Electricity Fundamentals

Transcription

1 Refrigeration and HVAC Electricity Fundamentals F0

2 Order no.: First Edition Revision level: 03/2016 By the staff of Festo Didactic Festo Didactic Ltée/Ltd, Quebec, Canada 2015 Internet: Printed in Canada All rights reserved ISBN (Printed version) ISBN (CD-ROM) Legal Deposit Bibliothèque et Archives nationales du Québec, 2015 Legal Deposit Library and Archives Canada, 2015 The purchaser shall receive a single right of use which is non-exclusive, non-time-limited and limited geographically to use at the purchaser's site/location as follows. The purchaser shall be entitled to use the work to train his/her staff at the purchaser s site/location and shall also be entitled to use parts of the copyright material as the basis for the production of his/her own training documentation for the training of his/her staff at the purchaser s site/location with acknowledgement of source and to make copies for this purpose. In the case of schools/technical colleges, training centers, and universities, the right of use shall also include use by school and college students and trainees at the purchaser s site/location for teaching purposes. The right of use shall in all cases exclude the right to publish the copyright material or to make this available for use on intranet, Internet and LMS platforms and databases such as Moodle, which allow access by a wide variety of users, including those outside of the purchaser s site/location. Entitlement to other rights relating to reproductions, copies, adaptations, translations, microfilming and transfer to and storage and processing in electronic systems, no matter whether in whole or in part, shall require the prior consent of Festo Didactic. Information in this document is subject to change without notice and does not represent a commitment on the part of Festo Didactic. The Festo materials described in this document are furnished under a license agreement or a nondisclosure agreement. Festo Didactic recognizes product names as trademarks or registered trademarks of their respective holders. All other trademarks are the property of their respective owners. Other trademarks and trade names may be used in this document to refer to either the entity claiming the marks and names or their products. Festo Didactic disclaims any proprietary interest in trademarks and trade names other than its own.

3 Safety and Common Symbols The following safety and common symbols may be used in this manual and on the equipment: Symbol Description DANGER indicates a hazard with a high level of risk which, if not avoided, will result in death or serious injury. WARNING indicates a hazard with a medium level of risk which, if not avoided, could result in death or serious injury. CAUTION indicates a hazard with a low level of risk which, if not avoided, could result in minor or moderate injury. CAUTION used without the Caution, risk of danger sign, indicates a hazard with a potentially hazardous situation which, if not avoided, may result in property damage. Caution, risk of electric shock Caution, hot surface Caution, risk of danger Caution, lifting hazard Caution, hand entanglement hazard Notice, non-ionizing radiation Direct current Alternating current Both direct and alternating current Three-phase alternating current Earth (ground) terminal Festo Didactic III

4 Safety and Common Symbols Symbol Description Protective conductor terminal Frame or chassis terminal Equipotentiality On (supply) Off (supply) Equipment protected throughout by double insulation or reinforced insulation In position of a bi-stable push control Out position of a bi-stable push control IV Festo Didactic

5 Table of Contents Preface... XV About This Manual... XVII To the Instructor... XIX Introduction Basic Concepts of Electricity... 1 DISCUSSION OF FUNDAMENTALS... 1 What is electricity?... 1 A brief history of electricity... 2 Electrical circuit... 2 Types of electrical power sources... 3 Symbols and circuit diagrams... 4 Safety rules... 7 Exercise 1 Introduction to the Training System... 9 DISCUSSION... 9 The training system and its components... 9 Installation of a module in the workstation Connection leads Training system components Power Source module Control Transformer module PROCEDURE Installation of the modules in the workstation Familiarization with the operation of the Power Source module Set up and connections Exercise 2 Switches DISCUSSION Introduction to switches Switch types Toggle switch Push-button switch Selector switch Switch configurations Single-pole single-throw switch Double-pole single-throw switch Single-pole double-throw switch Double-pole double-throw switch Introduction to the indicator light Training system modules Push Buttons module Switches module Indicator Lights module Festo Didactic V

6 Table of Contents PROCEDURE Setup Push-button switches Normally open push-button switch Normally closed push-button switch Toggle switches Single-pole single-throw toggle switch Single-pole double-throw toggle switch Exercise 3 Series and Parallel Circuits DISCUSSION Introduction to series and parallel circuits Series circuits Parallel circuits Three-way circuit PROCEDURE Setup Series and parallel circuits Series circuit indicator light controlled using two toggle switches connected in series Parallel circuit indicator light controlled using two toggle switches connected in parallel Series-parallel circuit indicator light controlled using a toggle switch connected in series with two toggle switches connected in parallel Circuit representing the interior lights in a car Exercise 4 Voltage, Current, and Measuring Instruments DISCUSSION The notion of current The notion of voltage Voltage and current: an analogy for better comprehension Voltage measurement using a voltmeter Current measurement using an ammeter Introduction to the multimeter Introduction to the clampmeter Introduction to alternating current AC voltage and current sine waves Frequency and period of a sine wave Peak value and RMS value of a sine wave Circuit parameter measurements in ac circuits Measuring voltage Measuring current VI Festo Didactic

