voltage) in a quantitative manner. 'This
experiment focuses on two inexpensive and versatile devices, a digital multimeter and an analog
volt-ohm meter (VOM), which are used extensively in measuring voltage and current.
Educational Objectives
•
•
•
•
Learn how to measure voltages in a DC circuit
Learn how to measure currents in a DC circuit
Learn how to operate a digital multimeter (DMM) in the DC voltage and current modes
Learn how to operate a VOM in the DC voltage and current modes
Problem Statement
1. Solve the "lemon battery" problem (see procedure #1).
2. Given batteries, measure the potential differences between the 2 terminals.
3. Given a DC circuit with light bulb and breakers, measure the potential differences and
currents at several points in the circuit.
4. Given a thermocouple, measure the voltage change when temperature varies.
_
5. Given a photo detector, measure the voltage change when light source varies.
Problem Formulation
The two basic electrical measurements are potential difference (or voltage) and current. The nature of
each quantity determines the method used for measurement. Different measurements affect the
placement of each type of meter in the electrical circuit.
This experiment begins with voltage measurements in simple two terminal systems. Once familiarity
is gained with metering and potential difference, a fabricated circuit is set up and current, as well as
voltage, measurements are taken. Potential difference is measured in volts. It is, as its name infers, a
measurement of the difference in the electrical potential energy between two bodies. The other
quantity measured in this lab is current. Unlike potential difference, current is a rate of flow not a
difference. Electrons flow from negative to positive potential. Current is
10 Basic Measurement Concepts & Practices: DC Voltage & Current
measured in Amperes with an ammeter. To measure current, the meter must become pan of the circuit. In
other words, the current flowing through the circuit must flow through the ammeter. In Fig. 1, the
ammeter placement is likened to a flowmeter.
This experiment uses two types of meters, a digital multimeter (DMM) and an analog meter (VOM).
Operation of these meters is relatively simple and should be described during your lab session. The range
of an analog meter determines the voltage or current (or resistance) which causes full scale deflection
(FSD). If the FSD is unknown always begin measurements with the highest range, then reduce the range if necessary.
This practice protects the meter from damage. On the face of the VOM are listed all of the scales. Be sure
you are reading the one to which the meter is set.
Digital meters display the reading for you. Like the analog meters, they have various ranges. The DMM's
display indicates which range you are reading. The range is changed by using the increment or decrement
keys (refer to the diagram describing your model of DMM in the appendices). Again always start with a
high range and decrement if necessary.
Example 1 Measuring the potential difference of two charged balls:
The DMM is used for the measurement. The set-up in Fig. 2 shows the DMM reading 1.232 V.
Notice that of the six possible digits, we are only using four. At this range the DMM can read hundreds
of Volts. By lowering the scale, we are able to increase the sensitivity of the meter. As the DMM is
decremented, the new reading is 1.23244 V.
Most people are familiar with common voltages, such as that in a car battery, your house, etc' To gain
experience with metering, this lab begins with some basic voltage measurements. 'The first
measurement is of the potential difference due to an unspecified chemical reaction. The next
measurement is of batteries, 9 V and 1.5 V.
Using these metering skills, measurements will be taken of voltage and content at various points in a
prefabricated circuit. The circuit is shown in Figure 3.
Remember that the ammeter must be a part of the circuit. When the DMM is used in the ammeter
mode, it will take the place of the short conductors in the diagram. There are four possible metering
locations, A - B, C - D, E - F, J - K. When the DMM is connected into any one of the gaps, the
others must be connected with a conductor. All loops must be closed before the power supply is
turned on. Follow the flow of current around the circuit and make sure that the current flowing
through A - B is equal to the sum of currents through C - D and E - F.
Introduction to DMM & VOM
The DMM is used for voltage and current measurements.1
Unlike its analog counterpart, there is no need for estimating the pointer position. The DMM
displays the reading to six digits. With an analog meter, such as the VOM shown in question 5, the
best accuracy and precision is obtained by selecting the appropriate scale. The pointer should be
deflected from 40% to 70% of the scale. If the pointer is deflected 20%, a lower scale should be
used. Likewise, a 95% deflection is close to "pinning" the pointer. This could lead to a damaged
meter and therefore a higher scale is necessary in the case of 95% deflection. The DMM is reliable
only when used within the appropriate range.
The manufacturer also specifies the total range of values in which the meter is designed to operate Operation
outside of these limits is not advisable. For example, the manufacturer's range of the voltmeter on the
Tektronics DMM 5120 is 3 mV to 300 V. Please note that the meter will read values outside of this range, but
these extreme readings are unreliable. The total ranges for the same DMM are given in Table 1.
When inside the reliable range, you may wish to vary the sensitivity of the reading. This is done easily using
the increment/decrement keys. To find the desired sensitivity, keep in mind the DMM always displays 6 digits.
If the display is not 6 digits long or there are zeros to the left of the decimal point in the first positions, then the
range is probably too high. The increment/decrement keys will move the decimal point. Sensitivities within
each range for TEK 5120 are given in Table 1. Always keep in mind the purpose of your measurements.
Sometimes smaller digits become insignificant in the overall project. In this case a higher range will suffice.
To use the DMM first select the quantity you want to measure. The DMM acts as a voltmeter, an ammeter and
an ohmmeter. You should refer to Appendix DMM1 at this point to become familiar with the operation of a
DMM. You should particularly read the description of the model you are using.
Next make the connections to the circuit. Set range to its highest selection with increment keys. Turn on the
power in the circuit. If necessary adjust the range or sensitivity. Take reading. The procedure is summarized in
the flow chart 1.
All indicated measurements are to be recorded on a spreadsheet in Excel. Refer to computer assignment #1. It
is important to label data correctly! The spreadsheet constitutes 40% of the grade for this experiment. For this
lab you will not need to print a blank spreadsheet. You may enter data directly into your computer.
Procedure
1. Consider the following scenario:
You are a world famous engineer from the E4 program. By a cruel twist of fate you have been shipwrecked
and are now on a deserted island m the Mediterranean. All you were able to salvage from the wreck were
enough parts to snake a crude radio, but you need a source of power. The island is abundant in citrus trees.
Recalling one of your labs in E4 you create a DC voltage supply using a lemon and pieces of two dissimilar
metals. The radio requires 1 V and .01A to operate. Do you have enough voltage and current ?
To find out,
Basic Measurement Concepts & Practices: DC Voltage & Current 13
1.1) Place brass and steel wire strips into the lemon. See Fig. 5.
14
Basic Measurement Concepts & Practices: DC Voltage & Current
scale you will use to read the deflection.
1.'7) Replace brass and steel wire strips by different metals. Repeat procedures 1.1 through 1.5.
2. Measure the potential difference between the two terminals of a 9 V battery with the DMM
and VOM.
Basic Measurement Concepts 8 Practices: DC Voltage & Current 15
3. Measure the potential difference between the two terminals of a 1.5 V battery with the DMM
and VOM.
4. At this point you are prepared to use your metering skills to measure the current and voltage ni
an electrical circuit. The circuit diagram is given in Fig. 7. Set the power supply to 9 V and set
current limit to 0.55 A but keen the output OFF.
Note: The current control in this case is designed such that excessive current is prohibited from
flowing to the light bulbs. This keeps the lights from burning out.
4.1)
Make sure you connect positive and negative terminals as shown in the diagram. Close all
circuit breakers, A-B, C-D, E-F and K-J. Now you are ready to turn the output ON.
Warning: Before you switch output on, make sure current control knob is turned completely
clockwise.
4.2)
Adjust the current control until any one of the light bulbs turns on. Continue adjusting until
bulb #1 is completely lit. Record which light bulb comes on first, second and third.
4.3)
As each light comes on measure the voltage across every bulb' Once bulb #1 is fully lit, STOP
adjusting the current control.
4.4)
With the current control adjusted so that all of the lights are lit, measure the current at all
nodes. Before connecting the ammeter in the circuit, turn power supply output off. Remember
that the ammeter must be made part of the circuit by placing it between two terminals of the
circuit break (i.e., placed between A and B). Now turn output back on. Make sure all nodes
are reconnected after a current measurement. Repeat all measurements.
5. Connect 2 terminals of the thermocouple to the DMM. Measure its voltage.
6. Warm up a junction of the thermocouple by your hand while observing the voltage changing on
DMM. How is the voltage changing related to the temperature changing (qualitatively)?
7. Connect a solar cell to DMM. Make sure it is facing some light source while measuring its
voltage.
8. Block the light source to the detector and observe the DMM reading. How is it changing?
16 Basic Measurement Concepts & Practices: DC Voltage 8 Current
Basic Measurement Concepts 8 Practices: DC Voltage 8 Current 17
REPORT
Your report should contain the following computer assignment as well as solutions to the questions
given out m lab.
Computer Assignment
I.
Complete the spreadsheet titled "Elect. Meas. Spread". (90 pts)
Checklist
18 Basic Measurement Concepts 8 Practices: DC Voltage 8 Current
BASIC MEASUREMENT CONCEPTS AND PRACTICES
RESISTANCE
Executive Summary
In 1827 G.S. Ohm, a German scientist, proved empirically that the electrical current flowing in certain
materials (metals) resulted in a voltage drop across the element that was directly proportional to the
current. This relationship is known as Ohm's Law and holds for any value of current. The constant of
proportionality is called resistance and is noted as R.
Ohm's Law is written as: V = I • R, where V is voltage measured in Volts, I is current measured in
Amps and R is measured in Ohms. This circuit law is still very important. It enables us to solve for
the current flow in an element if the voltage across it and its resistance are known. Or the voltage may
be solved for if both the current flow and the resistance have already been determined. When the
resistance of an element remains constant, the voltage across the element plotted against the current
through the element is a straight line with a slope of R (Fig. 3). Such elements are called linear circuit
elements.
Every material exhibits resistance. Conductors such as metal wires and ionized gases have very low
resistance. Insulators such as air, glass wood and plastic, also have resistances which are
extremely high compared to conductors. Semi-conductors such as silicon and germanium have
resistances between insulators and conductors. Super-conductors have extremely low resistances.
Resistance is measured in a variety of ways. In this experiment you will use a digital multimeter and a
power supply to measure the resistance of different components.
Educational Objectives
• Learn how to measure resistance using a DMM.
• Learn how to use the function keys of the DMM.
• Learn how to program the DC power supply.
• Learn how to plot and interpret characteristic current voltage curves
Background Information
When considering a resistor in a circuit, we use Ohm's Law to determine the resistance of a
linear element:
Basic Measurement Concepts & Practices: DC Voltage & Current 21
The power delivered to any circuit is given by the basic equation P = V.I. However, if the circuit
consists of a linear resistor then Ohm's law can be applied.
(2)
When power is supplied to a resistor, the current flow will heat the resistor (called Joule heating or
12R heating). Remember power is measured in Watts. If the resistor is in a space with adequate
ventilation and it has a large surface, the heat generated by the resistor will dissipate into the air. As
this occurs the temperature of the resistor will increase and reach a constant value for a given amount
of power supplied. If the resistor is physically too small to lose the heat to the air then its temperature
will continue to increase. Since the resistance of materials varies with temperature, the value of the
resistance may change if too much power is supplied to it. All resistor manufacturers state the
"power rating" of the element. If you exceed this power the resistor could overheat and "burn up"
resulting in a fire or an open circuit.
