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Revision 1 December 2014 Basic Electricity Part 1 Student Guide GENERAL DISTRIBUTION GENERAL DISTRIBUTION: Copyright © 2014 by the National Academy for Nuclear Training. Not for sale or for commercial use. This document may be used or reproduced by Academy members and participants. Not for public distribution, delivery to, or reproduction by any third party without the prior agreement of the Academy. All other rights reserved. NOTICE: This information was prepared in connection with work sponsored by the Institute of Nuclear Power Operations (INPO). Neither INPO, INPO members, INPO participants, nor any person acting on behalf of them (a) makes any warranty or representation, expressed or implied, with respect to the accuracy, completeness, or usefulness of the information contained in this document, or that the use of any information, apparatus, method, or process disclosed in this document may not infringe on privately owned rights, or (b) assumes any liabilities with respect to the use of, or for damages resulting from the use of any information, apparatus, method, or process disclosed in this document. ii Table of Contents INTRODUCTION ............................................................................................1 TLO 1 ELECTRICAL PRINCIPLES OF OPERATION ..........................................2 Overview .................................................................................................2 ELO 1.1 Composition of an Atom and Electron Flow ...........................3 ELO 1.2 Electrical Terms and Characteristics ........................................6 ELO 1.3 Electrical Terms .....................................................................10 ELO 1.4 Electrical Parameters ..............................................................13 ELO 1.5 Applying Ohm's Law .............................................................16 TLO 1 Summary ...................................................................................18 TLO 2 MAGNETISM ...................................................................................19 Overview ...............................................................................................19 ELO 2.1 Electron Domains and Law of Magnetism.............................19 ELO 2.2 Magnetic Terms .....................................................................21 ELO 2.3 Magnetic Materials.................................................................24 ELO 2.4 Left-Hand Rule for Current Carrying Conductors .................25 ELO 2.5 Left-Hand Rule for Coils .......................................................26 ELO 2.6 Hysteresis Losses and Magnetic Circuits ...............................28 ELO 2.7 Faraday's Law of Induced Voltage .........................................30 TLO 2 Summary ...................................................................................33 TLO 3 ELECTRICAL DRAWINGS .................................................................33 Overview ...............................................................................................33 ELO 3.1 Electrical Symbols .................................................................33 ELO 3.2 Types of Drawings .................................................................35 ELO 3.3 Circuit Terminology ...............................................................38 ELO 3.4 Circuit Protection Devices .....................................................43 TLO 3 Summary ...................................................................................46 TLO 4 BATTERIES......................................................................................46 Overview ...............................................................................................46 ELO 4.1 Battery Terminology ..............................................................46 ELO 4.2 Simple Voltaic Cell ................................................................50 ELO 4.3 Chemistry of a Lead-Acid Battery .........................................51 ELO 4.4 Series and Parallel Connected Batteries .................................53 ELO 4.5 Types of Battery Materials .....................................................55 ELO 4.6 Battery Hazards ......................................................................56 TLO 4 Summary ...................................................................................58 TLO 5 DC CIRCUIT ANALYSIS...................................................................58 Overview ...............................................................................................58 ELO 5.1 Total Resistance .....................................................................58 ELO 5.2 Voltage and Current Dividers ................................................72 ELO 5.3 Polarity of Voltage Drops ......................................................75 ELO 5.4 Kirchhoff's Laws ....................................................................77 ELO 5.5 Applying Kirchhoff's Laws ....................................................78 TLO 5 Summary ...................................................................................84 TLO 6 DC MOTORS ...................................................................................85 Overview ...............................................................................................85 ELO 6.1 Current Carrying Conductors .................................................85 iii ELO 6.2 Right-Hand Rule for Motors ................................................. 87 ELO 6.3 Torque in DC Motors ............................................................ 89 ELO 6.4 Counter-Electromotive Force (CEMF) in DC Motors .......... 91 ELO 6.5 DC Motor Control ................................................................. 92 ELO 6.6 Starting DC Motors ............................................................... 93 ELO 6.7 DC Motor Ratings ................................................................. 95 TLO 6 Summary................................................................................... 96 TLO 7 PRODUCING DC VOLTAGE ............................................................. 96 Overview .............................................................................................. 96 ELO 7.1 Methods of Producing DC Voltage ....................................... 97 ELO 7.2 Rectifiers .............................................................................. 103 ELO 7.3 Commutation ....................................................................... 107 ELO 7.4 DC Machine Components ................................................... 109 ELO 7.5 Conditions for Inducing Voltage ......................................... 111 ELO 7.6 Left-Hand Rule for Generators ............................................ 113 ELO 7.7 Terminal Voltage ................................................................. 115 ELO 7.8 DC Generator Ratings ......................................................... 117 TLO 7 Summary................................................................................. 118 BASIC ELECTRICITY PART 1 SUMMARY................................................... 119 iv Basic Electricity Part 1 Revision History Revision Date Version Number Purpose for Revision Performed By 11/6/2014 0 New Module OGF Team 12/9/2014 1 Added signature of OGF Working Group Chair OGF Team Introduction In this module, you will learn electrical terminology, laws of electricity, laws of magnetism, and how key power plant electrical components work. Power plants use electrical generators to produce and distribute electrical power throughout the station and to the grid for distribution and eventual sale (this is our product). Understanding how they work and how to monitor and control them is central to the plant operator. Rev 1 1 Objectives At the completion of this training session, the trainee will demonstrate mastery of this topic by passing a written exam with a grade of 80 percent or higher on the following Terminal Learning Objectives (TLOs): 1. Describe basic electrical theory principles of operation. 2. Describe the magnetic properties of materials and the use of magnetism in electrical applications. 3. Differentiate between types of electrical symbols, drawings, and diagrams. 4. Describe the operating characteristics, terminology, and hazards of a lead-acid battery and voltaic cell. 5. Analyze various DC circuits to find resistances, currents, and voltages at any given point within the circuit. 6. Describe the principles of operation, control, and characteristics of DC motors. 7. Explain how a DC generator produces DC voltage. TLO 1 Electrical Principles of Operation Overview In this section, you will learn basic electrical terms and how to use Ohm's Law. Understanding the relationships of basic electrical circuits is necessary for an operator to monitor and control plant electrical equipment. Objectives Upon completion of this lesson, you will be able to do the following: 1. Describe the basic composition of an atom and the concept of electron flow. 2. Define the following terms and their characteristics: electrostatic force, potential difference, electromotive force, ion charge, and Coulomb's Law. 3. Define the following electrical terms: conductor, insulator, resistor, voltage, current, electron, and conventional current flow, direct and alternating current, and real and ideal sources. 4. Describe the following electrical parameters, including the unit of measurement and the relationship to other parameters: voltage, current, resistance, conductance, power, inductance, capacitance, and frequency. 5. Given any two of the three component values of Ohmβs Law, solve for the unknown component value. 