7 Table of Contents PROCEDURE Setup Voltage measurements Current measurements Voltage and current measurements in a parallel circuit Exercise 5 Resistance and Ohm s Law DISCUSSION The notion of resistance Conductors and insulators Resistance measurement using an ohmmeter Ohm s law Short circuits, open circuits, and continuity Short circuits Open circuits Continuity The notion of electrical power The resistor Resistor color code How to test a resistor The variable resistor Training system module Resistors module PROCEDURE Setup Resistance measurements using an ohmmeter Troubleshooting switches using an ohmmeter Ohm s law and power calculations Circuit containing a 50 Ω resistor Circuit containing a 250 Ω resistor Testing continuity of a circuit using a test light Exercise 6 Solving Series Circuits and Kirchhoff s Voltage Law DISCUSSION Calculating the equivalent resistance in series circuits Kirchhoff s voltage law Voltage dividers Voltage divider consisting of two resistors Voltage divider consisting of a rheostat and a resistor Voltage divider consisting of a potentiometer Festo Didactic VII

8 Table of Contents PROCEDURE Setup Equivalent resistance and Kirchhoff s voltage law circuit with two resistors Solving the circuit through mathematical calculations Solving the circuit through circuit measurements Equivalent resistance and Kirchhoff s voltage law circuit with three resistors Solving the circuit through mathematical calculations Solving the circuit through circuit measurements Voltage divider consisting of two resistors Solving the voltage divider through mathematical calculations Solving the voltage divider through circuit measurements Light intensity control circuit implemented using a resistor and a selector switch Exercise 7 Solving Parallel and Mixed Circuits, and Kirchhoff s Current Law DISCUSSION Calculating the equivalent resistance in parallel circuits Kirchhoff s current law Solving mixed circuits Example Example Printed circuit boards Training system module Printed Circuit Board module PROCEDURE Setup Calculating and measuring the voltages and currents in a parallel circuit Solving the circuit through mathematical calculations Solving the circuit through circuit measurements Calculating and measuring the voltages and currents in a mixed circuit Solving the circuit through mathematical calculations Solving the circuit through circuit measurements Light intensity control circuit connected in parallel with a resistor Kirchhoff s voltage law Kirchhoff s current law Resistance measurements on a printed circuit board Voltage measurements on a printed circuit board Circuit A Circuit B VIII Festo Didactic

9 Table of Contents Exercise 8 Capacitors DISCUSSION Introduction to capacitors Operation of polarized capacitors Capacitance and voltage rating of polarized capacitors Capacitance measurement using a capacitance meter Calculating the capacitance of series and parallel capacitors Resistor-capacitor (RC) circuits Charging the RC circuit Discharging the RC circuit Applications of polarized capacitors Operation of non-polarized capacitors Capacitive reactance Equivalent capacitance and capacitive reactance of series and parallel ac capacitors Capacitor types How to test a capacitor Training system module Capacitors / Inductor module PROCEDURE Setup Safety discharge before using the capacitors Measuring the capacitance of a capacitor Determining the capacitance and capacitive reactance of an ac capacitor Connecting a circuit containing a capacitor Calculating the capacitance of series capacitors Calculating the capacitance of parallel capacitors Exercise 9 Electromagnetism and Inductors DISCUSSION Magnetism, magnets, and magnetic field Electromagnetism and electromagnets The solenoid Inductors Operation of inductors in dc circuits Operation of inductors in ac circuits Inductance Inductive reactance Equivalent inductance and inductive reactance of series and parallel inductors Applications of inductors Festo Didactic IX

10 Table of Contents PROCEDURE Setup Troubleshooting an inductor using an ohmmeter Calculating the inductive reactance of an inductor Connecting a circuit containing an inductor Calculating the reactance of inductors connected in series Calculating the reactance of inductors connected in parallel Exercise 10 Transformers DISCUSSION Introduction to transformers Transformer operation Transformer turns, voltage, and current ratios Step-up and step-down transformers Step-up transformers Step-down transformers Transformer voltage regulation Magnetizing current Types of transformers Control transformers Power transformers Isolation transformers Training system module Control Transformer module PROCEDURE Setup Calculating the ratios and ratings of a transformer Troubleshooting a transformer Measuring the ratios and ratings of a transformer Transformer voltage regulation Exercise 11 Relays and Contactors DISCUSSION Introduction to relays Operation of dc relays Operation of ac relays Relay applications Contactors Two-wire and three-wire control circuits Two-wire control circuit Three-wire control circuit X Festo Didactic