Problem Statement
1. Given 3 resistors, use the color chart to determine their values.
2. Given 3 resistors, use the DMM to measure their values and compare with 1.
3. Given a resistor (or a diode) connected in a circuit, measure the voltage and current in it.
4. Given V, I data as in 3, plot V-I characteristic curve using EXCEL.
22 Basic Measurement Concepts & Practices: Resistance
5.
Given a thermistor, observe its resistance at different temperatures.
Problem Formulation
In this experiment the energy source is to programmable DC power supply (PPS). Please refer to
Appendix PPS 1 at this point to become familiar with the operation of a PPS. You should
particularly read the description of the model you are using.
Procedure
All indicated measurements are to be recorded on a spreadsheet in Excel. Refer to computer
assignment #1. It is important to label data correctly! The spreadsheet constitutes 40% of the
grade for this experiment.
5.
This specific lab requires 1 Volt to start. See the example in Appendix PPS 1 for the implementation of
this step with your PPS.
Basic Measurement Concepts & Practices: DC Voltage & Current 2 3
6.
Measure the V-I characteristics of each resistor by increasing the supply voltage from 0 V to
20 V in 2 V steps. The circuit is set up to measure volts and amps. Select DCV or DCA
respectively. Record voltage and current at each step.
2 4 Basic Measurement Concepts & Practices: Resistance
Basic Measurement Concepts & Practices: DC Voltage & Current 2 5
REPORT
Your report should contain the following computer assignments as well as solutions to the questions given
out in lab.
Computer Assignment
1.
Create a spreadsheet in Excel and enter all data.Record for
each resistance from color chart, voltage and current in 10
steps, and resistance measured on DMM.
(40 points)
2.
Use the 10 step readings to plot the V-I characteristics-of
each resistor on a single graph (V as x-axis, I as y-axis,
note that the axes are the reverse of those in Fig. 1). Be
sure to label the graph with a title and label axes.
Indicate the units. Save the document and chart onto your
disk and then print them out.
(20 points)
27
PARALLEL & SERIES CIRCUITS
Executive Summary
The design of electric circuits requires an understanding of the relationships that exist in various
configurations. Series connections allow only one path for current while parallel connections allow
multiple paths for current but share a common applied voltage. Most circuits are combinations of the two
types.
Educational Objectives
•
Build series, parallel and combination circuits.
•
Use voltage division to provide different voltages in a series circuit.
•
Calculate the equivalent resistance of a parallel circuit.
•
Verify Kirchoff's Voltage and Current Laws.
•
Demonstrate the use of a Wheatstone Bridge.
Background Information
The series or tandem circuit is shown in Fig. I. Note that the current is the same throughout the
circuit. Using Ohm's Law:
V = IR
(1)
the potential difference across each element in the circuit is found. Since I is the same through each
element, if R1 R2
R3 the potential difference across each element will not be equal. Consider
potential with respect to node 0, which we will call the ground reference. At point 1, the potential
difference is V. At point 2 the voltage V has been reduced by Vi due to the current passing through
resistance R1 So at node 2 the potential difference with respect to ground is V - V1. Likewise at
node 3 the potential difference is V - V 1 - V2. Continuing around the circuit to node 0, the potential
28 Parallel & Series Circuits
difference is V - Vi - V2 - V3. We are back to ground and there is no potential difference
between ground and itself. This means that
V-Vl-V2-V3=0
(2)
and is stated concisely by Kirchoffs Voltage Law:
•
Around any loop, the algebraic sum of the voltages equals zero.
A complete circuit has no gaps or breaks to prevent current from flowing through it. Conversely,
an incomplete circuit has some path break or gap through which the current cannot flow. A
circuit with such a break is called an open circuit and is shown in Fig. 2. No current flows through
an open circuit. The point of discontinuity in an open circuit is considered as having infinite
resistance. (Solve Ohm's Law for the current through an element of infinite resistance.)
Though no current flows in an open circuit there is a potential difference across the gap. In fact, in the
circuit of Fig. 2 there is a potential difference of 20 V between B and A.
The opposite of an open circuit, a short circuit, provides a path of zero resistance. Fig. 3 depicts a circuit
in which one of the resistors is shorted. A short circuit (zero resistance) causes zero voltage drop across it.
A parallel circuit is shown in Fig.4. The potential difference across each resistive element is the
same. We assume negligible resistance in the connecting wires.
Referring to the parallel circuit in the figure, points 0, 1, 2 and 3 arc actually at the same potential and
constitute a single node. Likewise, points 4 to 7 are a single node. This greatly reduces the circuit
diagram, making it easier to read. Unlike the series circuit there are now multiple paths for the current.
Using Ohm's Law the current through each element can be determined. It is easily seen that the current
through any branch of this circuit is the same as any other branch if and only if the resistances are
equal. The current is not necessarily equal in all branches of this circuit, but is determined by the
configuration and values of the resistors. Once all of the branch currents are determined, the total
current, IT, is found using Kirchoff's s Current Law:
•
The NET current flowing into a node equals the current flowing out of the same node.
In equation form:
It = I1 + I2 + I3
(3)
Combinations of series and parallel circuits exploit the benefits of both types. An example is the
Wheatstone Bridge pictured in Fig. 5.
30 Parallel 8 Series Circuits
The configuration is four resistors arranged in a diamond shape. The voltage source is across either set
of opposite corners, in Fig.5 it is between A and D. There is a variable resistance in one leg that is
adjusted until the potential difference, Vo, between B and C is zero. This condition is called a balanced
bridge. The balance is achieved when the products of the opposite resistors are equal. The bridge of
Fig. 5 would be balanced when:
R1R=R3R2
As the value of the variable resistor is changed, the potential difference Vo, as well as the current in
this branch, will change proportionally. Typically the current in this branch is measured. A
galvanometer is commonly used for this measurement. This is a sensitive current measuring device
with a known small resistance, Rg*.
The Wheatstone bridge can be used as an ohmmeter, a pressure gauge, an anemometer, a flow meter,
or many other measuring devices. A thermistor, for example, may be placed in the circuit as the
variable resistance. This device changes resistance with varying temperature. The bridge will
unbalance with changes in temperature. Over a linear range, the current through the galvanometer will
be proportional to this temperature change.
Problem Statement
Given:
Find:
Series and parallel circuit configurations; an unknown resistance
Currents and voltages in each circuit, equivalent resistances.
Parallel 8 Series Circuits 31
Problem Formulation:
All of the metering skills learned to this point will be utilized in this lab. All resistors should be
measured prior to use. Remember:
An ammeter is connected in series with the circuit and
a voltmeter is placed parallel to the element.
You will first design a series circuit using at least three resistors. Measure all of the voltages in the
circuit. Measure the current through each element as shown in Fig.6. This is done to verify two
rules. First, the current in a series circuit is the same throughout the circuit' Second, Kirchoff's
Voltage Law states that the sum of voltages around a complete circuit is zero.
The equivalent resistance of a circuit is that resistance which would allow the same current flow as
the combination of resistors. For a series circuit it is given as:
Reg=R1+R2+............RN
(4)
where N is the number of resistors.
Calculate the equivalent resistance of the series circuit. Then replace the circuit with a resistor of
this value and calculate the current. It should be the same.
Next the effects of open and short circuits are determined by creating these conditions in your
circuit. Take care when measuring open circuits; there is usually considerable potential difference
across the gap.
By designing a parallel circuit, Kirchoff's Current Law can be verified. The effective resistance of a
This relationship will be checked similarly to that of the series circuit.
Finally as an example of series and parallel circuits, the Wheatstone Bridge will be used to measure an
unknown resistance. Before the advent of digital multimeters, the bridge was used as an accurate
alternative to the ohmmeter. What do the accuracy and precision of this bridge depend on?
Procedure
Before you proceed any further, review the Computer Assignment section to make sure you record all
pertinent data as you follow the procedures. This will save you time.
1-a. Select several resistors, at least three, and measure their resistance on the DMM. Use the board
supplied to make the series connection. For each configuration supply 10V DC and measure the
potential differences across each resistive element and the current through the each resistor.
b.
After you have measured the current through the third resistor, disconnect the first resistor
and observe the current through the circuit drop to zero. With the first resistor disconnected,
measure the voltage across each of the other resistors and across the gap in place of the first
resistor.
c. Then reconnect the first resistor and short out the second resistor (Fig.3). Measure the current
through the third resistor. Note the difference between the current with this configuration
and that in the configuration of step 1-a. Account for the difference. Measure the voltage
across all three resistors.
32 Parallel & Series Circuits
For voltage and current measurements refer to Fig.6. With this data confirm Kirchoff's
Voltage Law.
2.
Calculate the equivalent or total resistance of the circuit. Replace the circuit with this value of
resistance using the decade box. Consider the resistive circuit as a "black box". In this way,
the behavior of the circuit is analyzed without calculating the effect of the individual
components. See the comparison in Fig.7.
If the value of equivalent resistance is correct, it should produce the same current value as the
original circuit
3.
Repeat steps 1-a and 2 for a parallel connected circuit' Again use no less than three resistors.
4.
Set up the Wheatstone bridge shown in Fig .5. Your TAs will supply the 3 resistors. For
simplicity, let R1 = R3. Use a decade resistance box in place of the variable resistance. Supply
the bridge with 10V DC. Complete branch B-C with the DMM on DC Amps to measure the
current through this branch (M the range IQ AUTO).
Balancing Wheatstone Bridge for Unknown Resistor
5.
Balance the bridge (i.e. obtain negligible current through B-C branch) by adjusting the variable
resistance. Decrease the resistance incrementally recording current and resistance
measurements with each adjustment. When the bridge is balanced, confirm that R1 R - R3 R2
Determining ,Unknown Resistor by Balanced Wheatstone- Bridge Method
6.
Place an unknown resistor that your TA will provide in place of R2. Again balance the bridge
(i.e. obtain negligible current through B-C branch) by adjusting the variable resistance.
Determine the value of the unknown resistor.
Parallel 8 Series Circuits 33
REPORT
Your report should contain the following computer assignments as well as solutions to the questions given
out in lab.
Computer Assignment
1.
2.
Create a spreadsheet to record all data. Be sure to label
every section.
(40 pts)
Graph the current vs. varied resistance relationship of the Wheatstone bridge
for the unknown resistance determination. Keep in mind which variable you
changed, this is the independent variable. Be sure to clearly label the axes
and title the graph. (10 pts)
AC Signals
Executive Summary
Alternating current (AC) is used everyday in all aspects of life. It is probably the most common form of
delivery of electrical power. This is due to some of its characteristics, such as ease of transmission, conversion
and reliability. The voltage at your wall receptacle is AC, that is, the voltage alternates positive and negative
with a sinusoidal waveform. Electric power companies in North America provide a sinusoidal waveform with a
frequency of 60 cycles per second (60 Hz). Many appliances that plug into the wall socket do not actually run
on AC. Instead they convert the readily accessible AC into direct current (DC) by use of electronic circuits.