2 Rev 1 ELO 1.1 Composition of an Atom and Electron Flow Introduction Electricity is the flow of electrons through materials and devices. Tiny particles called electrons and protons produce electricity. These particles are not visible, but exist as subatomic particles in the atom. The Atom Elements are the basic building blocks of all matter. Atoms are the smallest components of matter that retain the identifying properties of an element. An atom consists of a positively charged nucleus surrounded by negatively charged electrons, so that the atom as a whole is normally electrically neutral. The figure below depicts a carbon atom with its components. Figure: The Atom The nucleus is composed of two kinds of subatomic particles, protons, and neutrons, as shown in the figure above. The proton carries a single positive charge equal in magnitude to the electron charge. The neutron is slightly heavier than the proton and is electrically neutral. Various combinations of these two particles exist in atoms, depending upon the element. The electron is the fundamental negative charge (-) of electricity and revolves around the nucleus, or center, of the atom in concentric orbits, or shells. The proton is the fundamental positive charge (+) of electricity and is located in the nucleus. The number of protons in the nucleus of any atom specifies the atomic number of that atom or element. For example, the carbon atom contains six protons in its nucleus; therefore, the atomic number for carbon is six. In its natural state, an atom of any element contains an equal number of electrons and protons. The negative charge (-) of each electron is equal in magnitude to the positive charge (+) of each proton; therefore, the two equal and opposite charges offset each other, and the atom is electrically neutral. Electron Transfer Some atoms can lose electrons and others can gain electrons, so it is possible to transfer electrons from one object to another. When this occurs, the equal distribution of negative and positive charges in the atoms no Rev 1 3 longer exists. One object will contain atoms with an excess of electrons and become negatively charged. The other object will contain atoms that are deficient in electrons and become positively charged. These objects, which contain billions of atoms, will then follow the same law of electrostatics as the electron and proton previously discussed. Free Electrons Free electrons are the electrons that can move around within an object. The greater the number of free electrons, the greater the objectβs negative electric charge. Thus, the amount electric charge is a measure of free electrons. Valence Electrons Valence electrons are the electrons in the outermost shell. When external energy, such as heat, light, or electrical energy, act on certain materials, the electrons in the individual atoms gain energy, become excited, and may move to a higher energy level. If enough energy acts on the atom, some of the valence electrons will leave the atom, as shown in the figure below. These electrons are free electrons. Figure: Free Electrons When the outer shell of an atom contains eight electrons, the atom becomes very stable, and very resistant to changes in its structure. This also means that atoms with one or two electrons in their outer shell can lose electrons much more easily than atoms with full outer shells. Note Note The movement of free electrons provides electric current flow in a metal conductor. Electrons are in rapid motion around the nucleus. While the electrostatic force is trying to pull the nucleus and the electron together, the electron is in 4 Rev 1 motion and trying to pull away from the nucleus. The unbalanced force keeps the electron in orbit around the nucleus. Electron Shells The electrons in an atom exist in different energy levels. The energy level of an electron is proportional to its distance from the nucleus. Higher energy level electrons exist in orbits, or shells, that are farther away from the nucleus. These shells nest inside one another and surround the nucleus. The nucleus is the center of all the shells. Letters identify the shells, beginning with the shell nearest the nucleus: as K, L, M, N, O, P, and Q. Each shell has a maximum number of electrons it can hold. For example, the K shell holds a maximum of two electrons and the L shell holds a maximum of eight electrons. As shown in the figure below, each shell has a specific number of electrons that it will hold for a particular atom. Figure: Energy Shells and Electron Quota There are two rules concerning electron shells that make it possible to predict the electron distribution of any element: 1. The maximum number of electrons that can fit in the outermost shell of any atom is eight. 2. The maximum number of electrons that can fit in the next-tooutermost shell of any atom is 18. Rev 1 5 Knowledge Check Electrons located in the outermost shell of an atom are called: A. free electrons. B. positrons. C. valence electrons. D. K shell electrons. ELO 1.2 Electrical Terms and Characteristics Introduction In this section, you will learn about electrostatic and electromotive forces within an atom. One characteristic of an atom is that the electron and the nucleus attract each other. Electrostatic force is the name of this attraction. Electrostatic force holds the electron in orbit. The lines in the figure below show this force. Figure: Electrostatic Force Without this electrostatic force, the electron, which is traveling at high speed, would not remain in its orbit (it would fly away). Bodies that attract each other in this way are termed charged bodies. The electron has a negative charge, and the nucleus (due to the proton) has a positive charge. First Law of Electrostatics The First Law of Electrostatics (also known as the Law of Electrical Charges) states that unlike charges attract and like charges repel. This law is a vital concept in the understanding of electricity. This force is present within every charged object and is the result of an electrostatic field that exists around each charged particle or object. Lines called "lines of force" as shown in the figure below illustrate this electrostatic field, and the force it creates. 6 Rev 1 The negative charge of the electron is equal and opposite of the positive charge of the proton. Electrostatic charge refers to these charges. Polarity refers to the charge sign (either positive or negative). Unlike charges attract each other, and like charges repel each other. Figure: Electrostatic Field Opposite Charges Charged objects repel or attract each other because of the way these electrostatic fields interact. When two objects of opposite charge are near one another, the electrostatic field is concentrated in the area between them, as shown in the figure below. Figure: Electrostatic Field between Opposite Charges When two objects of like charge are near one another, the lines of force repel each other, as shown in the figure below. Figure: Electrostatic Field Between Like Charges Potential Difference Potential difference is the term used to describe the size of the electrostatic force between two charged objects. If there are two objects with a potential Rev 1 7 difference, with a charged body between them, the charged body will try to move in one direction, depending upon the polarity of the charged body. The figure below shows the electrostatic force lines between three such charged objects. Figure: Potential Difference between Two Charged Objects If an electron is between a negatively charged body and a positively charged body, the potential difference will push the electron toward the positively charged object. The negatively charged object will repel the negatively charged electron; the positively charged object will attract the negatively charged electron, as shown in the figure above. Electromotive Force Due to the force of the electrostatic field, the electrical charges shown in the figure above have the ability to do work by moving another charged particle by attraction and/or repulsion. Potential refers to this ability to do work; therefore, if one charge is different from another, there is a potential difference between them. Electromotive force (EMF) is the sum of the potential differences of all charged particles in the electrostatic field. The basic unit of measure of potential difference is the volt. The symbol for potential difference is V, indicating the ability to do the work of forcing electrons to move. Ion Charge An atom that has lost or gained one or more electrons has an ion charge (ionized). If the atom loses one or more electrons, it becomes positively charged and is a positive ion. If an atom gains one or more electrons, it becomes negatively charged and is a negative ion. Coulomb's Law The strength of the attraction or of the repulsion force between two charged objects depends upon two factors: 1. the amount of charge on each object 2. the distance between the objects A larger charge on the charged objects results in a greater electrostatic field between the objects. A larger distance between the charged objects results 8 Rev 1 in a weaker electrostatic field between them. This leads us to the law of electrostatic attraction, commonly referred to as Coulombβs Law of electrostatic charges. Coulombβs Law states that the force of electrostatic attraction (or repulsion between two objects), is directly proportional to the product of the two charges and inversely proportional to the square of the distance between them as shown in the equation below: π1 π2 πΉ=πΎ 2 π Where: F = force of electrostatic attraction or repulsion (Newtons) K = constant of proportionality (N-m2/cm2) q1 = charge of first particle (Coulombs) q2 = charge of second particle (Coulombs) d = distance between two particles (meters) If q1 and q2 are both positively charged, or negatively charged, the force is repulsive. If q1 and q2 are opposite in polarity or charge, the force is attractive. Knowledge Check The force that holds electrons in their orbits is called: A. Electrostatic force B. Coulomb force C. Electromotive force D. Voltage Knowledge Check Select all that are correct: According to Coulomb's Law, the force between two charged objects... Rev 1 A. decreases as distance between the objects increases. B. increases as the distance between the objects increases. C. increases as the magnitude of either charge increase. D. is independent of the magnitude of charge on the objects. 9 ELO 1.3 Electrical Terms Introduction In this section, you will learn about commonly used electrical terms. Conductors Conductors are materials with electrons that are loosely bound to their atoms. Conductors permit free motion of a large number of electrons. Atoms with only one valence electron, such as copper, silver, and gold, are examples of good conductors. Of these three, copper is most common in conducting wire construction. Most metals are good conductors. Insulators Insulators, or nonconductors, are materials with electrons that are tightly bound to their atoms and require large amounts of energy to free the electrons from the influence of the nucleus. The atoms of good insulators have their valence shells filled with eight electrons. Any energy applied to such an atom distributes among a relatively large number of electrons, minimizing the energy applied to any one electron. Examples of insulators are rubber, plastics, glass, and dry wood. Resistors Resistors are made of materials that conduct electricity, but offer more opposition to current flow than good conductors. Semiconductor is an alternate term for these types of materials because they are neither good conductors nor good insulators. Semiconductors have more than one or two electrons in their valence shells, but less than seven or eight. Carbon, silicon, germanium, tin, and lead are examples of semiconductors. Each has four valence electrons. Voltage The volt (symbol V) is the basic unit of measure for potential difference. Voltage indicates potential difference between charged objects. The number of electrons that an object has gained or lost determines an objectβs electrical charge. The unit of an objectβs electrical charge is the coulomb. One coulomb equals 6.28 x 1018 (billion, billion) electrons. For example, if an object gains one coulomb of negative charge, it has gained 6,280,000,000,000,000,000 extra electrons. One volt is the potential difference that causes one coulomb of current to do one joule of work. In addition, one volt is that amount of force required to force one ampere of current through one ohm of resistance. Current The density of the atoms in copper wire is such that the valence orbits of the individual atoms overlap, allowing the electrons to move easily from one atom to the next. Free electrons can drift from one orbit to another in a random direction. When a potential difference (voltage) is applied, the direction of their movement is