11 Table of Contents Training system modules Relays module Contactors module Residential Bimetallic Thermostat module PROCEDURE Setup Troubleshooting a relay Controlling two indicator lights using a relay Two-wire control circuit Thermostat operation Heating element controlled using a thermostat and a contactor Thermostat heat anticipator setting Contactor push-to-test button Three-wire control circuit Circuit representing a blower motor controlled using start/stop push buttons and a contactor Exercise 12 Semiconductors DISCUSSION Introduction to semiconductors The diode Operating principles of a diode Characteristic voltage-current curve of a diode Diode types Procedure to test a diode using a multimeter Single-phase half-wave rectifier The light-emitting diode (LED) PROCEDURE Setup Testing a diode using a multimeter Single-phase half-wave rectifier Operation without rectification Operation with rectification Operation with rectification and filtering Light-emitting diode Festo Didactic XI

12 Table of Contents Exercise 13 Electrical Distribution DISCUSSION Introduction to the power network and distribution network Three-phase circuits Phase sequence Wye and delta configurations Distinction between line and phase voltages, and line and phase currents Circuit protection Fuses Circuit breakers Magnetic circuit breakers Thermal circuit breakers Ground fault circuit interrupter GFCI breaker Circuit breaker symbols Electrical panels Disconnect switch Power circuit versus control circuit Power circuit Control circuit Training system modules Circuit Breaker module Disconnect Switch module PROCEDURE Setup Operation of a fuse Operation of a circuit breaker Circuit with an excessive load Short-circuited circuit breaker Resistance, current, and voltage measurements in a disconnect switch Current measurement Voltage measurement Exercise 14 Troubleshooting Methods DISCUSSION Introduction to troubleshooting The voltmeter method The ohmmeter method PROCEDURE Setup Guided troubleshooting of a heating circuit Voltmeter method Ohmmeter method XII Festo Didactic

13 Table of Contents Unguided troubleshooting of a circuit representing a blower motor controlled using start/stop push buttons and a contactor Unguided troubleshooting of a circuit representing a heating/cooling system controlled using a selector switch and a thermostat Appendix A Equipment Utilization Chart Appendix B Glossary of New Terms Appendix C Fault Switches Index of New Terms Bibliography Festo Didactic XIII

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15 Preface Electricity is used in all aspects of modern society, be it in residential, commercial, or industrial applications. It is used for lighting, heating, refrigerating, ventilating, transport, communications, computations, and a host of other functions. While most power networks in the world operate in alternating current, direct current is also commonly used in applications that require low voltage or that use batteries as a power source. The Electricity Fundamentals Training System, Model 3460, is a complete introduction to electricity and to the electrical components used in HVAC systems. Through this program, you will learn how to connect, perform measurements, calculate, and troubleshoot circuits. Although electricity has been known to Man since ancient times, it is only in modern times that it began to be commonly used as a power source (photo courtesy of Postdlf). We invite readers of this manual to send us their tips, feedback, and suggestions for improving the book. Please send these to did@de.festo.com. The authors and Festo Didactic look forward to your comments. Festo Didactic XV

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17 About This Manual Manual objectives When you have completed this manual, you will be familiar with the basic concepts of electricity. You will be able to define voltage, current, resistance, power, and capacitance, and know how to measure these parameters using their respective measuring instruments. You will know the difference between dc and ac circuits. You will be introduced to the most common components used: power sources, switches, resistors, capacitors, inductors, solenoids, and relays. You will know what series and parallel circuits are, and be able to calculate the equivalent resistance and capacitance of series and parallel components. You will be familiar with Ohm s law, as well as Kirchhoff s voltage and current laws, and be able to apply these laws to electrical circuits. You will be introduced to the notions of magnetism and electromagnetism. Safety considerations Safety symbols that may be used in this manual and on the equipment are listed in the Safety Symbols table at the beginning of the manual. Safety procedures related to the tasks that you will be asked to perform are indicated in each exercise. Make sure that you are wearing appropriate protective equipment when performing the tasks. You should never perform a task if you have any reason to think that a manipulation could be dangerous for you or your teammates. Systems of units Units are expressed using the International System of Units (SI) followed by the units expressed in the U.S. customary system of units (between parentheses). Festo Didactic XVII

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19 To the Instructor You will find in this Instructor Guide all the elements included in the Student Manual together with the answers to all questions, results of measurements, graphs, explanations, suggestions, and, in some cases, instructions to help you guide the students through their learning process. All the information that applies to you is placed between markers and appears in red. Accuracy of measurements The numerical results of the hands-on exercises may differ from one student to another. For this reason, the results and answers given in this manual should be considered as a guide. Students who correctly performed the exercises should expect to demonstrate the principles involved and make observations and measurements similar to those given as answers. Festo Didactic XIX

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21 Sample Exercise Extracted from the Student Manual and the Instructor Guide