This experiment demonstrates the differences between AC and DC.
Most people realize that electromagnetic waves (e.g., radio waves, light waves) and sound waves are periodic.
'There are many more periodic phenomena in nature. One example is general climatic patterns. For example,
yearly temperature fluctuations around the Trans-Alaskan pipeline, averaged over the years 1941 through 1970
display a sinusoidal pattern [1]. Mathematically speaking, a periodic "waveform" would entail a mathematical
representation of these periodic phenomena, such as air pressure versus time (for sound waves through air) or
average temperature versus time (climatic data). The mathematical representation would be expressed in terms
of periodic functions, that is, functions whose values repeat themselves in a regular pattern with respect to the
independent variable.
Educational Objectives
•
•
•
To demonstrate and measure AC voltage.
To use a function generator.
To use an oscilloscope
Background Information:
3 8 AC Signals
the plots of AC voltage of Figure 2, the "scope" has two axes, voltage and time. Most modern
scopes are digital and provide functions much like "help" screens on the Macintosh. The scales are
displayed at the top of the screen. Time is in SEC / DIV (seconds per each division line) on the
horizontal axis' Voltage is given in VOLTS / DIV (volts per each division line) on the vertical
axis. These two scales are fundamental to using and reading an oscilloscope. As you will see,
these scales can be adjusted depending on the waveform of interest. The operation is fully
documented in the procedure section. By using the "scope", the amplitude and period of an AC
waveform can be determined.
Problem Statement
Given: An AC voltage.
Find: Its form, amplitude and period.
Procedure
Do not let the equipment intimidate you. It is all USER FRIENDLY. You will learn each piece of his
state of the art equipment step by step.
1.
2.
3.
Turn on the power for the function generator, DMM and the oscilloscope.
The connectors for use with the function generator and scope are called BNC. The cable is
coaxial. In the center is a copper wire conductor. Around this is a braided copper mesh wire. Look
at the cut open coax wire for detail.
Using the BNC to alligator clips input the voltage from the function generator to the DMM to
AC Signals 3 7
measure AC voltage. (For a refresher review the procedure to operate a DMM.) Note that the black
alligator clip is ground, or reference potential. The red is the signal potential with respect to that
reference. Make the proper connections and measure the RMS voltage. Record all data (amplitude,
frequency, RMS). Refer to Appendix FG 1 for the operation of your function generator.
4. Note: prior to outputting a signal, all specifications of the desired waveform must be selected.
Specifications are made using the five Designation sections on. the face of the function generator. For
this lab a sine wave will be generated A sine wave is a continuous signal with amplitude and frequency.
You will find an algorithm for producing a sine wave on your function generator to Appendix FG1.
Please note the Make and model number of the device you are using and look in the appropriate
section.
5.
Using the algorithm mentioned above, generate a sine wave of 3 V (amplitude), at 1 kHz
continuously. Refer to example 1 in the appropriate section of Appendix FG1.
6. Change the amplitude of the voltage wave six times. Keep in mind that the highest peak voltage you
can get out of the function generator is 10 V. Measure the RMS voltage on the DMM for each. Record.
7. Set the amplitude to 3 V. Vary the frequency of the waveform six times. Measure the RMS voltage on
the DMM for each. Record.
8.
Input the following: Square Wave, f = 1000 Hz, A = 6.0 V. Measure the RMS voltage on the
DMM. Record. DOE the waveform with proper scales on axes.
9. Turn off the output of the function generator and disconnect the DMM.
10. Connect the output terminal of the function generator to the input Channel 1 of the scope using a
BNC to BNC connector. Turn on the output of the function generator. (This should be set to the
square-wave of step 8.)
11. Turn on the scope with the POWER button.
12. Use the scale adjustments to view 2 cycles of the waveform on the screen. Refer to your drawing
from step 8.
13. Move the waveform so that you can easily read its Amplitude and Period. Record these on the
spreadsheet. From the period determine the frequency and compare this to the value entered in the
function generator.
14. Generate a 3 V sine wave of 1000 Hz and view it on the scope. Draw this wave indicating
period, amplitude, frequency, peak to peak voltage, RMS voltage and scales! Compare the
RMS value to that measured in step 6.
15. If there is an thing you do not understand - SEE THE TA.
3 8 AC Signals
References
[1] Lando& Lando, The Mathematics Teacher, Chapter 7, Section 6, p. 535, September 1977.
AC Signals 3 9
REPORT
Your report should contain the following computer assignments as well as solutions to the questions
given out in lab.
Computer Assignment
1.
Plot a sine wave and a cosine wave using Excel. Make a column of entries
from 0 to 10 in steps of 0.2 (i.e., step size = 0.2) . This will be the
variable t for the sin (t) and cos (t) functions. Plot the two functions
on the same chart.
Use Line Chart.
(40 pts)
TIME VARYING SIGNALS
Time varying waveforms are a fundamental phenomena in Engineering. The most common one is a
sound wave, although there are many other time varying waveforms in nature. These waveforms
are defined by their amplitude and frequency. Any repeating waveform can be reproduced by the
summation of various sinusoids of different frequencies. When these frequencies are all some
multiple of a base frequency they are called harmonics. Various methods have been developed to
determine the necessary harmonics. One method of analysis determines the combination of
sinusoids in the appropriate ratios that produce the given waveform. This method is called Fourier
analysis.
Educational Objectives
•
•
•
Associate sound and its waveform
Describe harmonics
Synthesize a sound
Background Information:
Notice the amplitude decreases with increasing harmonics and only the odd harmonics are present. Fig. 3
shows the fundamental and the first three harmonics of the square wave.
Fig. 4 shows how the square wave will look if you approximate the square wave with only a finite number of
terms of the infinite Fourier series representation of the square wave. Note: as a greater number of harmonics
are summed, the better the waveform resembles the square wave.
Applications
Light is another naturally occurring time varying waveform. Analysis of the frequency spectrum of light is
used to determine if a distant star is moving toward the earth or away from it. The Doppler effect is used to
make the analysis. You may have already studied the Doppler effect on the sound of a train horn. In front of
the train the sound waves are effectively compressed resulting in a high frequency sound. When the train has
passed the waves are effectively spread out and thus a low frequency sound results. Likewise, the wavelength
of light waves from an approaching star are compressed. This compression of the wavelengths cause the
corresponding frequencies to shift to the blue end of the frequency spectrum (higher frequencies). A star that
is receding from the earth will also have a shift in its frequency spectrum, but this time to the red end of the
spectrum (lower frequencies). This spectral analysis is used to determine the movement of the stars.
Problem Formulation
Sound is the result of changes in air pressure which propagate through space. One source of sound
waves we are all familiar with are the ones created by musical instruments. Since these waveforms
are periodic, the sound waves from them can also be represented by a Fourier series.
Time Varying Signals 4 5
Most musical instruments can be classified into one of two categories, strings or woodwinds. Each
category of musical instruments produce their sound waves by a different physical phenomena.
String instruments create sound when a player strikes the strings sending them into motion. When
the strings of the instrument begin to vibrate they interact with the air molecules around them. This
causes the air molecules to vibrate as well. The air is then responsible for carrying the vibrations
from the strings through space to your ear.
..
When a string is set into motion it can only set up certain discrete modes of oscillation (frequencies).
'These modes are determined by boundary conditions (finger placement), tension, and the mass per unit
length of the string. Note: The boundary conditions can be thought of as the two ends of the string that
are held fixed (nodes). The distance between these nodes is designated (L), the string tension is denoted
(T), and the mass per unit length of the string is designated '(g). To see how only certain discrete
frequencies can be set up on the string look at Fig. 5.
By examining the figure we see at the nodes (boundary conditions), the wave on the string has to have
zero displacement (the ends of the string are fixed). The formula below indicates the allowable
wavelengths that can be established on the string.
Fig.7 shows the frequency range for many instruments (note the frequency scale is logarithmic).
The ideal situation (for the lab) would be one in which the sound wave generated would be a
perfect sine wave. This is not usually the case. The shape of the instrument affects the pa r4 of
the wave form. Also, the manner in which the string is vibrated (bowed) will affect the wave
shape but not its frequency. The bow pulls back the string until it snaps forward' This is repeated
at high speed as the bow sweeps across the violin string. Vibrating a reed by blowing on it will
generate a saw-tooth like waveform. The reed in the mouth piece of a clarinet also vibrates as a
saw-tooth waveform when air is forced across its surface. The lip on the mouth piece of a brass
instrument vibrates more like a sine wave. Air passes through the instrument alternatively as the
reed or lip vibrates. A pipe organ produces a sound wave whose frequency is determined,
basically, by the length of the pipe. Keep in mind each instrument type has a different kind of
generator, hence different waveforms are produced by each type. The flute, recorder and pipe
organ have a single reed or lip as a vibrating source. The clarinet and saxophone have a
mechanical reed. The bassoon and English horn have double reeds. Trombone, trumpet and
French horn have lip reeds. The violin, viola, etc. are bowed strings while the harpsichord, harp
and guitar are plucked strings. The player can vary the length by pressing the string against the
finger board. Only four strings are needed to obtain many different notes on the violin. In the
piano the length of the strings can not be varied so 88 different strings are needed. In each case the
string will vibrate in such a way as to generate a large number of harmonics of the fundamental
frequency, fo. A good quality violin is said to be "rich" in harmonics because the two sounding
boards, the back and front surfaces of the instrument, are capable of vibrating at these frequencies.
They actually increase the harmonic content of the sound. The size, shape and material of an
instrument can affect which harmonics are strong and which are weak. Hence, each instrument
has its own characteristic sound. The piano has strings that will generate fundamental frequencies
from 27 to 4186 Hz. But the harmonic content of its sound goes beyond the human ear (20 kHz).
Procedure
All indicated measurements are to be recorded on a spreadsheet in Excel. Refer to compute
assignment #1. It is important to label data correctly!
1.
Instrument Play Back.
Obtain the HyperCard stack 'Time Varying Signals" and copy it on your hard disk.
Connect the sound output of your Macintosh to channel 1 of your oscilloscope via the computer
audio adapter. Set the scope to IV/DIV and 1mS/DIV. You may change these settings as needed.
Use Ch A input and set all buttons out.
The HyperCard stack (Fig. 8) will play a sample of the instrument when the corresponding
button is clicked. Each one will play the same note, G4, at about 392 Hz. For each
instrument look at the waveform on the scope. Make a sketch of its shape, looking for pure sine
waves, or triangle waves, or arbitrary waves. In the case of the violin it should be rich in
harmonics. Replay each instrument if necessary to sketch its waveform or store a representative
portion (a few wavelengths) of the waveform. Dtermine its fundamental frequency. You may
want to measure the frequency of each instrument on the Frequency Counter.
The suggested sequence of instruments to be played is as follows:
1- Recorder (flute-like)
2- Piano (normal)
3- Piano (with pedal)
4- Classical Guitar (finger tip)
5- Classical Guitar (finger nail)
6- French horn (open)
7- French horn (hand stopped)
8- Trombone
9- Violin (open string)
10- Clarinet
11- Clarinet (octave higher)
12- Clarinet (octave lower)
13- Symphony (Beethoven #6)
14- Violin and Flute Conc. (Vivaldi). Total playing time 9:40.