standardized. The strength of the potential 10 Rev 1 difference applied at each end of the wire determines how many electrons change from a random motion to a directional path through the wire. The movement or flow of these electrons is called electron current flow or simply current. If two charged objects that have a potential difference have a copper wire between them, all of the negatively charged free electrons will feel a force pushing them from the negative charge to the positive charge. The figure below depicts this force, which is opposite to the conventional direction of the electrostatic lines of force. To produce current, a potential difference must move the electrons. The symbol for current is (I), and the basic unit for current is the ampere (A). One ampere of current is the movement of one coulomb of charge past any given point of a conductor during one second of time. Figure: Electron Flow Electron Flow and Conventional Current The solid arrow shown in the figure below indicates the direction of electron flow. The flow of electrons is from the negative (-) side of the battery, through the wire, and back to the positive (+) side of the battery. The direction of electron flow is from a point of negative potential to a point of positive potential. Figure: Conventional Current vs. Electron Flow Rev 1 11 As electrons leave atoms during electron current flow, positively charged atoms (holes) result. The flow of electrons in one direction causes a flow of positive charges in the opposite direction. Conventional current is the term for this flow of positive charges, denoted by a dashed arrow in the figure above. As electrons flow from negative to positive, or from a higher potential to a lower potential, they create electrical effects. If there was a flow of positive charges in the opposite direction, the electrical effects are the same. Either electron flow or positive charge flow can describe the flow of electrical current. The effects of both types of flow are essentially equivalent. In this lesson, the effects of electrical current flow reflect electron flow. Direct Current and Alternating Current There are two general types of electric current flow: direct current (DC) and alternating current (AC). Direct current flows continuously in the same direction. An alternating current periodically reverses direction. An example of DC is the current flowing in an electrical circuit powered by a battery. An example of AC is the current used in most industries and households to power lights, motors, etc. Real and Ideal Sources An ideal source is a theoretical concept of an electric current or voltage supply (such as a battery) that has no losses and is therefore a perfect voltage or current supply. Analytical examples use ideal sources only since they do not occur in real life applications. A real source is a current or voltage supply that has some losses associated with it such as a battery or electrical generator. 12 Rev 1 Knowledge Check Match the following terms to their appropriate definitions. 1. Materials with electrons that are loosely bound to their atoms, or materials that permit free motion of a large number of electrons A. Conductor 2. Materials with electrons that are tightly bound to their atoms and require large amounts of energy to free them from the influence of the nucleus B. Resistor 3. Materials that conduct electricity, but offer opposition to current flow C. Insulator 4. Flow of positive charges (holes) through a conductor D. Conventional current ELO 1.4 Electrical Parameters Introduction The International (metric) System, also known as the SI System provides the basis of electrical measurement units. Units of electrical measurement include the following: Ampere β unit used to measure electrical current Volt β unit used to measure electrical potential difference Hertz β unit used to measure frequency Ohm β unit used to measure resistance to current flow Siemens β unit used to measure a materialβs ability to conduct current flow ο· Watt β unit used to measure power ο· Henry β unit used to measure electrical inductance ο· Farad β unit used to measure electrical capacitance ο· ο· ο· ο· ο· Voltage (Volt) Voltage, electromotive force (EMF), or potential difference, is the pressure or force that causes electrons to move in a conductor. In electrical formulas and equations, you will see voltage symbolized with a capital E, while on laboratory equipment or schematic diagrams, you will see voltage symbolized with a capital V. Both symbols indicate voltage and are equal representations. Rev 1 13 Current (Ampere or Amp) Electron current, or amperage, is the movement of free electrons through a conductor. In electrical formulas, current is symbolized with a capital I, while in the laboratory or on schematic diagrams, it is common to use a capital A to indicate amps or amperage (amps). Resistance (Ohm) Now that we have discussed the concepts of voltage and current, we are ready to discuss a third key concept called resistance. Resistance is the opposition to current flow. The amount of opposition to current flow produced by a material depends upon the amount of available free electrons it contains and the types of obstacles the electrons encounter as they attempt to move through the material. The symbol (R) represents resistance in equations. One ohm is that amount of resistance that will limit the current in a conductor to one ampere when the potential difference (voltage) applied to the conductor is one volt. The symbol for the ohm is the Greek letter capital omega (Ξ©). If a voltage difference acts on a conductor, current flows. The amount of current flow depends upon the resistance of the conductor: the lower the resistance, the higher the current flow for a given amount of voltage; the higher the resistance, the lower the current flow. The relationship between these three parameters is referred to as Ohmβs law, (πΈ = πΌ × π ) and will be covered in more detail later in the module. Conductance (Siemens) The opposite, or reciprocal, of resistance is conductance. Recall that resistance is the opposition to current flow. Since resistance and conductance are opposites, conductance is the ability to conduct current. For example, if a wire has a high conductance, it will have low resistance, and vice-versa. To calculate conductance, compute the reciprocal of the resistance. Siemens is the unit used to specify conductance, named in honor of German inventor Ernst Werner von Siemens. The symbol for electrical conductance is capital letter S. When used in a formula, the letter G represents conductance. The equation below is the mathematical representation of conductance obtained by relating the definition of conductance (1/R) to Ohmβs Law. 1 πΌ = πππ ππ π‘ππππ π For example, if a resistor (R) has a value of five ohms; its conductance will be 0.2 siemens. πΊ= 14 Rev 1 Power (Watt) Electricity generally performs work, such as turning a motor or generating heat. Specifically, power is the rate of performing work, or the rate of heat generation. The unit commonly used to specify electric power is the watt. In equations, the capital letter P denotes power, and the capital letter W denotes watts. Power is also described as the current (I) in a circuit multiplied by the voltage (E) across the circuit. The equation below is a mathematical representation of this concept. π = πΌ × πΈ or π = πΌπΈ Using Ohmβs Law for the value of voltage (E), πΈ = πΌ × π and using substitution laws, π = πΌ × (πΌ × π ) Therefore, we can describe power as the current (I) in a circuit squared multiplied by the resistance (R) of the circuit, or as the formula listed below: π = πΌ2π Inductance (Henry) Inductance is the ability of a coil to store energy, induce a voltage in itself, and oppose changes in current flowing through it. The symbol used to indicate inductance in electrical formulas and equations is a capital L. Henries are the units of measurement for inductance. The capital letter H denotes the henry. One henry is the amount of inductance (L) that permits one volt to be induced (VL) when the current through the coil changes at a rate of one ampere per second. The mathematical representation of the rate of change in current through a coil per unit time is: βπΌ βπ‘ The equation below is the mathematical representation for the voltage VL induced in a coil with inductance L. The negative sign indicates that voltage induced opposes the change in current through the coil per unit time. βπΌ βπ‘ A later section in this lesson presents additional detail on inductance. ππΏ = βπΏ Capacitance (Farad) Capacitance is the ability to store an electric charge, designated by the capital letter C. Capacitance (C) units are farads; capacitance is equal to the amount of charge (Q) that can be stored in a device or capacitor divided by the voltage (E) applied across the device or capacitor plates when the charge was stored. The equation below is the mathematical representation for capacitance. Rev 1 15 πΆ= π πΈ Frequency (Hertz) Frequency (measured in hertz) is the number of alternating voltage or current cycles completed per second. Knowledge Check Match the following terms to their appropriate definitions. 1. Henry A. Frequency 2. Farad B. Inductance 3. Siemen C. Capacitance 4. Hertz D. Conductance ELO 1.5 Applying Ohm's Law Introduction In this section, you will practice applying Ohmβs law to solve problems. In 1827, George Simon Ohm discovered that there was a definite relationship between voltage, current, and resistance in an electrical circuit. Ohmβs law defines this relationship, stated mathematically below. πΈ = πΌ × π or πΈ = πΌπ Applying Ohm's Law Ohm's law states the relationship between voltage, current, and resistance. It is possible to solve for any unknown value, given the other two values of the formula. The table below gives the steps necessary to calculate the unknown quantity. Step 1. Action Determine the unknown and choose the appropriate form of Ohm's Law. 2. Insert the known values into the equation. 3. Solve for the unknown quantity. 16 Result πΈ = πΌπ ; πΌ = πΈ π πΈ ; ππ π = πΌ Rev 1 Ohm's Law Demonstration 1 Given that I = 2 A, E = 12 V, find the circuit resistance. Step Action Result π = πΈ πΌ Insert the known values into the equation. π = 12 π 2π΄ Solve for the unknown quantity. π = 6 πβππ 1. Determine the unknown and choose the appropriate form of Ohm's Law. (πΈ = πΈ πΈ πΌπ ; πΌ = π ; or π = πΌ ) 2. 3. Ohm's Law Demonstration 2 Given that I = 4 A, R = 30 Ohms, find the circuit voltage. Step Action Result Determine the unknown and choose the appropriate form of Ohm's Law. (πΈ = πΈ πΈ πΌπ ; πΌ = ; or π = ) πΈ =πΌ×π 2. Insert the known values into the equation. πΈ = 4 π΄ × 30 πβππ 3. Solve for the unknown quantity. πΈ = 120 π£πππ‘π 1. π Rev 1 πΌ 17 Knowledge Check Given E = 260 V and R = 240 Ξ©, what current will flow through a circuit? A. 0.923 A B. 0.923 V C. 1.083 A D. 1.083 V Knowledge Check How much current would a hot tub draw if it will run at 220 V and the resistance is 8 Ξ©? A. 0.275 A B. 3.63 A C. 27.5 A D. 36.6 A TLO 1 Summary In this section, you learned electrical terminology that you will use throughout this course and your career. You also learned to apply Ohm's law, which is one of the most useful tools in analyzing electrical circuits. Now that you have completed this lesson, you should be able to: 1. Describe the basic composition of an atom and the concept of electron flow. 2. Define the following terms and their characteristics: electrostatic force, potential difference, electromotive force, ion charge, and Coulomb's Law. 3. Define the following electrical terms: conductor, insulator, resistor, voltage, current, electron, and conventional current flow, direct and alternating current, and real and ideal sources. 