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23 Exercise 5 Resistance and Ohm s Law EXERCISE OBJECTIVE When you have completed this exercise, you will be familiar with the notion of resistance, and know how to measure this parameter using an ohmmeter. You will be introduced to Ohm s law, and be able to calculate voltage, current, and resistance in electrical circuits. You will also know the concepts of conductors, insulators, short circuits, open circuits, and continuity in electrical circuits. You will also be familiar with the concept of power. Finally, you will be introduced to the Resistors module. DISCUSSION OUTLINE The Discussion of this exercise covers the following points: The notion of resistance Conductors and insulators Resistance measurement using an ohmmeter Ohm s law Short circuits, open circuits, and continuity Short circuits. Open circuits. Continuity. The notion of electrical power The resistor Resistor color code. How to test a resistor. The variable resistor Training system module Resistors module. DISCUSSION The notion of resistance Together with voltage and current, another notion is necessary to understand electricity: resistance. The resistance of a material represents the opposition of the material to current flow. The higher the resistance of the material, the more it prevents the flow of charge carriers. Resistance is measured in ohms (Ω) after German physicist and mathematician Georg Ohm who discovered the relationship between voltage, current, and resistance. In this manual, resistance is denoted using the letter. It is also possible to use the analogy of the water circuit to better understand the notion of resistance. In this analogy, resistance represents the size of the water pipe, as shown in Figure 62. Festo Didactic

24 Exercise 5 Resistance and Ohm s Law Discussion Low water pressure High water pressure Low voltage Power source (V) High voltage Pump Resistance (R) Water flow Current (I) Water reservoir Ground (a) Water circuit analogy Figure 62. Water circuit analogy. (b) DC circuit The same relationships are true between electrical charge, voltage, current, and resistance if we consider that electrical charge is equal to water capacity, voltage is equal to water pressure, current is equal to water flow, and resistance is equal to the size of the discharge tube. Consider, for example, the batteries connected to indicator lights shown in Figure 63. The battery in Figure 63a is connected to a circuit having a low resistance. This can be due to multiple factors, such as larger wires, wires made from a low-resistance material, or the indicator light having a low resistance. On the other hand, the battery in Figure 63b is connected to a circuit having a high resistance. High current Low current Charged battery Charged battery Voltage Voltage (a) Battery connected to a low-resistance circuit (b) Battery connected to a high-resistance circuit Figure 63. Relationships between current and resistance in circuits connected using wires with different resistance values. 76 Festo Didactic

25 Exercise 5 Resistance and Ohm s Law Discussion Conductors and insulators Depending on their resistance, materials can be classified in two categories: conductors and insulators. Conductors have a low resistance value, which means that they easily allow the flow of current. Examples of good conductors include most metals, with copper being by far the most commonly used. Atoms in a conductive material have their outer electron(s) loosely bonded. Some of those electrons would gladly propagate through the conductor lattice in the presence of an external force such as the one created by a electric field. Insulators, on the other hand, have a high resistance value, which means that they impede or prevent the flow of charge carriers. The outer electrons of the atoms in an insulator are tightly bound, which prevents them to move freely and thus prevents current flow. Examples of good insulators include glass, paper, Teflon, most plastics, and ceramic. Insulators are used in applications where preventing the flow of electrical current is required, such as in circuit boards, in electrical wire sleeves and coating, and to insulate transmission lines. Resistance measurement using an ohmmeter Resistance is measured using an ohmmeter. Just like a voltmeter, an ohmmeter measures the resistance between two points in a circuit. Because of this, it is necessary to connect the ohmmeter across (i.e., in parallel with) the two points where resistance is to be measured, such as across the terminals of a load. This is shown in Figure 64. In the figure, the indicator light has a resistance of 25 Ω. Therefore, when an ohmmeter is connected in parallel with the indicator light, it indicates a resistance of 25 Ω. Ohmmeter 25 Ω Indicator light 25 Ω COM + Figure 64. Using an ohmmeter to measure the resistance of an indicator light. An ohmmeter operates by applying a small voltage across the terminals to which it is connected, then measuring the current flowing through it. Using Ohm s law (covered in the next section of this exercise), the ohmmeter then calculates the resistance across its terminals. Due to its mode of operation, it is very important to use an ohmmeter only in circuits whose power source is removed. Doing otherwise could seriously damage the ohmmeter, as well as providing inaccurate measurements. Festo Didactic

26 Exercise 5 Resistance and Ohm s Law Discussion Just like all other components in an electrical circuit, ohmmeters have a circuit diagram symbol. The symbol shown in Table 11 is used in this manual to represent an ohmmeter. Table 11. Ohmmeter symbol. Component Symbol Ohmmeter Representing the ohmmeter in Figure 64 using its circuit diagram symbol results in the following circuit. Indicator light Figure 65. Using an ohmmeter to measure the resistance of an indicator light. Ohm s law The mathematical relationship between voltage, current, and resistance is credited to Georg Ohm and therefore is called Ohm s law. This law is expressed below: (5) where is the current flowing in a conductor, expressed in amperes (A) is the voltage applied across the conductor, expressed in volts (V) is the resistance of the conductor, expressed in ohms (Ω) Ohm s law can be reformulated in the following two equations: (6) (7) As these equations show, whenever two of the three parameters (voltage, current, and resistance) of a conductor or circuit are known, the other parameter 78 Festo Didactic