Time Varying Signals 4 9
Carefully sketch each waveform seen on the scope and record its frequency.
2.
Music Generator
Use the function generator now to generate sounds similar to those just observed. Set the
frequency to 392 Hz. Connect the output of the generator to the speakers.
Look at the waveforms on the scope and listen to them for the various functions available
from the generator, sine, triangle and square waves.
5 0 Time Varying Signals
-Scrap Page: Use this area to take notes, to record preliminary data, etc.
REPORT
Your report should contain the following computer assignments as well as solution to the questions
given out in lab.
Computer Assignment:
1.
2.
For those computer competent students, mah. a hard copy of your waveform
sketches. For the rest of you, hand in what you have. This should Include
all of the instruments as well as the waves generated by the function
generator. (30 pts)
Consider a sinusoidal wave of frequency 60 Hz. Plot at
least 3 cycles of this wave. Use Excel. Also plot on
separate graphs:
•
2nd harmonic
•
sum of the first 3 harmonics
•
3rd harmonic
• sum of the first 3 odd harmonics
(30 pts)
QUESTIONS
1.
Compare and contrast the sounds that you created and those of the instruments. Which
instruments can be approximated by the function generator? (20 pts)
2.
All of the instruments used for this recording were played at the note of C' What parameter of the
waveform would change if the note was changed to D? (consider amplitude, period, etc.)
(20 pts)
53
TEMPERATURE TRANSDUCERS
The ability to make accurate measurements of temperature, temperature change, and heat flow is
essential in a modern industrial society. The quality, operation, and efficiency of any device is
either directly or indirectly dependent on temperature. The measurement of temperature and its
related processes is made easier by the use of a thermal transducer. Transducers are devices
which change one physical parameter in accordance with changes in some other physical
parameter. The physical quantities of temperature transducers, for example, change
proportionally with temperature. Conversions can be performed to find temperature and heat flux
in their standard units.
Objective
•
•
Compare various temperature transducers: thermistor, thermocouple, and the thermometer
Determine the best transducer for any specific applications
Theory
By definition, a transducer transforms one form of a physical quantity into another form. Thermal
transducers deal specifically with temperature and thermal measurements such as temperature
gradient or heat flux. Operation of a temperature transducer is commonly based on the measurable
variance of a parameter associated with temperature changes in a given material. Other types of
thermal transducers exploit phenomena and effects associated with the thermal properties of
specific different materials, for example:
•
•
•
semiconductor conduction
liquid expansion in a glass tube
difference in coefficients of expansion in dissimilar metals
Transducers may be linear or nonlinear. With respect to the thermal transducers, a linear device has
a proportional relation between temperature and its transformed value. This is important, in that by
simple conversion the temperature is found in standard units. Nonlinear devices do not have this
proportionality between temperature and output. To convert these readings back to the desired units,
complicated equations or look up tables must be used.
As with all physical processes, time is required for the transducer to respond to the changes in its
environment. In this experiment the response time of the device is defined as the time required for a
system parameter to attain a value within 1096 of the final value. For rapidly changing temperature
applications this becomes a critical consideration in determining the best device for a particular
measurement.
The sensitivity of a device is a measure of its change in output with a small change in input.
Applications
Recently there has been great interest in using some of the Artificial Intelligence (AI) techniques in
5 4 Temperature Transducers
controlling systems that are hazardous and/or inaccessible to human operators. One branch of AI,
Expert Systems has proven effective in these applications. An Expert System is a sophisticated
method of teaching the computer to respond to changes in a system or environment as would a
human expert in that field. In other words, the computer becomes the expert. The computer must
have access to the same information as its human counterpart' Since the computer cannot read dials
and gages visually, all measurement data must be converted to signals understandable by a
computer.
At Nippon Steel Corporation in Japan, for example, an expert system has been developed to monitor
and control the blast furnaces. Temperatures, as well as other quantities, are measured using
transducers, and the information that the computer receives is a voltage signal reflecting the
measured parameters. This system is in daily use and proven to be very effective.
Problem Statement
Given:
Find.Determine:
Temperature range of 3 temperature transducers (thermometer, thermistor, and
thermocouple)
Calculate the sensitivity, thermal response and linear range of each transducer.
Determine the appropriate uses, advantages, and disadvantages of each.
Problem Formulation:
Depending on the circumstances and uses, there are a variety of devices from which to select a
transducer. As in all experiments, be sure to consider all aspects of the measurement, type of
material, dimensions, temperature range to be considered, type of display, application, etc. Given
below are some brief descriptions of several transducers.
The thermocouple is a thermoelectric device consisting of two dissimilar metals joined at one end.
The device is based on the discovery of Seebeck in 1821 that an electromotive force (emf) exists
across a junction of two dissimilar metals (called Seebeck voltage). This phenomenon is due to the
sum of two other independent effects that are temperature related.
Fig. 1 depicts a thermocouple circuit with two metals, A and B, with two junctions, 1 and 2. The
temperatures at the two junctions are different, T1 and T2.The voltage at the terminal a-a' is related
to the temperature difference between the two junctions and to the properties of the metals used' If
one of the junctions is held at a constant known temperature (such as an ice bath or
temperaturecontrolled oven), the voltage at a-a' can be used to determine the temperature at the
other junction. The junction that is held at the known temperature is called the reference junction.
Temperature Transducers 55
Although all dissimilar metals exhibit this behavior, the most commonly used combinations an:
Copper-Constantan (T-type)
Iron-Constantan (J-type)
Chromel-Alumel (K-type)
Platinum-Rhodium (S or R type)
5 6 Temperature Transducers
where T is the temperature and A, B, and C are determined from the experimental data'
Basically, this equation solves for the plot of thermistor resistance as a function of temperature.
A typical plot is shown in Fig. 2.
Since thermistors are semiconductor devices, they are subject to deterioration at high
temperatures. They are therefore limited to measurements below about 300 C.
The liquid-in-glass thermometer is probably the most common temperature measurement
instrument. A bulb at the lower part of the thermometer holds the major part of the liquid, which
expands when heated and rises in the capillary tube upon which a scale is etched. Common
liquids include alcohol and mercury. Alcohol has a higher coefficient of expansion than mercury
but is limited to low temperatures because it boils away at high temperatures. The range of
mercury thermometers is from -38 C to 315 C.
Another type of transducer is based on bimetallic expansion of metals. It consists of strips or
coils of dissimilar metals joined and fixed to a case at one end. The other end has a pointer
attached to it. A change in temperature causes an unequal expansion of the metals, thus causing
the pointer to move across a calibrated temperature scale marked on the thermometer's case. The
readout is generally a dial.
Readings will be made for each of the three transducers as they are subjected to various known
temperatures. A calibration curve can then be drawn for each one. The temperatures considered
are that of ice water and boiling water as well as room and body temperature. The known
temperature will be compared to the reading of each transducer.
Procedure
All indicated measurements are to be recorded on a spreadsheet in Excel. Refer to Computer
Assignment #l. It is important to label the data correctly! The spread sheet constitutes 40% of the
grade for this experiment.
Note: When recording and plotting curves for the thermistor and thermocouple, remember that
their temperature is transformed into resistance and voltage respectively' Use these readings
as they are, do not try to reconvert them into a true temperature reading. Later you may
correlate these readings to temperatures using your calibration curves.
CALIBRATION
1. Record the temperature (T) of the thermometer, the resistance (R) of the thermistor, and the voltage
(V) of the thermocouple at room temperature. Remember to have the reference end of the thermocouple
in ice water always (0C) and to replenish the ice in the ice water as the experiment progresses.
2.
Place the thermometer, thermistor, and thermocouple in the ice water cup you used for
thermocouple reference in part 1. Record T, R, or V of the transducers.
2. Withdraw the transducers one by one and record intermediate values (time, reading) as the
temperature of the device stabilizes to room temperature' This set of data will be used to plot
characteristic curves of reading (T, V or R) as functions of time.
4.
Repeat 2 & 3 using your hand to warm the transducers as they stabilize to body temperature.
(Note: Maximum room temperature recorded in part 3 and maximum body temperature recorded in part
4 will be used for computer assignment #2.)
Temperature Transducers 5 7
RESPONSE TIMES
5. Heat a pot of water until it boils. In order to avoid breaking the thermometer dine to sudden
expansion, insert it slowly into the boiling water. Record the temperature and time every 5
seconds for at least the first 15 s and every 15 s afterwards until it stabilizes. Remove the
thermometer and record its value every 15 seconds until it reaches room temperature. Repeat
for the thermistor and thermocouple. These data will be used to draw your response curves.
6.
Connect the power supply, resistor, thermistor, and thermocouple as in Fig. 3. You must
switch thermocouple and thermistor leads into DMM set to proper measurement mode. Use
separate pairs of red and black leads for each element.
7 . Set the power supply voltage to 30V and connect it to the power resistor.
8. While the resistor is heating, do Computer Assignment #2. It will take about 17 minutes for the
resistor to stablize at its high temperature.
9.
After 17 minutes the temperature stabilizes at its maximum (approximately 157` C). Record V,
and R. Include these data in your plot. Do not turn off the power.
10. Remove thermocouple from the heating resistor and place it in the open air and record the time it
takes for voltage to stabilize at room temperature (using the same intervals as in part 5). Repeat
this process a few times measuring the value of voltage at several different times between the
equilibrium points. Make enough measurements to plot the characteristic curve of voltage as a
function of time for the thermocouple between the heating resistor temperature and room
temperature.
11. Repeat Step 10 placing the thermocouple in ice-water bath rather than open air and record the time
it takes for voltage to stabilize at 0' C. Repeat this process a few times measuring the value of
voltage at several different times between the equilibrium points. Make enough measurements to
plot the characteristic curve of voltage as a function of time for the thermocouple between the
heating resistor temperature and the ice-water bath.
12. Use the same processes (numbers 10 and 11 above) to find the characteristic curves of the
thermistor, measuring the resistance instead of the voltage.
13. Turn the voltage supply OFF and allow the heating resistor to cool.
5 8 Temperature Transduce rs
If time permits, complete the following addition. This is for extra credit ONLY! There is no penalty
for failure to complete this section.
Extra-40points.
SELF HEATING EFFECT OF THERMISTOR
14. Connect the thermistor to the power supply as in Figure 4.
15.
Apply 10 V DC to the circuit and record the current and voltage of the thermistor every 30
seconds until the circuit stabilizes. < Repeat for 15V and 20V.
16.
Plot resistance as a function of current for each voltage applied.
UNITS
REFERENCETEMPERATURES
Ice water = 0.00 C.
Room temperature = 22.0 - 25.0 C.
Body temperature = 36.5 C.
Boiling water = 100.0 C.
Heating resistor high temperature = 157.0 C.
Temperature Transducers 5 9
REPORT
Your report should contain the following computer assignments as well as solutions to the questions given out
in lab.
Computer Assignment
1.
Create a spreadsheet in EXCEL and enter all data. Include
the reference temperatures, your calibration temperatures,
resistances, and voltages.
(20 pts.)