4. Describe the following electrical parameters, including the unit of measurement and the relationship to other parameters: voltage, current, resistance, conductance, power, inductance, capacitance, and frequency. 5. Given any two of the three component values of Ohmβs Law, solve for the unknown component value. 18 Rev 1 TLO 2 Magnetism Overview Certain metals and metallic oxides have the ability to attract other metals. This property is magnetism, and the materials that have this property are termed magnets. Some magnets occur naturally; manufacturing processes can produce others. Understanding magnetism and its role in electrical generation is necessary to monitor and operate electrical machines. Objectives Upon completion of this lesson, you will be able to do the following: 1. Describe the relationship between magnetic materials, electron domains, and the law of magnetism. 2. Define the following magnetic terms: flux, flux density, permeability, magnetomotive force, and reluctance. 3. Describe the following materials as they relate to permeability, giving an example for each type of material: ferromagnetic, paramagnetic, and diamagnetic. 4. Apply the Left-Hand Rule for current carrying conductors to determine the direction of lines of magnetic flux. 5. Apply the Left-Hand Rule for coils to determine the polarity of a coil. 6. Describe the operation of a simple magnetic circuit including effects of hysteresis. 7. Given Faradayβs Law of Induced Voltage, describe how varying parameters affect induced voltage. ELO 2.1 Electron Domains and Law of Magnetism Introduction In this section, you will learn how electron domains cause magnetic attraction. Electron Domains Magnetism is a result of electrons spinning on their axis around the nucleus of an atom, as shown in the figure below. Rev 1 19 Figure: Producing a Magnetic Field In magnetic materials, the atoms have areas called domains that align in such a way that their electrons tend to spin in the same direction as shown in the figure below. When the domains align such that electrons spin in the same direction, the object develops magnetic poles. Figure: Magnetic Domains Magnetism Certain metals and metallic oxides have the ability to attract other metals. Magnetism is the name for this property, and the materials that have this property are called magnets. Some magnets occur naturally; manufacturing processes can produce others. Law of Magnetism The alignment of atom domains results in the formation of magnetic poles at each end of the magnet. These poles are the north magnetic pole and the 20 Rev 1 south magnetic pole. The law of magnetism states that like magnetic poles repel and unlike magnetic poles attract, as shown in the figure below. Figure: Magnetic Attraction and Repulsion Knowledge Check The alignment of electrons spinning around their nuclei creates magnetic fields. A. True B. False Knowledge Check Select all that are true. According to the Law of Magnetism... A. unlike magnetic poles attract. B. like magnetic poles repel. C. magnets can be made of any kind of material. D. magnetism is caused by metal forging and does not occur naturally. ELO 2.2 Magnetic Terms Introduction In this section, you will learn common magnetic terms. Rev 1 21 Magnetic Flux Magnetic flux is the group of magnetic field lines emitted outward from the north pole of a magnet. The symbol for magnetic flux is the Greek letter Ξ¦ (phi). The weber (Wb) is the SI unit for magnetic flux. One weber is equal to 1 x 108 magnetic field lines. Magnetic Flux Density Magnetic flux density (B) is the amount of magnetic flux that passes through a certain area, perpendicular to the direction of magnetic flow, also commonly called magnetic induction. The figure below depicts magnetic flux density. The flux density units are Weber/meter2 in SI or in Tesla in CGS units. Figure: Flux Density Permeability Permeability is a measure of the ability of a material to support the formation of a magnetic field within itself; or the degree of magnetization that a material obtains in response to an applied magnetic field. The Greek letter ΞΌ represents magnetic permeability. Permeability (µ) refers to the ability of a material to concentrate magnetic lines of flux. The higher permeability, the greater the materialβs ability to concentrate magnetic flux; this increases the materialβs probability of becoming magnetized. Magnetomotive Force Magnetomotive force (MMF) is the strength of a magnetic field in a coil of wire. The amount of current flowing in the turns of the coil determines the MMF: the more current, the stronger the magnetic field; the more turns of wire, the more concentrated the lines of force. Reluctance Reluctance is the opposition to the production of flux in a material, corresponding to resistance. Reluctance is inversely proportional to permeability. Iron cores have high permeability and, therefore, low 22 Rev 1 reluctance. Air has a low permeability and, therefore, a high reluctance. The figure below shows four arrangements with varying reluctance. Figure: Different Physical Forms of Electromagnets Generally, different types of materials have different values of reluctance as shown in the figure above. The air gap is the air space between two poles of a magnet. Air is nonmagnetic and does not concentrate magnetic lines of flux. Since air has a very high reluctance, the size of the air gap affects the value of reluctance: the shorter the air gap, the stronger the field in the gap. A larger air gap provides space for the magnetic lines to spread out. Knowledge Check Match the following terms to their appropriate definitions. 1. Opposition to the production of flux in a material A. Reluctance 2. The ability of a material to concentrate magnetic lines of flux B. Magnetic flux 3. The group of magnetic field lines emitted outward from the north pole of a magnet C. Permeability 4. The strength of a magnetic field in a coil of wire D. Magnetomotive force Rev 1 23 ELO 2.3 Magnetic Materials Introduction Magnetic materials have the ability to be magnetized, and are those materials that can be either attracted or repelled by a magnet. The most commonly used magnetic materials are iron and steel. A permanent magnet is made of a very hard magnetic material, such as cobalt steel, that retains its magnetism long after removal of the magnetizing field. A temporary magnet is a material that loses its magnetism upon removal of the magnetizing field. Classification of Magnetic Materials There are two classes of magnetic materials: magnetic or nonmagnetic, based on the highly magnetic properties of iron. There are three subgroups of magnetic materials, based on their relative permeability. 1. Ferromagnetic Materials Ferrites are nonmagnetic, but have the ferromagnetic properties of iron. Ferrites are made of ceramic material and have a relative permeability that ranges from 50 to 200. Coils for RF (radio frequency) transformers commonly use ferrites. Iron, steel, nickel, cobalt, and the commercial alloys of alnico and peralloy are examples of ferromagnetic materials. 2. Paramagnetic Materials These materials have a relative permeability of slightly more than one, and lose their magnetism upon removal of the magnetizing field. Aluminum, platinum, manganese, and chromium are examples of paramagnetic materials. 3. Diamagnetic Materials These materials have a relative permeability of less than one, and magnetic fields repel them. Bismuth, antimony, copper, zinc, mercury, gold, and silver are examples of diamagnetic materials. Knowledge Check Match the followings terms to their appropriate definitions. 1. Iron, steel, nickel, cobalt, alnico and peralloy A. Diamagnetic material 2. Aluminum, platinum, manganese, and chromium B. Ferromagnetic material 3. Bismuth, antimony, copper, zinc, mercury, gold, and silver C. Paramagnetic material 24 Rev 1 ELO 2.4 Left-Hand Rule for Current Carrying Conductors Introduction In 1819, a Danish scientist named Oersted discovered the relationship between magnetism and electrical current. Oersted found that when an electric current flowed through a conductor, the conductor produced a magnetic field around that conductor. The figure below depicts the magnetic field produced by current flow through a conductor. Figure: Magnetic Field Produced by Current Carrying Conductor Left-Hand Rule for Current Carrying Conductors A convenient way to determine the relationship between the current flow through a conductor and the direction of the magnetic lines of force around the conductor is the left-hand rule for current carrying conductors. Step Action 1. Determine the direction of electron flow. 2. Wrap your left hand around the conductor with the thumb pointing in the direction of electron flow. 3. Your fingers are coiling around the conductor in the direction of the magnetic lines of flux. The illustration below helps explain the use of the left-hand rule. Figure: Left-Hand Rule for Current Carrying Conductors Rev 1 25 Left-Hand Rule for Current Carrying Conductors Note Remember that this rule works with electron flow only. When using conventional current, a right-hand rule is used to depict the magnetic lines of force. Left-Hand Rule for Current Carrying Conductors Step In order to use this rule, imagine a copper wire in front of you, with electron flow moving from your left to your right. Employing the steps for use of the left-hand rule: 1. Determine the direction of electron flow. The problem stated that electron flow was from your left to your right. 2. Wrap your left hand around the conductor with the thumb pointing in the direction of electron flow. In order to do this, your left thumb must be pointing from left to right, which means your hand wraps around the conductor with the palm facing down. 3. Your fingers are coiling around the conductor in the direction of the magnetic lines of flux. Your fingers are curling over the top of the conductor, down the far side and under the conductor back to you. This is the direction of the magnetic lines of flux induced by current in this conductor. Knowledge Check The left-hand rule for current carrying conductors will work for both electron flow and conventional flow problems. A. True B. False ELO 2.5 Left-Hand Rule for Coils Introduction Bending a straight conductor into a loop has two results: 1. Magnetic field lines become denser inside the loop. 2. All lines inside the loop align in the same direction. Left-Hand Rule for Coils When a conductor is shaped into several loops, it is considered to be a coil. To determine the polarity of a coil, use the left-hand rule for coils. 