27 Exercise 5 Resistance and Ohm s Law Discussion can be calculated. These equations also show that, for a given resistance, the current flowing in a conductor or circuit is directly proportional to the voltage applied to it. For example, if the voltage doubles, the current also doubles. Consider, for example, the circuit shown in Figure 66 of a power source connected to an indicator light. Suppose that we know two of the three parameters of the circuit and that we want to calculate the third using Ohm s law. The following three cases show an example for each possible missing parameter (current, voltage, and resistance, respectively). If the power source voltage is equal to 24 V and the resistance of the indicator light is equal to 50 Ω, it is possible to calculate the source current flowing in the circuit using the following equation: Ω 0.48 Alternatively, if the source current flowing in the circuit is equal to 0.8 A and the resistance of the indicator light is equal to 62.5 Ω, it is possible to calculate the power source voltage using the following equation: Ω 50 Finally, if the power source voltage is equal to 100 V and the source current flowing in the circuit is equal to 0.25 A, it is possible to calculate the indicator light resistance using the following equation: Ω Power source Indicator light Figure 66. Power source connected to an indicator light. Short circuits, open circuits, and continuity Now that we are able to calculate the current using Ohm s law, we can look at three important notions related to the resistance of a circuit: short circuits, open circuits, and continuity. Festo Didactic

28 Exercise 5 Resistance and Ohm s Law Discussion Short circuits A short circuit occurs when electrical current is allowed to flow in a circuit along a path that was not at first intended, most often along a path whose resistance is much lower than that of the normal path. A typical short circuit involves bypassing the load altogether, thus making the circuit resistance tend toward 0 Ω. Using Ohm s law for calculating current ( /), it is easy to calculate that, for a given voltage, a resistance that tends toward 0 Ω causes the current to increase to a very high value. Consider, for example, the circuit in Figure 67 showing a power network (represented by the transmission lines and power equipment) supplying electrical current to a domestic house. To power source House rated current To power source Short circuit Power equipment Power equipment Very high current House rated current To power source To power source (a) Circuit without short circuit (a) Circuit with short circuit Figure 67. Circuits illustrating the effects of a short circuit. In Figure 67a, current passes through the house and is therefore limited by the house resistance (i.e., by the combined resistance of all electrical equipment in the house). In Figure 67b, however, a short circuit is added that enables current to flow without passing through the house. This could represent, for example, a tree that fell on the transmission lines, causing the two lines to connect. When following the short circuit, current is limited only by the wire resistance, which is very low (wires are designed to prevent the flow of current as little as possible). Because of this, while current will continue to flow normally in the house, an extremely high current will flow in the short circuit. Such a current causes the wires to overheat and could potentially damage the power equipment. Short circuits are thus highly undesirable. It is possible to identify a short circuit between two points in a circuit by measuring the resistance across these two points using an ohmmeter. If the ohmmeter indicates that the resistance across the two points is equal to 0 Ω, or very close to it, a short circuit is present between the points. In that case, verify the circuit connections to locate and remove the short circuit. 80 Festo Didactic

29 Exercise 5 Resistance and Ohm s Law Discussion Open circuits An open circuit occurs when there is no longer any path for current to flow in a circuit. In other words, the circuit resistance is infinite. Using Ohm s law for calculating current ( /) confirms that, when the circuit resistance is infinite, no current flows through it. Open circuits can happen voluntarily, such as when a switch is set to its open state. Open circuits can also happen by accident, either due to faulty connections or to malfunctioning equipment. A common example of malfunctioning equipment causing an open circuit is a burned out light bulb. This happens because the tungsten wire breaks, thereby removing any contact between the conducting wires and causing the light bulb to be in open circuit condition. It is possible to identify an open circuit between two points in a circuit by measuring the resistance across those two points using an ohmmeter. If the ohmmeter indicates that the resistance across the two points is infinite (or overload), an open circuit is present between the points. Continuity Continuity between two points in a circuit simply indicates that electrical current can flow between the two points and therefore that the circuit is not open. It is possible to determine whether there is continuity between two points in a circuit by measuring the resistance across these two points using an ohmmeter. If the ohmmeter indicates that the resistance across the two points is anything but infinite, there is continuity between the points. Testing for continuity is an important tool when troubleshooting (i.e., when searching for faults in) faulty circuits. It enables the location of wrongly connected wires and malfunctioning equipment. When no ohmmeter is available for continuity testing, it is also possible to setup a small continuity testing circuit such as the one in Figure 68. Terminals A and B of this test light circuit are connected to each of the two points between which continuity is to be measured. When the power source is turned on, the indicator light turns on if there is continuity between the two points and remains turned off if not. The measuring instrument called a continuity tester basically consists of standard batteries, and a buzzer or a small light. Indicator light A Power source B Figure 68. Indicator light circuit used for testing continuity. Festo Didactic