2. Plot the measured T, V and R,
versus the actual reference
temperatures (given on page 8) of ice water,
room
temperature and body temperature for each of the
three
devices
(10 pts. )
3. Plot the characteristic curves for the thermocouple and the
thermistor (i.e., V vs. temperature for the thermocouple and
R vs. temperature for the thermistor).
(10 pts.)
4. Make response time plots of each temperature transducer.
(10 pts.)
QUESTIONS
1.
Describe a scenario in which each transducer used is far superior to the other two.
(20 pts.)
2.
For the Thermocouple described in the Problem Formulation section, sketch the voltage as a
function of temperature.
(20 pts.)
61
"Iron rusts from disuse; stagnant water loses its purity ands weather becomes
frozen: even so does inaction sap the vigor of the mind."
Leonardo da Vinci
CALORIMETRY
Executive Summary
Calorimetry is the science of measuring quantities of heat and their associated temperature
changes. This concept is the experimental foundation of thermodynamics. Experimentalists use
calorimetry to quantify the relationship between temperature and energy content. In more
complicated chemically reacting systems, experimentalists use calorimetry to measure the heat
released during chemical reactions. This experiment deals with the former, by using the
fundamental principles of calorimetry to determine the heat capacity of a material, in order to
establish a quantitative relationship between energy content and temperature.
Educational Objectives
•
•
•
•
Measure the specific heat and the heat capacity of an unknown liquid.
Demonstrate calorimetry.
Measure the heat of vaporization.
Measure the heat of fusion.
6 2 Calorimetry
vapor). The ratio of heat added, Q, to the mass of material, m, under-going the phase change is
called the latent heat of phase change. Examples are:
Heat of vaporization - liquid to vapor
Heat of Fusion - solid to liquid
Heat of Sublimation - solid to vapor
These heats are defined in reverse order as well. The same quantity of heat is reIeased when 1 g of
water is condensed as is absorbed when it is vaporized.
When measuring phase transitions, it is important to limit the analysis to the constant temperature
period. Otherwise, the value determined will be incorrect, since it will include the heat needed to
change the temperature of the material.
Problem Statement
Given: Water and an unknown fluid.
Find: The heat capacity and the specific heat of the unknown fluid and heats of fusion and
vaporization of the water.
Problem Formulation:
To determine the amount of heat necessary to raise the temperature of a given amount of a fluid,
obviously the fluid must first be contained in some vessel along with an element to measure the
temperature as the material is heated. As heat is added, the temperatures of the vessel and element
also rise. These represent a loss of heat to the fluid's environment and must be considered in any
calculations.
First, note that the Equation (2) can be rewritten as:
The apparatus must be calibrated by first conducting the experiment with a fluid of known specific heat, such as
H20. Measure the heat added, the temperature change, and the mass of the water. This leaves only the last two
terms in Equation 4 which may be lumped together into a common term (remember the mass and specific heat
of each are constant). Solve for this calibration term. Knowing this term, any change in temperature may be used
to calculate the heat dissipated in the vessel and element.
The experiment is run again with a test fluid. This time find the specific heat and heat capacity of
calorimetry 63
the unknown fluid' Remember: the specific heats and masses of the vessel and element are
constant. Don't forget to subtract the heat losses!!
To determine the heats of vaporization and fusion, heat is added to the ice water in order to take it
from a solid to a liquid state. This is the heat of fusion. More heat is added to change the water
from liquid to vapor. This is the heat of vaporization. Since the temperature of the water is
constant during the phase change, monitoring the temperature and stirring constantly will assure
valid results.
Procedure
All indicated measurements are to be recorded on a spreadsheet in Excel. Refer to computer
assignment # 1. It is important to label data correctly! The spreadsheet constitutes 40% of the
grade for this experiment.
Calibration
1. Weigh the empty hot pot (Fig. 1) on the electronic balance. Fill approximately one-third
with water. Reweigh this partially filled container. Determine the mass of water added.
6 6 Calorimetry
Report
Your report should contain the following computer assignments as well as solutions to the
questions given out in lab.
Computer Assignment
1.
2.
Create a spreadsheet in Excel and enter all data.
Include
calculation term, power output of hot pot,
interval
readings, times, etc.
(40 pt s)
Use the 2 minute interval readings to plot the relationship between
heat added and change in temperature for the water and for the test
fluid. (Hint: These are proportional.)
Indicate dependent and independent variables.
(20 pts)
Questions
1.
a)
(10 pts)
The enthalpy of combustion of benzoic acid (C6H5COOH), which is commonly used as the
standard for calibrating constant-volume bomb calorimeters, has been accurately determined
to be -3226.7 kJ/mol. When 1.9862 g of benzoic acid is burned, the temperature rises from
21.84' C to 25.67' C. Find the heat capacity of the calorimeter. (Assume that the quantity of
water surrounding the calorimeter is exactly 2000 g.)
b)
Calculate the temperature rise of one liter of water exposed to a power input of 60 W for 30
minutes.
2.
Describe the principle of calorimetry learned in this experiment. (10 pts)
3.
Was there a difference in the mass measurements using the electronic balance and the trip
balance? Which is more accurate? (10 pts)
4.
Compare and contrast the bomb calorimeter, (see your chemistry textbook), and the calorimeter
used in this lab. (10 pts)
5.
Which fluid would make a better insulator, water or the test fluid? (Bonus - 10 pts)
6 8 Calorimetry
6.
This experiment involved some approximations and assumptions. List some of them and state
the errors they may have caused. How would you improve this experiment to get more
accurate results (using the same equipment)? (Bonus - 10 pts)
CONVECTIVE HEAT TRANSFER
Executive Summary
A hot piece of material will cool faster when air is blown by the object. If the air is blown by
using a fan of some sort, we call this forced convection. If the air passes by the object due to rising
of the warmed air, we call it natural convection. The word "convection" refers to the motion of
fluid (air, in this example) and the subsequent transport of energy away from (or towards) by virtue
of this fluid motion. Homeowners can purchase "convection ovens", which differ from regular
ovens mainly in that the former have fans to circulate the hot air and the latter depend on natural
convection (and radiation) to transfer the heat to the food being cooked. In engineering design of
ovens, process units, radiators for cars, cooling fins for electrical units, etc., it is important to
understand the quantitative dependence of this heat transfer rate on fluid velocity. This experiment
provides an example of atypical measurement of this.
Educational Objectives
•
•
•
•
Define and measure heat transfer coefficients.
Describe the dependence of heat transfer coefficient on fluid velocity.
Use an anemometer.
Describe the underlying theory behind the so-called "wind-chill factor."
70 Convective Heat Transfer
depends on properties of the fluid (air), such as thermal conductivity, density, etc., but usually it
does not depend on characteristics of the surface. h also depends strongly on the velocity of the fluid
past the surface. One's comfort outdoors during the winter depends on wind velocity as well as
temperature. This is a reflection of the fact that one loses heat faster when the wind velocity is higher
and, apparently, the body can sense rate of heat loss. Of course, radio broadcasters feel that their
audience can only think of one environmental condition at a time so they express this effect of wind
velocity in terms of an "equivalent" temperature, which is determined by calculating the temperature
difference in still air which would produce the same rate of heat loss as that in air at the prevailing
wind speed and temperature. This is then reported as the "wind chill factor" in degrees Fahrenheit.
h
At low air speeds, the flow is laminar (smooth) and h is usually directly proportional to air speed. At
higher air speeds, the flow is turbulent (more chaotic) and the convective heat transfer is much
higher, resulting in h being proportional to air speed raised to a power between 1.5 and 2. In this
experiment, when you turn your fan on, the flow will most likely be turbulent.
7 2 Convective Heat Transfer
Convective Heat Transfer 73
74 Convective Heat Transfer
REPORT
Computer Assignment
1.
Create a spread sheet in Excel as in Fig. 3. Enter all data. Also
include Report items 1, 2 and 3 (above) in the
spreadsheet.
(60 pts)
Questions
1. How long does it take to reach steady-state? (10 pts)
2.
With the fan on, does (3 depend on voltage and, if so, can you guess why? (15 pts)
3.
With the fan off, does h depend on voltage and, if so, can you guess why? (15 pts)
77
THERMAL CONDUCTIVITY
As seen in many of the experiments so far, the mobility of electrons in a material greatly affects its
characteristics' Do the electrons move easily through the substance? Are electrons excited thermally,
electrically, or optically in this material? Metals, for example, exhibit high electrical conductivities
because electrons travel through them easily. Metals also transfer heat easily. The ability of a material
to transfer heat through itself is called thermal conductivity. Metals are high in thermal conductivity.
Conversely, plastics and ceramics resist the movement of electrons and the flow of heat. These
materials are high in thermal resistivity, which is the reciprocal of thermal conductivity.
Educational Objectives
•
•
•
Measure the thermal conductivity of solids.
Calculate heat flux through solids.
Use a heat flux transducer.
Applications
The concept of exploiting a given material's thermal conductivity is demonstrated in air
conditioning, the soldering iron and the radiator.
Can you find a modern day application? 10 extra credit points go to the student with the most
unique and ingenious idea*.
Thermal Conductivity 79
Procedure
1.
Select one of the sample materials and set it up as in Figure 2. Turn on the lamp and the fan.
Connect the transducer to the DMM set to read DC mV. Remember: always start with the
highest range on the DMM, and work down to the proper range.
8 0 Thermal Conductivity
REPORT
Your report should contain the following computer assignments as well as solutions to the questions
given out in lab.
Computer Assignment
1.
Create a spreadsheet in Excel to record your data. Include the dimensions of the sample and
temperatures, as well as the Wattage of the light bulb and the heat flux in English and
SI units. Use a formula set up to calculate each thermal conductivity.
(5O pts)
8 2 Thermal Conductivity
4.
Using the relation of thermal conductivity with electrical conductivity as discussed in lab
lecture and considering the design of the apparatus, why might the measured thermal
conductivity of a sample be different from the actual value? Which type of sample is most
affected by the experimental apparatus - a good thermal conductor or a poor thermal
conductor? (Bonus: 10 pts)
5.
See the Applications section. (10 pts)
OPTICS: SOURCES & DETECTORS
The study of light and vision, chiefly the generation, propagation, and detection of electromagnetic
radiation having wavelengths greater than x-rays and shorter than microwaves.
Educational Objectives
•
Measure the range, sensitivity and dynamic response of different photo detectors, using
photoemitters, and other light sources.
•
Show that the visible light spectra (colors) are a function of their wavelengths.
•
Measure the wavelength of each gas in the spectral tubes.
•
Compare light sources and detectors.
84 Optics: Sources & Detectors
Photo detectors can be divided into two basic types, Thermal, and Wavelength sensitive Photo diodes.
The former senses a change in temperature and outputs a voltage proportional to the temperature
change. The latter functions due to the Photoelectric effect, where protons (light particles) of
appropriate energy strike the semiconductor material and causes it to conduct electricity.
Spectra are of three main types - continuous, bright-line, and absorption. A continuous spectrum is
produced from an incandescent solid or liquid, such as the sun of the tungsten fiIament of an ordinary
electric lamp. A bright-line spectrum is produced by the excitation of a gaseous element either by a
high voltage electric discharge or by heating. Absorption spectra are produced when light from an
object which is actually providing a continuous spectrum is seen through some cooler absorbing
medium.