26 Rev 1 Step Action 1. Determine the direction of electron flow. 2. Wrap your left hand around the coil, with your fingers pointing in the direction of electron flow. (see illustration below) 3. Your thumb will be pointing to the north pole of the induced magnetic field. The figure below illustrates the left-hand rule for coils. Figure: Left-hand rule for Coils Left-Hand Rule for Coils Demonstration Consider a coil lying on the desk in front of you. If electrons are flowing through the coil, up the side nearest you and over the top of the coil away from you, use the left-hand rule for coils to identify the north magnetic pole induced by the coil. Since the electrons are flowing upward on the near side of the coil and then over the top of the coil away from you, your left hand should be placed with the fingers pointing around the coil in the same direction. The palm will be away from you, and your fingers will point up and away from you over the coil. Your left thumb will point to your right. This is the direction of the induced north magnetic pole. Rev 1 27 Knowledge Check A student is properly demonstrating the left-hand rule for coils to another student. If his fingers wrap around the coil in the direction of current flow, his thumb will be pointing... A. vertically down from the coil. B. toward the south magnetic pole. C. vertically up from the coil. D. toward the north magnetic pole. ELO 2.6 Hysteresis Losses and Magnetic Circuits Introduction In this section, you will learn about hysteresis and magnetic circuits. Hysteresis After magnetizing a ferromagnetic material in one direction, the material will not relax back to zero magnetism upon removal of the imposed magnetic field. Ask class to give the definition of a ferromagnetic material and some common examples of the type of material, as a review of a previous module ELO. Hint Hysteresis Loop A hysteresis loop exists because some of the magnetic domains in the material remain aligned after removal of the magnetizing field. This property is residual magnetism and is desirable in some applications, such as an electromagnet. However, in a device such as a coil, residual magnetism is undesirable because considerable energy is required to realign the magnetic domains as the current reverses direction many times per second. Hysteresis is the name for this phenomenon. Hysteresis means a lagging behind. The magnetic flux in an iron core lags behind the magnetizing force because of the energy required to align the magnetic domains in the material. Hysteresis losses refer to this expenditure of energy to realign magnetic domains in a ferromagnetic material. The figure below shows an example of a hysteresis loop for a particular ferromagnetic material. The larger the area enclosed by the loop, the greater the hysteresis losses associated with the material. 28 Rev 1 Figure: Hysteresis Loop Magnetic Circuits Many common electrical components take advantage of the properties of electromagnetism discussed above. Electrical contactors, starters, relays and solenoids all rely on electromagnets for operation. The figure below shows a circuit where electrical energy creates magnetic flux that actuates a moveable contact. Figure: Simple Magnetic Circuit If the switch in the figure above is closed, electric current flows through the circuit. The current magnetizes the core of the coil, creating a powerful magnet. The magnet attracts the movable armature, and the armature moves towards the magnet (closed). This movement can close valves, close sets of electrical contacts, etc. Opening the switch interrupts current flow, the magnetic field collapses and the spring on the armature returns it to its original position (open). Rev 1 29 Knowledge Check The expenditure of energy to realign magnetic domains in a ferromagnetic material is called... A. polarity reversal. B. hysteresis. C. hysteresis loss. D. magnetic permeability. ELO 2.7 Faraday's Law of Induced Voltage Introduction In 1831, Michael Faraday discovered electromagnetic induction. Faraday found that if a conductor intersects with lines of magnetic force, or if magnetic lines of force intersect with a conductor, a voltage, or EMF, is induced into the conductor. Induced Voltage Consider a magnet with its magnetic lines of force from the north pole to the south pole as shown in the figure below. If a conductor (C), connected to a galvanometer (G), moves across the magnetic field, it will indicate the presence of voltage, or EMF on the galvanometer. When the conductor is stationary, the galvanometer indicates zero EMF. If we move the conductor outside the magnetic field at position 1, the galvanometer still indicates zero EMF. If we move the conductor to position 2, intersecting the lines of magnetic force, the galvanometer will deflect to point A. If we move the conductor d to position 3, the galvanometer will return to zero. By reversing the direction in which the conductor is moved (position 3 to position 1), the same results will be noticed, but of opposite polarity. If the conductor is stationary in the magnetic lines of force, at position 2, the galvanometer will indicate zero. The results derived from this example show that there must be relative motion between the conductor and the magnetic lines of force in order to induce an EMF or voltage in the conductor. 30 Rev 1 Figure: Induced EMF Electric generators demonstrate the most important application of this relative motion between a conductor and a magnetic field. For example, in a DC generator, a cylindrical housing contains electromagnets. Conductors, in the form of coils, rotate on a core such that the coils continually cut the magnetic lines of force. The result is a voltage induced in each of the conductors. These conductors are connected in series, and the induced voltages are added together to produce the generatorβs output voltage. Faraday's Law The magnitude of the induced voltage depends on two factors: 1. The number of turns of a coil 2. How fast the conductor cuts across the magnetic lines of force, or flux The equation below is the mathematical representation for Faradayβs Law of Induced Voltage. ππππ = βπ βΞ¦ βπ‘ Where: Vind = induced voltage N = number of turns in a coil ΞΞ¦ = change in flux Ξt = change in time Faraday's Law Example Step 1. 2. Rev 1 Given: Flux = 4 Wb. The flux increases uniformly to 8 Wb in a period of 2 seconds. Find induced voltage in a coil that has 12 turns, if the coil is stationary in the magnetic field. ππππ = βπ βπ· βπ‘ π₯π· = 8 ππ β 4 ππ = 4 ππ 31 Step Given: Flux = 4 Wb. The flux increases uniformly to 8 Wb in a period of 2 seconds. Find induced voltage in a coil that has 12 turns, if the coil is stationary in the magnetic field. 3. π₯π‘ = 2π 4. βπ· 4 ππ 2 ππ = = βπ‘ 2π π 5. ππππ = β12(2) = β24 π£πππ‘π Lenz's Law Lenzβs Law determines the polarity of the induced voltage described by Faraday. Lenz discovered that the induced voltage has a polarity that will oppose the change causing the induced voltage. When current flows due to the induced voltage, a magnetic field is set up around that conductor such that the conductorβs magnetic field reacts with the external magnetic field. This reaction produces an induced voltage, which opposes the change in the external magnetic field. The negative sign in the mathematical statement of Faradayβs Law is an indication that the EMF is in such a direction as to produce a current whose flux, if added to the original flux, would reduce the magnitude of the EMF. Knowledge Check According to Faraday's Law, which of the following factors influence the magnitude of induced voltage? (Select all that are correct) 32 A. Diameter of the conductor B. Length of the conductor C. How fast the conductor cuts across the magnetic lines of flux D. Number of turns in the coil Rev 1 TLO 2 Summary In this section, you learned the basic laws of magnetism, magnetism effects on electric current, and magnetism effects on voltage. You also learned how magnetic circuits are used as relays, solenoids and other useful circuit components. Now that you have completed this lesson, you should be able to: 1. Describe the relationship between magnetic materials, electron domains, and the law of magnetism. 2. Define the following magnetic terms: flux, flux density, permeability, magnetomotive force, and reluctance. 3. Describe the following materials as they relate to permeability, giving an example for each type of material: ferromagnetic, paramagnetic, and diamagnetic. 4. Apply the Left-Hand Rule for current carrying conductors to determine the direction of lines of magnetic flux. 5. Apply the Left-Hand Rule for coils to determine the polarity of a coil. 6. Describe the operation of a simple magnetic circuit including effects of hysteresis. 7. Given Faradayβs Law of Induced Voltage, describe how varying parameters affect induced voltage. TLO 3 Electrical Drawings Overview This section introduces the different types of electrical drawings and the purpose of each type. You will also learn the common symbols used and how to interpret the drawings. Operators must frequently use electrical drawings to understand equipment response. This capability is necessary to operate the power plant. Objectives Upon completion of this lesson, you will be able to do the following: 1. Given common standard electrical symbols in the lesson, identify the component that the symbol represents. 2. Identify the following types of diagrams: schematic diagrams, oneline diagrams, and block diagrams. 3. Define the following electrical circuit terms and components: resistivity, temperature coefficient of resistivity, resistance temperature detector, electrical circuit, open circuit, closed circuit, short circuit, series circuit, and parallel circuit. 4. Describe the principles of the following circuit protection devices: protective relays, fuses, circuit breakers. ELO 3.1 Electrical Symbols Introduction In order to read and interpret electrical system diagrams and schematics, personnel must be thoroughly familiar with the many symbols used. With Rev 1 33 mastery of these symbols, it will be relatively easy to understand most electrical diagrams and schematics. Electrical Symbols The figure below contains common symbols for many circuit components. Most suppliers will provide a dictionary of symbols with drawings, but knowledge of common symbols is necessary to interpret drawings. Figure: Common Electrical Drawing Symbols 34 Rev 1 Knowledge Check Match the electrical symbols with their components. A. Fuse 1. B. Battery 2. C. Diode 3. D. Capacitor 4. E. AC power source 5. F. Relay 6. ELO 3.2 Types of Drawings Introduction In this section, you will learn to identify the different types of electrical drawings and the uses for each. Schematic Diagrams Schematic diagrams are the standard way to show information about electrical and electronics circuits. On schematic diagrams, graphic symbols represent the component parts, the previous section presented some of these symbols. Because graphic symbols are small, it is possible to have diagrams in a compact form. Lines represent wires connecting components. The resultant schematic shows the relationship of those components with one another. As an example, look at a schematic diagram of a two-transistor radio circuit in the figure below. This diagram, from left to right, shows the components in the order the circuit uses them to convert radio waves into sound energy. By using this schematic, it is possible to trace the operation of the circuit from outside antenna to headset. Because of this important feature of schematic diagrams, they are widely used in construction, maintenance, and servicing of all types of electronic circuits. Rev 1 35 