30 Exercise 5 Resistance and Ohm s Law Discussion Figure 69 shows a circuit where continuity can be measured at different points in the circuit using an ohmmeter. Note that the switches are considered to be in the state in which they are shown in the circuit and the power source is turned off. A B C D E Power source F G H Indicator light I Figure 69. Circuit for measuring continuity between different points. Continuity is examined in the following points: B-C: There is no continuity between these points because the toggle switch is in its open state, thereby preventing current flow. D-E: There is no continuity between these points because the NO pushbutton switch is in its open state, thereby preventing current flow. F-G: There is continuity between these points because the NO pushbutton switch is in its closed state, thereby allowing current flow. A-H: There is continuity between these points because, even though two of the three switches are in their open state, one is in its closed state, thereby allowing current flow. H-I: Normally, there is continuity between the terminals of the indicator light because this device allows current flow (it has a definite current value). However, the device can possibly malfunction (such as if it is burned out) and prevent current flow. In this case, there would be no continuity. The notion of electrical power Power is defined as the rate at which work is produced. Power thus depends on time. Electrical power is measured in watts (W) after Scottish inventor and mechanical engineer James Watt, who developed the concept of horsepower. Power is usually denoted using the letter, and can be measured using a wattmeter. Wattmeters, however, are less common than voltmeters, ammeters, and ohmmeters and are not covered in this manual. You will see later that power can be calculated using the other circuit parameters. 82 Festo Didactic

31 Exercise 5 Resistance and Ohm s Law Discussion The electrical power supplied by a power source depends on the power source voltage and current. Similarly, the electrical power dissipated by a load depends on the voltage that is applied to it and on the current that flows through it. Both can be calculated using the following equation. (8) where is the electrical power, expressed in watts (W) is the voltage of the power source or applied to the load, expressed in volts (V) is the current of the power source or flowing through the load, expressed in amperes (A) When used in conjunction with Ohm s law, it is possible to calculate any parameter between voltage, current, resistance, and power, as long as at least two of these parameters are known. All possible variants of the equation are summarized in the following chart. Each parameter in the center is equal to each expression located in its quarter of the circle. Figure 70. Chart for calculating voltage, current, resistance, and power from any two other parameters. Festo Didactic

32 Exercise 5 Resistance and Ohm s Law Discussion Consider, for example, the circuit shown in Figure 71 of a power source connected to an indicator light. Power source Indicator light Figure 71. Circuit for power calculations. If the voltage applied to the indicator light is equal to 40 V and the resistance of the indicator light is equal to 50 Ω, it is possible to calculate the power supplied to the indicator light using the following equation: Ω 32 W Alternatively, if the indicator light has a resistance of 25 Ω and it consumes a power of 40 W, it is possible to calculate the current flowing in the circuit using the following equation: 40 W 25 Ω It is also possible to calculate the power rating of the power source from its voltage and current ratings. For example, if its voltage rating. is equal to 24 V and its current rating. is equal to 4 A, the power source rating. can be calculated using the following equation: A 96 W This value indicates the maximal power that the power source can supply to a load. Using a power source to supply more power than its ratings can cause overheating and seriously damage the power source. The resistor Resistors are common electrical components that are designed to have a specific resistance value. Resistors are very common elements of electronic circuits, being found in almost all electronic devices. Figure 72 shows a selection of resistors of various sizes and resistance values. 84 Festo Didactic

33 Exercise 5 Resistance and Ohm s Law Discussion Figure 72. Selection of resistors of various sizes and resistance values (photo courtesy of Riedon, all rights reserved). An important property of resistors is that they limit the flow of current in a circuit. By connecting a resistor in series in a circuit, it is thus possible to decrease and control the amount of current in the circuit. Another important property of resistors is that they convert electrical energy into heat. The higher the current flowing in the resistor, the more heat it produces. This property can be detrimental in certain circuits, as the heat generated may be undesirable and thus requires to be evacuated from the device using a fan, such as in a computer. However, the heat generated by a resistor can also be the purpose of its use. For example, most of the heating elements used for cooking are resistors. Other examples include electric baseboards, water heaters, and fan heaters. The filament in an incandescent light bulb is also essentially a resistor. Usually the size of a resistor is an indication of its ability to dissipate heat. The bigger the resistor is, the more heat it can dissipate. Like most electrical components, resistors have a certain tolerance, which indicates by how much their resistance can vary from the nominal rating. The tolerance of a resistor is generally expressed as a percentage of its nominal resistance, and can be as low as 1% for high-precision resistors to about 20%. The circuit diagram symbol for a resistor is shown in Table 12. Table 12. Resistor symbol. Component Resistor Festo Didactic Symbol or 85