In this lab we will only observe some examples of continuous spectra and bright line spectra.
Applications
•
•
Manufacturing - Parts are counted, inspected, & sorted by appropriate placement of emitter
detector pairs along a production line.
Photography - Determines if level of light is appropriate for taking pictures.
•
Security - Detects intrusion when its light beam is interrupted.
•
Communications - Transmits and receives information that has been coded into light waves
or pulses.
Problem Statement
Given:
Find:
Compare:
A variety of light sources and detectors, spectrometer, and monochrometer.
The sensitivity range, and dynamic response of the photo detectors.
The spectral composition of the light sources.
Optics: Sources & detectors 8 S
Procedure
Before you make measurements, read through the Computer Assignment section so that you can
record pertinent data.
1) For three sets of LED - Photo transistor pairs, do parts A, B and C below. Start with infrared
transmitter-receiver pair since it will result in strongest signal. Note that the signal quality may
deteriorate with different pairs.
2) Repeat parts A, B, & C for a US photocell receiver and incandescent lamp as the transmitter.
Make sure you block stray light by covering the transmitter-receiver pair.
3)
Follow the procedure in part D.
B - Sensitivity Determination:
Reduce the function generator output to zero volts, then gradually increase the input voltage until a
change in output voltage is seen in the oscilloscope. Record these voltages. Make sure the volt/div
adjustment is set such that you achieve full deflection on the screen. This will help the accuracy of
-
1)
Use the spectroscope, spectrometer, and monochrometer to observe, determine, and compare
the wavelengths of the different light sources.
2)
Find the bandwidths of the LED's.
3)
Find the range of wavelengths detectable with the eye.
4)
Observe and describe the effect of filters on the bandwidth.
5) Use the table top spectroscope to observe the spectral bands, lines, and measure the wave lengths of
the different spectral tubes.
6) Use the hand held monochrometer to observe and measure the spectral bands and lines of the different
spectral tubes.
Optics: Sources & Detectors 89
REPORT
Your report should contain the following computer assignments as well as solutions to the
questions given out in lab.
Computer Assignment
1.
Create a spreadsheet in Excel and enter all data. For each
emitter/detector type include type of input waveform,
amplitude and frequency, fidelity of output wave shape, and
amplitude.
(40 pts)
2. Make a plot of frequency vs. amplitude for each
emitter/detector pair. Be sure to identify the type of
source and detector.
(15 pts)
3.
List the colors (spectra) of the white light sources as seen through
the spectroscopes and displayed by the prism. (5 pts)
2. How could you explain this statement: In spectroscopy, each element signs its own name.
(5 pts)
3.
When you look at a piece of cloth under white light and say it is "blue", exactly what does
this mean? (5 pts)
4.
If you looked at a red light through a piece of blue glass, what would the effect be? (5 pts)
5.
What can you say about the nature of light energy from a source which gives a bright-line
spectrum? (5 pts)
6. What type of emitter/detector pair has the greatest frequency range? (5 pts)
7 . What type of emitter/detector pair has the best sensitivity? (5 pts)
8.
What type of emitter/detector pair has the best response time? (5 pts)
91
THE CAPACITOR & CAPACITIVE CIRCUITS
The capacitor is formed by assembling two conductive plates opposite each other with a suitable
dielectric sandwiched between them. A wire is connected to each plate such that the capacitor can
be connected in electric circuits.
Educational Objectives:
•
•
•
Review R-C time constants.
Measure the capacitance by observing its charging and discharging time in R-C circuits.
Verify capacitive reactance.
Applications
•
Used in motor starting circuits, noise reduction, frequency selective and non-selective
circuits, energy storage, filter circuits.
9 2 The Capacitor 8 Capacitive Circuits
The Capacitor & Capacitive Circuits 9 3
9 4 The Capacitor & Capacitive Circuits
Compare the calculated values of your series and parallel connected capacitors with the values
using the manufacture's specifications. Be sure to record all data; you will need it to answer
the questions!
9 6 The Capacitor & Capacitive Circuits
REPORT
Your report should contain the following computer assignments as well as solutions to the
questions given out in lab.
Computer Assignment
1.
Create a spreadsheet in Excel and enter all data. Calculate
capacitance of each capacitor in procedure step I and
combinations of capacitors in step 3.
2. Make a plot of frequency vs. voltage for step 2.
(35 pts)
(15 pts)
QUESTIONS
1.
What are the special characteristics that capacitors exhibit? (10 pts)
2'
Is there any difference between Resistance and Reactance? Explain. (10 pts) ,
3.
What features of capacitors must we consider to maximize its use in a circuit? (10 pts)
4.
What happens inside the R-C series circuit at low frequencies? At high frequencies?
(10 pts)
9 8 The Capacitor & Capacitive Circuits
5.
What are the percent differences between your calculated values of the Capacitors and the
manufacturer's specified values?
(10 pts)
CONTROL SYSTEMS
Executive Summary .
One practice of engineering that is common to different disciplines is systems engineering. Although
different disciplines in engineering would deal with different kinds of systems, the underlying mathematical
representations for these systems are very similar and common to all fields of engineering.
Educational Objectives
•
•
To become familiar with control systems.
To design a computer-controlled system
Suggested Preparation
Bring a floppy disk with enough space to save the LabVIEW VIs you will create during the first session of
the lab.
Background Information:
A system is an arrangement of components connected or related so that they act as an integrated unit. A
control system, furthermore, is a system that commands, directs or regulates itself or another system. Two
major control system types are: open loop and closed loop systems.
An open loop system is one in which the control process is independent of the output. A gas range is an
example of an open-loop control system. It will give off a pre-adjusted amount of heat as long as it has the
same setting. In open loop systems, the control action is achieved by proper calibration of the system.
A closed loop system, on the other hand, is one in which the control process is directly or indirectly
dependent on the output. Closed loop systems have a characteristic called feedback which distinguishes
them from open loop systems. Feedback is that property which allows the output of the system to be
compared with the input such that the correct action may be taken for the regulation of the output. A
building's heating system is an example of a closed-loop control system. Fig. 1 depicts the block diagram for
such a system. It is composed of smaller components that work together to regulate the temperature of a
room and thus the building. It utilizes a thermostat to turn the heating elements on or off as the room
temperature rises and falls. Note that each unit represented in the block diagram may be considered as an
individual system. On the other hand, we have not shown the thermostat as one element because it has two
functions: (1) to measure the room temperature and compare it with the desired temperature and (2) to
decide whether to turn the furnace on or off. The variation in the outdoor environment is the primary reason
for the unpredictable change in the room temperature. If the outside conditions (temperature, wind, solar
insolation, etc.) were predictable, we could design an open loop heating system that would operate
continuously to supply heat at a predetermined rate just large enough to replace the heat lost to the outside
environment. No feedback would be necessary. Of course, the real world does not behave so nicely, so we
must adjust the heat-output rate of our system according to what the actual room temperature is.
Control Systems 101
On-off Control
This type of control has two possible values for the control signal depending on the error. For the heater
example, the furnace would be on if the error is positive (room is colder than desired) and off if the error is
negative (room is warmer than desired). For very quick systems, one might want to leave a certain zone for
the output, called the neutral zone, to avoid frequent on-off switching (called chattering) which might shorten
the life of the system.
Proportional Control
Some systems that require fine control may not be served well with an on-off control. One alternative is to
have the control signal equal a proportion of the error.
Other Kinds of Control Schemes
The control schemes discussed above are the classical basic schemes. Except for the on-off control,
all off them are linear schemes. All of these linear schemes work best with linear processes' With the
accessibility of the computer, one is no longer limited to simple schemes as the ones given above but
may easily design nonlinear, discontinuous and/or adaptive algorithms that try to optimize the
system performance.
Problem Formulation
Your task for the next two weeks is to design and test control systems to keep the temperature of a
heating element constant. The first week will be devoted to the design of the system. You will test
Recommended Steps:
1) Write down an algorithm before you start programming.
2) Check your algorithm with your TA or instructor.
3) Try your program with the dummy controller VI that is provided before you try the real thing!
4) Show your completed program to your TA or instructor.
Procedure: Session 2
ON/OFF Controller
1) Modify your ON/OFF controller such that it will accomodate the driver (Control.Actual) that will active
the physical set-up.
2) Set the ON Voltage to 10 V. Set the reference input to 4 mV. Answer the appropriate questions on the
worksheet.
3)
Set the ON Voltage to 30 V. Set the reference input to 4 mV. Answer the appropriate questions on the
worksheet.
4)
With the ON Voltage set at 30 V, change the reference input to 1.5 mV. Answer the appropriate
questions on the worksheet.
5)
Place a fan at about 30 em from the heating element. Turn it on at the LOW setting. Describe what
happens (on the worksheet).
Control Systems 103
6)
Turn the fan off. Describe what happens (on the worksheet).
Proportional Controller
1) Modify your PID controller such that it will accomodate the driver Control.Actual, or copy
the PID controller provided onto your Public workspace.
2) Let the heating element cool down. Set K; and Kd to 0 and Kp to 50. Set the reference input
to 4 mV. Answer the appropriate questions on the worksheet.
3) Let the heating element cool down. Set Kp to 100. Set the reference input to 4 mV. Answer
the appropriate questions on the worksheet.
4)
Set the reference input to 1.5 mV. Answer the appropriate questions on the worksheet.
5) Place a fan at about 30 cm from the heating element. Turn it on at the LOW setting. Describe
what happens (on the worksheet).
6)
Turn the fan off. Describe what happens.
Proportional-Integral (PI) controller (Note from this point on, assume the system
has reached steady state if the output is within ± 5 % of the desired setting)
1)
2)
3)
4)
Let the heating element cool down. Set K; to 0.5, Ka to 0 and Kp to 50. Set the reference input
to 4 mV' Answer questions on the worksheet.
Set the reference input to 1'5 mV' How long does it take to reach steady state?
Place a fan at about 30 cm from the heating element. Turn it on at the LOW setting. Describe
what happens.
Turn the fan off. Describe what happens.
Proportional-Integral-Derivative (PID) controller
1) Let the heating element cool down. Set K; to 0.5, Kd to 10 and Kp to 50' Set the reference
input to 4 mV. Answer the appropriate questions on the worksheet.
2) Set the reference input to 1.5 mV. How long does it take to reach steady state (answer on the
worksheet)?
3) Place a fan at about 30 cm from the heating element. Turn it on at the LOW setting.
Describe what happens (on the worksheet).
4)
Turn the fan off. Describe what happens (on the worksheet).
5) Experiment with Kp, K;, and Kd such that you will have least overshoot and fastest
response time. Record your optimum settings and results.
Design
Based on your experience with this system, can you suggest an algorithm that will maximize
response time, minimize oveshoot and steady state error?
Control Systems 105
REPORT
The first session of this lab involves no report. You must have your instructor grade your VI before
you leave the lab. Save your VI on a floppy disk for the next session. For the second session, fill
out the worksheet.