Figure: Schematic Diagram One-line Diagrams The one-line, or single-line, diagram shows the components of a circuit using single lines and the appropriate graphic symbols. One-line diagrams show two or more conductors connected between components in the actual circuit. The one-line diagram shows all pertinent information about the sequence of the circuit, but does not give as much detail as a schematic diagram. Normally, the one-line diagram shows highly complex systems without showing the actual physical connections between components and individual conductors. The figure below shows a typical one-line diagram. Figure: One-line Diagram 36 Rev 1 Block Diagrams A block diagram shows the relationship between component groups, or stages in a circuit. In block form, it shows the path through a circuit from input to output, as shown in the figure below. The blocks are squares or rectangles connected by single lines with arrowheads at the terminal end, showing the direction of the signal path from input to output. Normally, the necessary information to describe the stages of components is contained in the blocks. Figure: Block Diagram Wiring Diagrams A wiring diagram is a very simple way to show wiring connections in an easy-to-follow manner. These types of diagrams are often included with home appliances and automobile electrical systems. Wiring diagrams show the component parts in pictorial form, with the components identified by name. Most wiring diagrams also show the relative location of component parts and color coding of conductors or leads. The figure below shows a typical wiring diagram. Figure: Wiring Diagram Rev 1 37 Knowledge Check Match the following terms to the appropriate definitions. 1. Shows wiring connections to trace the operation of the circuit from beginning to ending in an easy-to-follow manner, standard way to show information about electrical circuits. A. One-line diagram 2. Shows highly complex systems without showing the actual physical connections between components and individual conductors. B. Wiring diagram 3. Shows the relationship between component groups, or stages in a circuit. C. Schematic diagram 4. Shows wiring connections in an easy-tofollow manner. D. Block diagram ELO 3.3 Circuit Terminology Introduction In this section, you will learn common terminology used to discuss electrical circuits. Resistivity Resistivity is the measure of the resistance a material imposes on current flow. The resistance of a given length of conductor depends upon the specific resistance of the conductor material, the length of the conductor, and the cross-sectional area of the conductor, as shown in the equation below. πΏ π΄ Where: π =π R = resistance of conductor, Ξ© Ο = specific resistance or resistivity, cm-Ξ©/ft L = length of conductor, ft A = cross-sectional area of conductor, cm2 Specific resistance, denoted by the Greek letter Ο (rho), denotes a material's inherent resistance, and allows comparisons of different materials' 38 Rev 1 resistances without regard to size, shape, length, or area. A higher rho value indicates higher resistance. Temperature Coefficient of Resistivity Temperature coefficient of resistivity, Greek letter Ξ± (alpha), is the amount of change of the resistance of a material for a given change in temperature. A positive value of Ξ± indicates that R increases with temperature; a negative value of Ξ± indicates R decreases; and zero Ξ± indicates that R is constant. For a given material, Ξ± may vary with temperature; therefore, charts are often used to describe how resistance of a material varies with temperature. The equation below shows the relationship between resistance and temperature in a material. π π‘ = π π + π π (πΌπ₯π) Where: Rt = resistance of a material at a higher temperature Ro = resistance at 20°C Ξ± = temperature coefficient ΞT = temperature rise above 20°C Resistance Temperature Detector (RTD) Temperature detecting devices such as resistance temperature detectors (RTD) use this phenomenon of changing resistance with changes in temperature to correlate temperature with a measured resistance change. A RTD is a temperature probe made from a material that exhibits a linear coefficient of resistance. As temperature changes, the resistance of the RTD will vary in a predictable fashion. With a constant amount of current flowing in the detector circuitry, a change in resistance will cause a change in the voltage drop across the RTD (Ohmβs Law, E = I x R). When calibrated to react to this voltage drop, a temperature meter indicates a substanceβs temperature. Electrical Circuits Each electrical circuit has at least four basic parts: ο· ο· ο· ο· A source of electromotive force Conductors Load or loads Some means of control In the closed circuit below, the source of EMF is the battery and the conductors are wires that connect the various component parts. The resistor is the load and a switch is the circuit control device. Closed Circuit A closed circuit, shown below, is an uninterrupted, or unbroken, path for current from the source (EMF), through the load, and back to the source. Rev 1 39 Figure: Closed Electrical Circuit Open Circuit An open circuit, or incomplete circuit, exists if a break in the circuit occurs; preventing a complete path for current flow. The figure below shows examples of open circuits interrupting current flow. Figure: Open Circuits Short Circuit A short circuit is a circuit that offers very little resistance to current flow and can cause dangerously high current flow through the circuit. An inadvertent connection between two points in a circuit usually causes a short circuit, which offers little or no resistance to current flow compared to the designed circuit. Shorting resistor R in the figure below will probably cause the fuse to blow. 40 Rev 1 Figure: Short Circuit Series Circuit A series circuit is a circuit where there is only one path for current flow. In the series circuit shown in the figure below, the current will be the same at any point in the circuit. This means that the current flow through R1 is the same as the current flow through R2 and R3. Figure: Series Circuit Parallel Circuits Parallel circuits are circuits that have two or more components connected across the same voltage source, as shown in the figure below. Resistors R1, R2, and R3 are in parallel with each other and the source. Each parallel path is a branch with its own individual current. When the current leaves the source V, part I1 of IT will flow through R1; part I2 will flow through R2; and part I3 will flow through R3. Current through each branch can be different; however, voltage across each branch of the circuit will be equal. Rev 1 41 V = V1 = V2 = V3 Figure: Parallel Circuit Knowledge Check Match the terms with their appropriate definitions. 1. A circuit with a break that prevents a complete path so that no current flows A. Series Circuit 2. A circuit that offers very little resistance to current flow and can cause dangerously high current flow through the circuit B. Parallel Circuit 3. A circuit that has two or more components connected across the same voltage source C. Open Circuit 4. A circuit where there is only one path for current flow D. Short Circuit 42 Rev 1 ELO 3.4 Circuit Protection Devices Introduction In this section, you will learn about devices used to protect electrical circuits from undesirable electrical conditions. These devises protect equipment and people from currents and voltages outside their normal operating ranges. Relays A protective relay is automatic device that senses an abnormal condition and closes contacts. When these contacts close, they complete the circuit breaker trip coil circuit and trip the breaker open to protect the rest of the circuit from the from the abnormal condition. Some typical protective relay parameters monitored are over current, over voltage, under frequency and under voltage. The figure below shows two example relays. Figure: Relays Fuses A fuse is a simple circuit protection device. It derives its name from the Latin word "fusus," meaning, "to melt." Fuses have been in use almost from the beginning of the use of electricity. The earliest type of fuse was simply a bare wire between two connections. The wire was smaller than the conductor it was protecting and, therefore, would melt before damage to the conductor occurred. Some "copper fuse link" types are still in use, but most fuses no longer use copper as the fuse element (the part of the fuse that melts). After changing from copper to other metals, tubes or enclosures were developed to hold the melting metal. The enclosed fuse made possible the addition of filler material, which helps to contain the arc that occurs when the element melts. Rev 1 43 For many low power uses, the filler material is not required. A simple glass tube is used. The use of a glass tube gives the added advantage of being able to see when a fuse is open. Fuses of this type are common in automobile or small electronic circuits. The figure below shows several fuses and the symbols used to denote fuses on schematics. Figure: Typical Fuses and Schematic Symbols Circuit Breakers While a fuse protects a circuit, it destroys itself in the process of opening the circuit. After correcting the problem that caused the increased current or heat, personnel must replace the destroyed fuse with a new fuse in the circuit. A circuit protection device that can be used more than once solves the problem of replacement fuses. Resetting the device restores its protection capability without parts replacement. This device is called a circuit breaker because it breaks (opens) the circuit, when pre-determined conditions are sensed, or can be used to manually open a circuit. The figure below shows a typical circuit breaker and the appropriate schematic symbols. 44 Rev 1 Figure: Typical Circuit Breaker and Schematic Symbols Operating Experience There have been many incidents throughout the industry where improper operation or lack of full understanding of the proper circuit breaker operation have contributed to plant events. Review SER A 98-0035 and discuss operator/technician responsibility and human performance barriers that should have prevented this event. Knowledge Check A device which senses abnormal conditions and closes contacts is called a: Rev 1 A. breaker B. safety sensor C. relay D. Thermal fuse 45 TLO 3 Summary In this section, you learned common electrical symbols used in drawings, the different types of electrical drawings, terminology for different circuit types, and how temperature affects electrical resistance. The section also introduced circuit protective devises used to protect equipment and personnel from abnormal conditions. Now that you have completed this lesson, you should be able to: 1. Given common standard electrical symbols in the lesson, identify the component that the symbol represents. 2. Identify the following types of diagrams: schematic diagrams, oneline diagrams, and block diagrams. 3. Define the following electrical circuit terms and components: resistivity, temperature coefficient of resistivity, resistance temperature detector, electrical circuit, open circuit, closed circuit, short circuit, series circuit, and parallel circuit. 