34 Exercise 5 Resistance and Ohm s Law Discussion Resistor color code The resistance value of axial resistors, such as the one shown below, is often marked on the resistor body using a color code. Most resistors have four bands (sometimes five bands when more precision is desired). The color of the first and second bands indicates the first and second digits of the resistance value. The third band indicates the multiplier value, and the fourth band indicates the tolerance value. Table 13. Resistor color code. Color First Band Second Band Multiplier Black Tolerance Brown ±1% Red ±2% Orange Yellow Green Blue Violet Gray White Gold ±5% Silver ±10% For instance, the resistance of the resistor shown in Table 13 is 100 Ω ±5%. The first band is brown (this corresponds to digit 1), the second band is black (this corresponds to digit 0), the third band is brown (this corresponds to a multiplier of 10), and the fourth band is gold (this corresponds to a tolerance of ±5%). The resistance value of high-power resistors is usually printed on the resistor body. When the resistance of a resistor equals or exceeds 1000 Ω it is usually expressed in kilohms (kω). For instance, a 4700 Ω resistor is expressed as a 4.7 kω resistor. The characteristics to consider when selecting or replacing a resistor are the size, nominal resistance, operating temperature range, rated power, tolerance, resistance range, rated voltage, and maximum operating voltage. How to test a resistor A resistor is tested by measuring its resistance using an ohmmeter. The measured resistance should be within the range of the nominal value indicated on the resistor. If the measured resistance is null or infinite, the resistance needs to be replaced. Make sure that the resistor is isolated from the circuit during the measurement. 86 Festo Didactic

35 Exercise 5 Resistance and Ohm s Law Discussion The resistance can also be determined by applying a voltage across the resistor, and measuring the voltage and the current flowing through it. The measured voltage and current are then used to calculate the resistance. The variable resistor A variable resistor is a resistor whose resistance can be adjusted in a predetermined range. This enables the resistor to be used for accurate current control, as the resistance of the variable resistor can be adjusted between different values as required to control the amount of current flowing in the circuit. Variable resistors also allow connection of a voltage divider, a device that allows the output voltage of the resistor to be adjusted to a variable fraction of the input voltage. Voltage dividers are covered in the next exercise. Most variable resistors are constructed as shown in Figure 73. As the figure shows, a variable resistor basically consists of a circular resistive element with two terminals allowing connection at both ends. A rotating slider is mounted in the center of the rotating element and can slide along the whole length of the element. This slider also ends with a terminal. On the other side of the slider, a knob allows rotation of the slider along the resistive element. When using the variable resistor as a current controller, current enters through the input terminal and exits through the slider terminal, which means that the output terminal is not used. By rotating the slider, it is thus possible to vary the length of the resistive element through which current must flow before exiting by the slider terminal. The further the slider is from the input terminal, the longer the resistive element, and the higher the resistance of the variable resistor. Resistive element Slider Output terminal Input terminal Slider terminal Figure 73. Back view of a variable resistor. Variable resistors are divided into two categories: rheostats and potentiometers. Both are very similar in construction and are only differentiated by the fact that a potentiometer can be used as a voltage divider or as a variable resistor, depending on how its terminals are connected. Because of this, potentiometers can be used in certain applications in which rheostats are not sufficient. Potentiometers can also be converted into rheostats by simply connecting two of their three terminals together. Table 14 shows the common circuit diagram symbols for a rheostat and for a potentiometer. Note the arrow in the potentiometer symbol that allows a third connection to the potentiometer, as expected by the third terminal of the potentiometer used in voltage dividers. A trimmer or preset is a miniature adjustable electrical component. It is meant to be set correctly when installed in a device, and never seen or adjusted by the device's user. Trimmer potentiometers, also called trimpots, are small potentiometers commonly used on circuit boards to calibrate equipment. Festo Didactic

36 Exercise 5 Resistance and Ohm s Law Discussion Table 14. Rheostat and potentiometer symbols. Component Symbol Rheostat or Potentiometer or Figure 74 shows an example of a circuit containing a rheostat. In this circuit, the rheostat is used to make a dimmer, which is a light switch allowing the intensity of the light to be varied. This is achieved by increasing or decreasing the resistance of the rheostat. The higher its resistance, the lower the current flowing in the light and the less intensity it produces. 120 V Dimmer. 0 Ω to 1000 Ω Light 144 Ω Figure 74. Circuit of a power source supplying power to a dimmer. Suppose the light bulb has a resistance of 144 Ω and the rotating knob of the dimmer is set so that the dimmer resistance. is maximal (1000 Ω). Since the power source voltage is equal to 120 V (RMS) 3, the current flowing in the circuit is equal to: Ω 0.10 The power. dissipated in the dimmer is thus equal to: Ω W The power dissipated in the light is: 144 Ω W 3 Unless specified, line current and voltage are always RMS values. 88 Festo Didactic

