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Introduction to Engineering

Experimentation

Murat Tanyel Robert Quinn

Drexel University

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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. Print out your spreadsheets (procedures 1-4). Print out any graph that you were required to plot. (50 pts) 2. 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)

3. 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)


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 in 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


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.

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.

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.

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: Series and parallel circuit configurations; an unknown resistance Find: 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. Create a spreadsheet to record all data. Be sure to label every section. (40 pts) 2. 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. Turn on the power for the function generator, DMM and the oscilloscope. 2. 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.

3. 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. 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)

2. 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: Temperature range of 3 temperature transducers (thermometer, thermistor, and

thermocouple) Find.- Calculate the sensitivity, thermal response and linear range of each transducer. Determine: 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)


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.


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


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.

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

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:

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. Create a spreadsheet in Excel and enter all data. Include calculation term, power output of hot pot, interval readings, times, etc. (40 pt s)

2. 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. (10 pts) a) 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 h 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. 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


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: A variety of light sources and detectors, spectrometer, and monochrometer. Find: The sensitivity range, and dynamic response of the photo detectors. Compare: 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

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.

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.

Optics: Sources & Detectors 89

REPORT


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!


REPORT


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. (35 pts) 2. Make a plot of frequency vs. voltage for step 2. (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)


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) 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. 2) Set the reference input to 1'5 mV' How long does it take to reach steady state? 3) Place a fan at about 30 cm from the heating element. Turn it on at the LOW setting. Describe

what happens. 4) 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?



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) How would this current be divided between R2 and R3? Calculate. d) 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.


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.


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 use LabVIEW to get rough sketches for the transfer functions of your filters. You will be provided a VI named Frequency Stepper and Logger. This VI communicates with the function generator and the oscilloscope and makes the function generates step through a specified set of sine wave frequencies, calculates and plots the peak to peak voltage of the oscilloscope waveform against frequency. In other words, it performs the measurement you

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 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.

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.

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.

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:

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


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


QUESTIONS 1. 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)

2. 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) First choose the type of output, either current or voltage. (See Fig. PPS 1. 1, key 1 or 2). ii) 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

*What is the voltage potential difference from the positive ten-ninal to the negative if +32V and -32V are used respectively?

iii) 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).

iv) 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)

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