Worksheet
ON/OFF Controller
2.a) How long does it take to reach steady state?
2.b) What is the steady state error (as a percentage of the desired setting)?
3.a) How long does it take to reach steady state?
3.b) What is the steady state error?
4.a) How long does it take to reach steady state?
4.b) What is the steady state error?
5)
Describe what happens.
6) Describe what happens.
Proportional Controller
2.a) What is the maximum overshoot (as a percentage of the desired setting)?
108
Control Systems
2.b) How long does it take to reach steady state?
2.c) What is the steady state error?
3.a) What is the maximum overshoot (as a percentage of the desired setting)?
3.b) How long does it take to reach steady state?
3.c) What is the steady state error?
4.a) How long does it take to reach steady state?
4.b) What is the steady state error?
5)
Describe what happens.
6)
Describe what happens.
Proportional-Integral (PI) controller
1.a) What is the maximum overshoot?
1.b) How long does it take to reach steady state?
1.c) What can you say about the steady state error?
Control Systems 109
2)
How long does it take to reach steady state?
3)
Describe what happens.
4)
Describe what happens.
Proportional-Integral-Derivative (PID) controller
1.a) What is the maximum overshoot?
1.b) How long does it take to reach steady state?
1.c) What can you say about the steady state error?
2)
How long does it take to reach steady state?
3)
Describe what happens.
4) Describe what happens.
5)
Record your optimum settings and results:
110 Control Systems
Design
Show your design to your instructor.
OVERVIEW OF BASIC CIRCUIT CONCEPTS
Educational Objectives
•
•
Review how to measure voltage and current in a DC circuit
Review and verify Kirchoff s Voltage and Current Laws, Ohm's Law, Voltage and current
division rules.
Suggested Preparation
Refer to the Basic Measurement Concepts 1, 2 & 3 and Parallel & Series Circuits experiments
for review of concepts.
Overview of Basic Circuit Concepts 113
c)
d)
How would this current be divided between R2 and R3? Calculate.
Measure the current at points C and D. Verify your calculation in step (c).
ELECTRIC NETWORK THEOREMS
Educational Objectives:
To test the predictions of two important network theorems: Thevenin's Theorem and the
Maximum Power Transfer Theorem.
Background Information:
Thevenin's Theorem
Any linear active one-port network can be replaced by a single voltage source, equal to the open
circuit voltage of the one-port, in series with the network in which all independent sources have
been set to zero.
Consider the linear circuit represented by the box of the top panel of Figure 1(LAN: linear active
network) which contains assorted sources and resistors, and has a single "port" by which it can be
connected to the outside world. We attach a load resistor, RL, at the port as shown, and observe that
RL draws load current, i1, and voltage, v1, from the network.
In the center panel of Figure 1, a voltage source has been added in series with the load so as to
oppose the current flow. We have increased the voltage of this source until the current, i2, is
brought to zero. When zero current is flowing at a port, we say the port is "open circuited".
Therefore, in the center panel, the port voltage (not v2) is the open circuit voltage of the LAN, Voc.
This, by KVL, is equal and opposite to the voltage of the external source we have applied.
In the bottom panel, all independent sources inside the LAN have been turned to zero, creating a
linear passive network, LPN. This means that voltage sources have been replaced by short circuits
118 Electric Network Theorems
(zero voltage) and current sources have been replaced by open circuits (zero current). The only source
now active is the external source of the center panel, Voc. Since this is the only active source, we now
expect the current to flow in the direction shown as i3 in the bottom panel.
According to Thevenin's theorem, the load should receive the same current in the bottom panel
configuration as it did in the top panel. To prove that this is the case, apply the superposition principle.
In the top panel, with the LAN sources active and the Voc source zero, current i1 flows in the load. In
the bottom panel, with the LAN sources all zero and the Voc source active, the load
current is i3. Now, according to the superposition principle, the current flow when all sources are
active should be the sum of the currents produced by each acting alone. But this sum is zero according
to the center panel. Therefore, i1 and i3 must be equal in magnitude, but opposite in direction. If we
reverse the polarity of the Voc source in the third panel, the load receives exactly the current and
voltage it did from the original network.
Maximum Power Transfer Theorem To draw the maximum power from a resistive, LAN, the load
resistance should be set equal to the Thevenin equivalent resistance of the LAN.
Proof: Consider a LAN with Thevenin equivalent resistance Req to which a load resistor, RL is
connected, as shown in Figure 2. The power to RL is p = i2 RL.
Electric Network Theorems 119
Problem Formulation
There are three parts to this experiment. In part 1 your task is to determine, by experiment, the
value of load resistance which will draw maximum power from a LAN you will build. In part 2,
you will determine through measurements, the values of the Thevenin open circuit voltage and
equivalent resistance of your LAN, and then build a Thevenin equivalent circuit. In part 3, you
will verify the maximum power theorem and Thevenin's theorem using results of parts 1 and 2.
Procedure
The circuit you will use as the LAN is shown in Figure 3. You will be given 5 resistors, each of
which can be connected in any of the positions (except one resistor with longer leads which must
be used to reach between non-adjacent terminal posts). The 10 volt source is the lab power supply
(set to pos, l OV). The load resistor, RL, is a resistor box. You may want to use the color code on
the resistors to try to calculate the expected Thevenin values' However, such calculation is difficult
for this configuration since no two resistors are in series or in parallel.
3. Thevenin Equivalent Measurements.
a)
Disconnect the load resistor box and measure and record the LAN's open circuit voltage
across terminals a-b.
b)
Disconnect the supply voltage and replace it by a short circuit as shown in Figure I (NOTE:
Be sure to disconnect the supply before adding the short!) Use the lab ohmmeter to measure
the resistance looking back into terminals a-b with the source replaced by a short circuit.
3. Verification of the Theorems:
a)
Compare the RL value for the peak you located in Part 1-c to the Thevenin resistance
measured in Part 2.
Electric Network Theorems 121
b)
Using the open circuit voltage and equivalent resistance values measured in Part 2, construct
a Thevenin Equivalent circuit. That is, set the Lab power supply to provide the open circuit
voltage value, and set a resistor box to Rte. Connect these two in series and apply this
equivalent circuit to a second resistor box representing a load. Set the load resistance to a
few of the values used in Part l and compare the voltage provided by the equivalent circuit to
that read in part 1 for the same load.
Electric Network Theorems 123
REPORT
4.
Discussion: Were the theorems verified? If not, explain discrepancies. (Discuss reasons for
differences between expected and measured results'):
(30 pts)
126 AC Impedance
Fig. 2 depicts plots of current and voltage waveforms associated with each of these circuit
elements. Note that the current and voltage in the resistor are in phase (pass through their
maximum and minimum values at the same time), while the other two elements cause either a + or
900 phase shift between voltage and current' In the inductor, the current wave has its maximum 900
the voltage has its maximum. We say that the inductor current lags the inductor voltage by 900 . For
the capacitor, the current has its maximum 900 before the voltage. Therefore, we say that in the
capacitor, current leads the capacitor voltage by 900 .
Problem Formulation
You are to investigate the voltage and current relationships in a pure capacitance, as well as in R-L
and R-C series connected circuits. Such relationships are best expressed in a phasor diagram.
Procedure
1. Assemble the circuit shown in Figure 4. Use resistance and capacitance boxes for R and C. It is
very important that you pay attention to the proper connection of the black (ground) lead from
any of the test equipment such as the signal generator and the oscilloscope. These must always
go to the same point in a circuit under test' Since the black leads from both A and B scope inputs
are connected internally within the oscilloscope, it is only necessary to connect one of these to
the circuit.
General Procedure for all tests:
To measure impedance, we need the ratio of voltage magnitude to current magnitude, as well
as the phase angle between voltage and current. We will get the information for both voltage
and current from the oscilloscope. However, since the oscilloscope can only portray
waveforms of voltages supplied to input A or input B, we must convert the current waveform
to a voltage for viewing. We can use the resistor for this since the current and voltage of a
resistor always have exactly the same waveform. (In the series connection of Figure 4, the
same current flows in both R and C.)
For all runs: Use both A and B scope inputs and vertical MODE and select both CHI and CH2 using
switches under the screen. After gain and sweep rate adjustments, you should see two sine
waves. Identify which is voltage (across both R and C or L), and which represents
QUESTIONS
1)
For parts 2 and 3, did increasing the frequency make the circuit behave more (or less) like a
pure resistor? Explain.
(10 pts)
2)
Compare calculated C to the value selected on the lab C box. Account for differences. (10 pts)
3)
If you had a low frequency signal which contained a lot of high frequency noise, which
circuit below do you think would be best in reducing the noise?
(10 pts)
FILTERS
Executive Summary
The behavior of many circuits may be described by considering the entire circuit as a unit and
concentrating on only the input and the output (Fig. 1). The input is called the excitation and the
output is the response. Many characteristics such as amplitude, frequency, phase, power
dissipation, of the response are of interest to the designer. The frequency response of an AC circuit
describes the behavior or response to input signals at different frequencies. The study of how the
output changes with respect to changes m the frequency of the input is called frequency analysis.
The characteristics of the circuit that relates output to input as a function of frequency is called the
transfer function, H(jw).
Educational Objectives
•
•
Study frequency characteristics of some basic filters
Learn about bode plots
134 Filters
Background Information
Filters are frequency selective circuits which utilize combinations of different circuit elements whose
impedances vary with frequency in such a way that certain signals will be suppressed while other
signals will appear at the output. The circuit of Fig. 2 is a low-pass filter. If the input to this circuit is
the voltage applied across the series connection of the resistor (R) and the capacitor (C) while the
output is the voltage across the capacitor, then the transfer function for this fiIter is:
Problem Statement
Given: A circuit composed of a resistor and a capacitor.
Find: Its frequency response.
Procedure
For this experiment, you will
will be provided a VI named
the oscilloscope and makes
calculates and plots the peak
performs the measurement you
use LabVIEW to get rough sketches for the transfer functions of your filters. You
Frequency Stepper and Logger. This VI communicates with the function generator and
the function generates step through a specified set of sine wave frequencies,
to peak voltage of the oscilloscope waveform against frequency. In other words, it
Filters 137
would carry out manually by sweeping through the frequencies you specify. The control panel
for this VI is given in Fig. 8. Although the controls for this VI are well labeled and self
explanatory, a brief discussion is provided to indicate some subtle features.
The two controls in the lower left, under the Sweep Frequencies label, determine the range of frequencies to
sweep (starting and ending frequency). Under the Auto-Sweep Parameters label, two controls are provided,
one to control how much the sine frequency is incremented at each measurement (labeled Incr. (Hz)) and the
other how long to wait between measurements (labeled Read Delay (sec)). Note that if you specify the
frequency increment to be 0 Hz, the instrument goes into a logarithmic mode. In this mode, it tries to cover
the specified frequency range with larger resolution as it steps through its range. For example, if you specify a
range from 10 Hz to 10 kHz and set the frequency increment to 0, the instrument will go through 10, 20, 30,
40, 50, 60, 70, 80, 90, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 2000, 3000, 4000, 5000, 6000,
7000, 8000, 9000 and 10000 Hz. The button labeled Auto-Sweep should be kept on (pressed) to make the
measurements automatically. The button labeled Save Plot is used when one would like to save the data
displayed in the plot as an Excel file. This button should be pressed before the start of the measurements. The
lower right control (Amplitude (V)) sets the amplitude of the sine wave and should be kept at 5 V. The control
to its left selects the waveform to be applied to the circuit. This should be kept at sinusoidal (default).