37 Exercise 5 Resistance and Ohm s Law Discussion Since the power dissipated in the light is very low, the resultant lighting is weak. On the other hand, if the rotating knob of the dimmer is set so that the dimmer resistance. is small (100 Ω), the current flowing in the circuit is equal to: Ω 0.49 The power. dissipated in the dimmer is thus equal to: Ω W The power dissipated in the light is: 144 Ω W Finally, if the dimmer is set to 0 Ω, we have: The power dissipated in the light is: Ω Ω W Festo Didactic

38 Exercise 5 Resistance and Ohm s Law Discussion Training system module Resistors module Resistor Ground terminal Fault switches IEC symbol for a resistor Figure 75. Resistors module. The Resistors module consists of resistors having various ratings. All resistors have a tolerance of 5%. The module is provided with some openings to dissipate heat. The Resistors module is also equipped with four fault switches and two ground terminals. 90 Festo Didactic

39 Exercise 5 Resistance and Ohm s Law Procedure Outline PROCEDURE OUTLINE The Procedure is divided into the following sections: Setup Resistance measurements using an ohmmeter Troubleshooting switches using an ohmmeter Ohm s law and power calculations Circuit containing a 50 Ω resistor. Circuit containing a 250 Ω resistor. Testing continuity of a circuit using a test light PROCEDURE High voltages are present in this laboratory exercise. Do not make or modify any banana jack connections with the power on unless otherwise specified. Setup In this section, you will install the training system modules in the workstation. 1. Refer to the Equipment Utilization Chart in Appendix A to obtain the list of equipment required to perform this exercise. Install the equipment required in the workstation. Make sure that all fault switches are set to the O (off) position. Resistance measurements using an ohmmeter In this section, you will use an ohmmeter to measure the resistance across the resistors of the Resistors module, and verify if the measured values are within the tolerance indicated on the front panel of the module. You will also measure the resistance of an indicator light. Then, you will determine whether these components allow continuity or not. 2. Select the ohmmeter (Ω) function of the multimeter. Touch the probe tips together and read the resistance on the display. Resistance on the display when the probe tips are touching Ω Resistance on the display when the probe tips are touching = 0 Ω 3. Isolate the probe tips and read the resistance on the display. Resistance on the display when the probe tips are isolated Ω Resistance on the display when the probe tips are isolated = infinite resistance value. Depending on the ohmmeter used, an infinite resistance value may be indicated by a 1, OL, or Overflow on the display. Festo Didactic

40 Exercise 5 Resistance and Ohm s Law Procedure 4. Measure the resistance of the resistors pointed by an arrow in Figure 76, and record the values. Figure 76. Measure the resistance of the resistors pointed by an arrow Ω 50.9 Ω 495 Ω Ω 496 Ω Figure 76. Measure the resistance of the resistors pointed by an arrow. 92 Festo Didactic

41 Exercise 5 Resistance and Ohm s Law Procedure 5. Are the measured resistances within the tolerance of the resistors indicated on the front panel of the Resistors module? Yes No Yes 6. Compare the size of the resistors (50 Ω, 250 Ω, and 500 Ω) of the Resistors module. What can you conclude about the size of these resistors versus the power they can dissipate? The resistors having a higher power rating are bigger. 7. On the Printed Circuit Board module, locate and observe the size of resistors,,. What can you deduce about the power these resistors can dissipate? a Resistors,, are specially designed to be mounted on printed circuit boards. This type of resistor is called surface-mount resistor. The Printed Circuit Board module will be explained in Exercise 7. The power that these resistors can dissipate is very low. 8. On the Indicator Lights module, measure the resistance across a 24 V indicator light. Record the value below. Indicator light resistance Ω Indicator light resistance 33 Ω (approximately) 9. Do your measurements in this section confirm that the indicator light operates properly? Yes No Yes Festo Didactic

42 Exercise 5 Resistance and Ohm s Law Procedure 10. What can you conclude from the resistance values you measured in steps 4 and 6 about the continuity between the terminals of the different components? Briefly explain. The resistance values measured in steps 4 and 6 are different from infinity, which means that current can flow reasonably freely in the components. This confirms that there is continuity between the terminals of the different components. Troubleshooting switches using an ohmmeter In this section, you will use an ohmmeter to measure the resistance across the switches of the Switches module and of the Push Buttons module in different states. Then, you will use the measured resistance values to determine whether the switches operate properly or not. 11. Using an ohmmeter, measure the resistance across the switches of the Switches module for each state of the switches. Make your measurements on the 24 V terminals only. Record each resistance value below. Double-pole single-throw toggle switch resistance (upper) when the switch is in the Closed state Ω Open state Ω Double-pole single-throw toggle switch resistance (lower) when the switch is in the Closed state Ω Open state Ω Double-pole double-throw toggle switch resistance When the switch is set to position A Terminal A Ω Terminal B Ω When the switch is set to position B Terminal A Ω Terminal B Ω Double-pole single-throw toggle switch resistance (upper) when the switch is in the Closed state = 0 Ω 94 Festo Didactic