4. Describe the principles of the following circuit protection devices: protective relays, fuses, circuit breakers. TLO 4 Batteries Overview In this section, you will learn how batteries and voltaic cells function, how they are charged and discharged, and hazards they pose. Batteries provide back-up power to vital loads. Operators must understand batteries to monitor and ensure their proper operation. Objectives Upon completion of this lesson, you will be able to do the following: 1. State the purpose of a battery and define the common terms as they relate to batteries and voltaic cells. 2. Describe the operation of a simple voltaic cell. 3. State the chemical equation that occurs when a lead-acid battery is being charged or discharged. 4. Describe the relationship between total battery voltage, cell voltage, and current for a series-connected and parallel-connected battery. 5. State the advantage of each of the common types of batteries. 6. Describe common battery hazards and precautions associated with battery use. ELO 4.1 Battery Terminology Introduction Modern technology uses batteries for a wide variety of services. The purpose of a battery is to store chemical energy and to convert this chemical energy into electrical energy when the need arises. To study battery operation and characteristics, it is necessary to understand a few terms used with batteries. 46 Rev 1 Battery Terminology The table below includes some key battery terms. Term Definition Voltaic Cell The term voltaic cell is a combination of materials used to convert chemical energy into electrical energy. A voltaic or chemical cell consists of two electrodes made of different types of metals or metallic compounds placed in an electrolyte solution. Battery A battery is a group of two or more voltaic cells, usually connected in series in order to obtain a desired voltage. Each individual cell usually produces about 1.5 VDC. Electrode An electrode is a metallic compound, or metal, which has an abundance of electrons (negative electrode) or an abundance of positive charges (positive electrode). Electrolyte An electrolyte is a solution that is capable of conducting an electric current. The electrolyte of a cell may be a liquid or a paste. If the electrolyte is a paste, the cell is a dry cell; if the electrolyte is a solution, it is a wet cell. Specific Gravity Specific gravity is the ratio comparing the weight of any liquid to the weight of an equal volume of water. The specific gravity of pure water is 1.000. Lead-acid batteries use an electrolyte, which contains sulfuric acid. Pure sulfuric acid has a specific gravity of 1.835, since it weighs 1.835 times as much as pure water per unit volume. Since the electrolyte of a lead-acid battery consists of a mixture of water and sulfuric acid, the specific gravity of the electrolyte will fall between 1.000 and 1.835. Normally, the solution of water and sulfuric acid electrolyte for this type of battery has specific gravity is less than 1.350. A hydrometer measures specific gravity of a liquid. A simple hydrometer consists of a glass float inside a glass tube, as shown in the figure below. The glass hydrometer float has a weight at one end to maintain it vertical, and seals at both ends. A scale calibrated in specific gravity runs lengthwise along the body of the float. The float is free to move vertically inside the glass tube, and the fluid with the unknown specific gravity partially fills the glass tube. Depressing the suction bulb, inserting the hydrometer base into the electrolyte, and releasing the suction bulb draws electrolyte solution into the hydrometer. As the fluid enters the tube, the hydrometer float will reach a certain equilibrium level in the fluid. Rev 1 47 The extent to which the hydrometer float protrudes above the level of the fluid depends on the specific gravity of the fluid. The reading on the float scale at the surface of the fluid is the specific gravity of the fluid. Figure: Simple Hydrometer Battery Terminology The table below includes additional battery terms and their definitions. Term Definition Ampere-Hour One ampere-hour is a current of one ampere flowing for one hour. If you multiply the current in amperes by the time of flow in hours, the result is the total number of ampere-hours. Ampere-hours normally indicate the amount of energy a storage battery can deliver. Primary Cell Primary cells are cells that cannot be recharged after their voltage output has dropped to a value that is not usable. Dry cells used in flashlights and transistor radios (e.g., AA cells, C cells) are examples of primary cells. Secondary Cells Secondary cells are cells that will accept recharging to nearly their original condition. The most common example of a secondary, or rechargeable cell, is the leadacid automobile battery. 48 Rev 1 Term Definition Capacity The capacity of a storage battery determines how long the storage battery will operate at a certain discharge rate, usually stated in ampere-hours. For example, discharging a 120 ampere-hour battery at 10 amps per hour will be completely discharge the battery after 12 hours. Shelf Life The shelf life of a battery is the time that a battery may be stored and retain at least 90 percent of its original capacity. Charge The charge of a battery may refer to one of two things: ο· ο· Discharge Relative state of capacity of the battery Actual act of applying current flow in the reverse direction to return the battery to a fully charged state Discharge is the act of drawing current from a battery. Knowledge Check Match the following terms with their appropriate definition. 1. cells that cannot be returned to a good condition, or recharged after their voltage output has dropped to a value that is not usable A. Capacity 2. a solution which is capable of conducting an electric current B. Primary cell 3. a current of one ampere flowing for one hour C. Ampere-hour 4. the length of time that a storage battery will operate at a certain discharge rate; usually given in ampere-hours D. Electrolyte Rev 1 49 ELO 4.2 Simple Voltaic Cell Introduction The purpose of a battery is to store chemical energy and to convert this chemical energy into electrical energy when the need arises. A chemical cell (or voltaic cell) consists of two electrodes of different types of metals or metallic compounds and an electrolyte solution, which is capable of conducting an electric current. Simple Voltaic Cell A good example of a voltaic cell is one that contains zinc and copper electrodes. The zinc electrode contains an abundance of negatively charged atoms, and the copper electrode contains an abundance of positively charged atoms. Upon insertion of both of these electrodes in an electrolyte, chemical action begins. The zinc electrode will accumulate a much larger negative charge because some of it will dissolve into the electrolyte. The atoms that leave the zinc electrode have a positive charge; the negatively charged ions of the electrolyte attract these atoms. The positively charged atoms repel the positive charged ions of the electrolyte toward the copper electrode as shown in the figure below. Figure: Chemical Production of Electricity This action causes removal of electrons from the copper electrode, leaving it with an excess of positive charge. Upon connection of a load across the electrodes, the forces of attraction and repulsion will cause the free electrons in the negative zinc electrode to move through the connecting wire and load, and toward the positive copper electrode as shown in the figure below. The potential difference that results allows the cell to function as a source of applied voltage. 50 Rev 1 Figure: Electron Flow through a Battery Knowledge Check Components of a simple voltaic cell include _____________. Select all that are correct. A. electrolyte solution B. terminals C. hydrochloric acid D. two electrodes ELO 4.3 Chemistry of a Lead-Acid Battery Introduction In this section, you will learn the chemical action that produces electricity in a lead-acid battery. Discharge and Charging of a Lead-Acid Battery In a lead-acid battery, an electrolytic solution of diluted sulfuric acid (H2SO4) acts electro-chemically on two types of lead. The positive plate consists of lead peroxide (PbO2), and the negative plate is sponge lead (Pb), as shown in the figure below. Figure: Chemical Action during Discharge Rev 1 51 Discharge When a lead-acid battery discharges, the electrolyte separates into H2 and SO4. The H2 will combine with some of the oxygen formed on the positive plate to produce water (H2O), and thereby reduces the amount of acid in the electrolyte. The sulfate (SO4) combines with the lead (Pb) of both plates, forming lead sulfate (PbSO4), as shown below. πππ2 + ππ + 2π»2 ππ4 β 2ππππ4 + 2π»2 π Charging When charging a lead-acid battery, the action described in the discharge reverses because the electron flow reverses. This reversed electron flow drives the lead sulfate (PbSO4) off the plates and back into the electrolyte (H2SO4). The return of acid to the electrolyte will reduce the sulfate on the plates and increase the specific gravity of the electrolyte. This will continue to happen until the process drives all of the lead sulfate from the plates and back into the electrolyte, as shown in the figure below. Figure: Chemical Action during Charging Chemically, the reaction is: 2ππππ4 + 2π»2 π β πππ2 + ππ + 2π»2 ππ4 Gasses during Charging During charging, and as a lead-acid battery charge nears completion, operators frequently raise the charging current to drive the remaining lead sulfate off the plates. This liberates hydrogen (H2) gas at the negative plate, and oxygen (O2) gas at the positive plate. The excessive current also ionizes the water (H2O) in the electrolyte. Since hydrogen is highly explosive, and oxygen is highly flammable, it is necessary to provide adequate ventilation to the battery whenever charging is in progress. In addition, do not allow any smoking, electric sparks, or open flames near a charging battery. Electrolyte Specific Gravity and State of Charge The specific gravity of the electrolyte decreases as the battery discharges and increases to its normal, original value as it is charged. The decrease in 52 Rev 1 specific gravity on discharge is proportional to the ampere-hours discharged. Since specific gravity of a lead-acid battery decreases proportionally during discharge, the value of specific gravity at any given time is an approximate indication of the batteryβs state of charge. To determine the state of charge, compare the specific gravity of the electrolyte with the full charge specific gravity value from the manufacturerβs data. Knowledge Check The electrolyte in a lead-acid battery is ___________________. A. made of sulfuric acid and mineral oil B. chosen for its properties as a non-conductor C. a solution of sulfuric acid and pure water D. not involved in the chemical reactions, but just works as an insulating medium between the electrodes ELO 4.4 Series and Parallel Connected Batteries Introduction In this section, you will learn the characteristics of series connected and parallel connected batteries. Series Cells When connecting several cells in series as shown in the figure below, the total voltage output of the battery is equal to the sum of the individual cell voltages. In the example of the batteries shown in the figure below, the four-1.5 V cells provide a total of 6 volts. When connecting cells in series, the positive terminal of one cell connects