Low-Pass Filter Transfer Function
1. Set up the circuit of Fig. 2 (low-pass filter) using the decade resistance and capacitance boxes and the
function generator for the AC voltage source. Monitor Vout(t), the output voltage on
Filters 139
Filters 141
LABORATORY REQUIREMENTS
Participants in this laboratory are required to complete the following computer assignments and answer
the questions distributed in the laboratory. Individual student grades will be determined by
performance in the laboratory as well as the quality and degree to which the work meets these
requirements.
Computer Assignment
1. Print out the graphs from your spreadsheets (procedure 7).
(80 pts)
QUESTIONS
1.
Band Pass filters are used to attenuate both high and low frequencies while passing a band of
frequencies in between. How would you build a Band Pass filter? (10 pts)
143
RESONANCE
Engineering has many disciplines, mechanical, electrical, materials, chemical, civil, architectural to
name a few. Though each of these areas deals with a different kind of system, there is a parallelism
between them all. This lab demonstrates one of these basic parallels using a mechanical system and
an electrical system. There is a natural frequency associated with all systems, materials, circuits,
buildings, even bridges. The strong reaction that occurs when an excitation is presented to a system at
its natural frequency is called resonance. This phenomena explains why a glass will break when a
singer hits a note of just the right frequency. In the past, disastrous results have followed planners not
considering resonance effects.
Educational Objective
•
•
•
Point out analogs among mechanical and electrical systems'
Find the natural frequency of an RLC circuit.
Define resonance and demonstrate the effect of changes in circuit parameters on resonant
frequency.
Background Information:
All periodically oscillating systems have an associated natural frequency determined by the system's
components and the configuration. The classic example of a mechanical oscillating system is shown
in Fig' 1 below.
Resonance 14 5
Fig. 2 shows the correspondence between electrical and mechanical systems. The external
oscillations are counterpart to the AC generator while the mass is analogous to compliance or
capacitance, the spring is like an inductor, and the dashpot damping is modeled like the losses in a
resistor.
Mechanical systems and electrical circuits have natural frequencies associated with them also. In
the circuit below the resonant frequency is given as:
When the generated frequency is equal to the natural frequency the circuit resonates causing the potential
differences and the current to have maximum amplitude. Resonance curves are made for forced oscillations
using varying values of resistance. An example is given in Fig. 3
In Fig. 2 the electrical system is a series RLC circuit. The resonant frequency, given in Eq. 7, remains the same
if the elements are rearranged into a parallel combination such as shown in Fig. 4. The new circuit will
experience a resonance effect at the same frequency.
The difference is that for the parallel combination the resonant frequency causes the total current to reach its
MINIMUM. This parallel resonance is sometimes called antiresonance due to its minimizing rather than
maximizing the total current.
Applications:
MICROWAVE: Just as every material and configuration of elements has a resonant frequency so do water
molecules. At this frequency the molecules vibrate and rotate. This action produces heat. The waves emitted in
your microwave oven at home are set to this frequency. These microwaves do not have the same effect on other
materials such as porcelain, plastic, etc. This allows the heating of food containing water without heating the
container.
Problem Statement:
Given: RLC circuit configurations
Find: Resonant frequency both by computation and experimentally.
is also maximum. By solving for the power at resonance, the current at which half-power occurs
can be found and thus the associated frequency.
Procedure
All indicated measurements are to be recorded on a spreadsheet in Excel. Refer to computer
assignment #1. It is important to label data correctly! The spreadsheet constitutes 40% of the grade
for this experiment.
Resonance 147
Preparatory Calculations & Work - Series Resonance
1) Pick up an inductor. Read off its inductance value from its mount
148 Resonance
Sinusoidal voltage: 2.5 V (p-p), channel 1 setting: 100 mV/div, start frequency: 100 Hz, end frequency: 15000
Hz, frequency step: 100 Hz.
Resonance 149
REPORT
Your report should contain the following computer assignments as well as solutions to the
questions given out in lab.
Computer Assignment
1. Print out the graph for step3 with appropriate labels. (30 points)
2. Print out the antiresonance curve of step 6.
(40 points)
TRANSFORMERS
A transformer is a coupled electronics circuit, where the distinguishing feature is that the
coupling between the two loops is due to magnetic flux rather than electrical current.
Educational Objectives:
•
•
•
Verify transformer action
Project and build a step-down transformer
Demonstrate mutual inductance
Applications
•
•
•
Radio, television, home entertainment
Electrical power transmission
Power supplies for electrical instruments
Background Information
A transformer is created when two inductors are arranged so that some of the flux of either of the
two is linked with the other: This flux linkage is obtained by building the inductors on a common
dielectric core. The core can simply be a hollow structure (air core transformer), or it can be a
magnetic material such as ferrite.
Transformer operation
From Faraday's Law we know that a voltage is induced in a coil which contains a time-varying
magnetic flux, regardless of the source of the flux' Let us therefore consider a second coil, having
N2 turns, positioned in the neighborhood of the first coil, having N1 turns, as shown in Fig Ia. In
this case we have formed a simple transformer having two pairs of terminals in which coil 1 is
referred to as the primary winding (the one that is driven by a source) and coil 2 as the secondary
winding (the one which connects to the load).
Transformers 15 5
It is clear that the voltages consist of self-induced voltages due to the inductances L1 and L2 and
mutual voltages due to the mutual inductance M.
Ideal Transformer
Procedure
A. Air Core Step-down Transformer
1. Cut approximately 19 feet of wire and wind 100 turns on the bobbin' This first winding is the
primary coil. (i.e. Np = 100), (See Fig. 2.).
Note: make sure you remove (strip) insulation from both ends. Leave enough extra wire on each
end so future electrical connections can be made easily.
Transformers 15 9
ADDENDUM 1: A PROCEDURE TO DETERMINE MUTUAL INDUCTANCE
MORE ACCURATELY
160 Transformers
ADDENDUM 2: A PROCEDURE TO DETERMINE INDUCTANCE OF A
COIL
Transformers 161
REPORT
Your report should contain the following computer assignments as well as solutions to the questions
given out in lab.
Computer Assignment
QUESTIONS
1.
2.
A') What effect would greatly increasing the frequency have on Vout?
(5 pts)
B.) What effect would greatly decreasing the frequency have on Vout?
(5 pts)
If the diameter of L1 and L2 were increased with everything else remaining the same, how
would this affect the transformer?
(10
pts)
4.
Why do we use iron cores in transformers?
(10 pts)
Appendix DMM1 163
Appendix DMM1
Appendix PPS1 165
APPENDIX PPS1: GENERAL INSTRUCTIONS FOR OPERATING THE POWER
SUPPLY
A power supply does what its name implies: supply power. However, in the electronics literature
the name Power Supply is identified with those devices that convert AC electrical power to DC
electrical power. This narrow definition leaves out devices such as batteries, generators,
transformers although they also supply power to various electrical circuits. Most electronic
instruments arc equipped with their own power supplies that convert the lines voltage (AC) to the
operating DC voltage of the instrument and provide enough current for the instrument to run.
(Remember power is voltage times current, P = VI.) The power supply you would see in a
laboratory is one whose output voltage can be programmed and one which can maintain that
voltage with some measure of accuracy over the range of current values it is capable of delivering.
In other words, they are elaborate constant voltage sources. Some of them can also be operated in a
constant current source mode.
Tektronix PS 5010 Programmable Power Supply
i)
ii)
First choose the type of output, either current or voltage. (See Fig. PPS 1. 1, key 1 or 2).
The output of the PPS. has three terminals given in Fig. PPS 1.1 as neg., pos., and neutral'
The neutral (common) can be considered electrically as 0 Volts. Both positive and
negative are measured with respect to this neutral point or 0 V. Positive voltages are up to
32 volts and negative to -32 volts.
166 Appendix PPS1
iii)
iv)
*What is the voltage potential difference from the positive ten-ninal to the negative if
+32V and -32V are used respectively?
To enter either positive or negative values first push SUPPLY SELECT (key 3). Then
push the pos or neg (key 4 or 5) followed by the numeric value (from number pad)
including the decimal point. Upon completion of the number you must enter the data by
pushing ENTER (key 6).
Make all necessary connections' Double Check your connections. Turn on the PPS.
with key 7. A flowchart is given below (Flowchart PPS 1.1).
Appendix FG1 167
APPENDIX FG1: GENERAL INSTRUCTIONS FOR OPERATING THE FUNCTION
GENERATOR
A function generator is an electronic device that can produce various periodic functions as a
voltage variation with time. The most common voltage variations (waveforms) are sinusoid,
square, triangular and sawtooth. The user can specify the amplitude of the voltage variation and its
frequency.
Tektronix AFG5101
The AFG 5101 is a digital function generator. Its range of frequencies is: 0.01 Hz to 12MHz.
Figure 6.3 is the illustration of AFG 5101. Note the five designations on the face of the function
generator.
Designations on function generator:
Designation 1: PARAMETER keys define the waveforms selected for the output Each key will
define the waveform selected for output. Each key will display its present value. To
change this value use the DATA keyboard.
• _ FREQ displays the present frequency.
Appendix SCI 171
APPENDIX SCI: GENERAL INSTRUCTIONS FOR OPERATING THE
OSCILLOSCOPE
Brief Introduction to the Scope - TEK 2424L
When working with time varying voltages, it is often difficult to envision the voltage waveform
from amplitude and time data exclusively. The data must be plotted and then evaluated. It is
possible to obtain a graphical representation directly by using an oscilloscope (or "scope". The
oscilloscope displays a plot of the amplitude of a time varying voltage waveform with respect to
(w.r.t.) time. For a sinusoidal input the screen of the oscilloscope would display a plot like the top
one in Fig. 2, AC Signals. Its axes are voltage and time.
For this lab you will view a sine-wave on the scope. The wave will be generated by the function
generator. Check to see if its parameters (i.e. Volt/div, sec/div) are compatible with those of the
function generator (i.e. amplitude, frequency). Consider the divisions on the screen as lines on a
piece of graph paper. The vertical axis is in volts and is defined by volts/division. Time is the
independent variable on the horizontal axis read in sec/division. In this sense the scope as more
restrictive than plotting by hand. However, consider the necessary procedure to plot the waveform
by hand (i.e. collection of data). How would you measure this voltage?
You may turn on the scope with the POWER button (#1 in Fig. SC1.1). The scales of each axes is
displayed at the top of the screen.
172 Appendix SC1
seconds. of this waveform. (How many cycles would that be?) The display is similar to the Etch a
-Sketch toy in that it has two independent drives. One drive is for the horizontal direction, the other is
for the vertical. The scope generates its own horizontal linear sweep to produce a time base.
Horizontal and Vertical controls are enclosed in boxes on the front panel. To move the waveform use
the position buttons in each box. (See Figure SC1.1)