to the negative terminal of the next cell. The current flow through batteries connected in series is the same as for one cell. The advantage of connecting cells in this manner is that multiple seriesconnected battery cells exhibit a higher voltage output than a single cell. Rev 1 53 Figure: Battery Cells in Series Parallel Cells When connecting cells in parallel, the total current capacity of the battery is equal to the sum of the individual cell amperages. When connecting cells in parallel, all the positive terminals connect together, and all the negative terminals connect together, as shown in the figure below. The total voltage output of a battery connected in parallel is the same as that of a single cell. Cells connected in parallel have the same effect as increasing the size of the electrodes and electrolyte in a single cell. The advantage of connecting cells in parallel is that it will increase the current-carrying capability of the battery. Figure: Battery Cells in Parallel 54 Rev 1 Internal Resistance Internal resistance in a chemical cell is due mainly to the resistance of the electrolyte between electrodes. Current flowing through a battery will produce a voltage drop across the battery due to this internal resistance, lowering the batteryβs terminal voltage. This resistance to current flow through the battery itself can limit the amount of current the battery is able to produce when it is discharging. Knowledge Check A series connected battery provides a higher voltage than connecting the same cells in parallel. A. True B. False ELO 4.5 Types of Battery Materials Introduction The type of electrolyte the battery uses determines its basic category; there are wet and dry cells. The electrolyte of a cell may be a liquid or a paste. If the electrolyte is a paste, the cell is a dry cell. If the electrolyte is a liquid solution, the cell is a wet cell. Carbon-Zinc Cell The carbon-zinc cell is one of the oldest and most widely used types of dry cells. The carbon in the battery is a rod in the center of the cell, which acts as the positive terminal. Zinc comprises the case, and acts as the negative electrode. The electrolyte for this type of cell is a chemical paste-like mixture that fills the space between the carbon electrode and the zinc case. Sealing the cell prevents any of the liquid in the paste from evaporating. The advantage of a carbon-zinc battery is that it is durable and very inexpensive to produce. The cell voltage for this type of cell is about 1.5 volts. Alkaline Cell The alkaline cell has an alkaline electrolyte of potassium hydroxide. Zinc comprises the negative electrode, and manganese dioxide comprises the positive electrode. The typical alkaline cell also generates 1.5 volts. The alkaline cell has the advantage of an extended life over that of a carbon-zinc cell of the same size; however, it is usually more expensive to produce. Nickel-Cadmium Cell The nickel-cadmium cell is a secondary cell, and the electrolyte is potassium hydroxide. The negative electrode is nickel hydroxide, and the positive electrode is cadmium hydroxide. The nominal voltage of a nickelcadmium cell is 1.25 volts. The nickel-cadmium battery has the advantage of being a dry cell that is a true storage battery with a reversible chemical reaction (i.e., it can be recharged). The nickel-cadmium battery is a rugged, Rev 1 55 dependable battery. It gives dependable service under extreme conditions of temperature, shock, and vibration. Due to its dependability, it is ideally suited for use in portable communications equipment. Knowledge Check Match the battery type with the appropriate description. 1. Electrolyte is a paste A. Wet cell 2. Rechargeable dry cell B. Dry cell 3. Longer life than carbon zinc cell C. Nickelcadmium cell 4. Electrolyte is a liquid solution D. Alkaline cell ELO 4.6 Battery Hazards Introduction In this section, you will learn the dangers posed by batteries and methods to minimize these hazards. Shorted Cell It is possible to have a short circuit in a cell. Possible causes include the following: faulty separators, lead particles or other metals forming a circuit between the positive and negative plates, buckling of the plates, or excessive sediments in the bottom of the cell. The primary cause of some of these occurrences is overcharging and over-discharging of the battery, which causes sediment to build up in bottom of the cell due to flaking of active material and buckling of cell plates. Avoid overcharging and over-discharging at all costs. Shorted cells cause a great reduction in battery capacity. Each shorted cell reduces battery capacity by a fraction equal to one divided by the total number of cells. Hydrogen and Oxygen Gas Generation A lead-acid battery cannot absorb all the energy from the charging source when the battery is nearing the completion of the charge. This excess energy dissociates water by way of electrolysis into hydrogen and oxygen. The positive plate produces oxygen, and the negative plate produces hydrogen. This process is gassing. 56 Rev 1 Gassing is first noticed when cell voltage reaches 2.30-2.35 volts per cell and increases as the charge progresses. At full charge, the amount of hydrogen produced is about one cubic foot per cell for each 63 amperehours input. If gassing occurs and the gases collect, they produce an explosive mixture of hydrogen and oxygen. It is necessary to provide adequate ventilation near the charging battery and keep the area free of any open flames or spark-producing equipment. When the battery voltage is greater than 2.30 volts per cell, gassing will occur and cannot be prevented entirely. To reduce the amount of gassing, limit charging voltage level to 2.30 volts per cell. For example, limit charging voltage level to 13.8 volts for a 12-volt battery with 6 cells (2.30 volts/cell x 6 cells = 13.8 volts). Heat Generation For best battery service, maintain the operating temperature of a battery in the band of 16-27°C (60-80°F). Whenever the battery is charged, the current flowing through the battery will cause heat generation by the electrolysis of water. The current flowing through the battery (I) will also cause heat to be generated (P) during charge and discharge as it passes through the internal resistance (Ri), as illustrated using the formula for power below. π = πΌ 2 π π Higher temperatures will give some additional capacity, but they will eventually reduce the life of the battery. Very high temperatures, 52°C (125°F) and higher, can actually do damage to the battery and cause early failure. Low temperatures will lower battery capacity but also prolong battery life under floating (i.e., slightly charging) operation or storage. Extremely low temperatures can freeze the electrolyte, but only if the battery is low in specific gravity. Knowledge Check Battery temperatures exceeding 105°F can cause damage and early failure of the battery Rev 1 A. True B. False 57 TLO 4 Summary In this section, you learned the types of batteries, the chemical reactions in which batteries produce electricity, and the hazards of battery operation. Now that you have completed this lesson, you should be able to: 1. State the purpose of a battery and define the common terms as they relate to batteries and voltaic cells. 2. Describe the operation of a simple voltaic cell. 3. State the chemical equation that occurs when a lead-acid battery is being charged or discharged. 4. Describe the relationship between total battery voltage, cell voltage, and current for a series-connected and parallel-connected battery. 5. State the advantage of each of the common types of batteries. 6. Describe common battery hazards and precautions associated with battery use. TLO 5 DC Circuit Analysis Overview In this section, you will learn to analyze DC circuits and determine currents, voltages, and resistances in the circuits. Operators must be able to analyze basic circuits in order to understand how electrical circuits and machines operate and how they may fail. Objectives Upon completion of this lesson, you will be able to do the following: 1. Calculate total resistance for a series or parallel circuit. 2. Explain the terms voltage divider and current divider. 3. Given a DC electrical circuit, identify the polarity of the voltage drops in the circuit. 4. State Kirchhoffβs voltage law and current law. 5. Solve problems for voltage and current using Kirchhoffβs laws. ELO 5.1 Total Resistance Introduction In this section, we will review how to calculate the total resistance in series and parallel circuits, and work problems calculating resistance. Each type of DC circuit includes certain characteristics that determine the way its voltage and current behave. To begin analysis of the voltages and currents at each part of a circuit, an understanding of these characteristics is necessary. Series Circuits A series circuit is an electrical circuit in which there is only one flow path for current, and it passes through all circuit components sequentially. There may be many different types of circuit components, but one current path goes to each component sequentially. 58 Rev 1 The figure below shows an example of a simple series circuit with three resistors. Figure: Series Circuit Parallel Circuit A parallel circuit has multiple branches through which current can flow, with the circuit voltage applied across each of the circuit branches. Current will flow through each branch based on the voltage applied and the resistance of that branch, with no effect from the other branches. The figure below shows a simple parallel circuit with three resistors. Figure: Parallel Circuit Compound Circuit A compound circuit has portions that are in series and portions that are in parallel. To analyze a compound circuit, calculate equivalent resistances and replace the more complex parts of the circuit with simpler equivalents, and then solve for the individual sections. The figure below shows a simple compound circuit. Rev 1 59 Figure: Compound Circuit Resistance in Series Circuits The table below gives direction for finding the total (or equivalent) resistance in a series circuit. Step Action 1. Determine the type of circuit (series, parallel, or compound). 2. If it is a series circuit, continue. If not, go to the appropriate section for guidance. 3. Add the individual resistance values. 4. The sum of the individual resistances is the total or equivalent resistance. The total resistance in a series circuit is equal to the sum of all the parts of that circuit, as shown below. π π = π 1 + π 2 + π 3 β¦ ππ‘π. Where: RT = total resistance R1, R2, and R3 = resistance in series 60 Rev 1 Figure: Resistance in a Series Circuit Resistance in a Series Circuit Example A series circuit has a 60Ξ©, a 100Ξ©, and a 150Ξ© resistor in series (see figure above). What is the total resistance of the circuit? Solution: π π = π 1 + π 2 + π 3 = 60 + 100 + 150 = 310 πΊ Voltage in a Series Circuit The total voltage across a series circuit is equal to the sum of the voltages across each resistor in the circuit (see figure below). ππ = π1 + π2 + π3...etc. Where: VT = total voltage V1 = voltage across R1 V2 = voltage across R2 V3 = voltage across R3 Figure: Voltage Drops in a Series Circuit Rev 1 61 Voltage Drops in Series Circuits You may now apply Ohmβs law to the entire series circuit or to individual component parts of the circuit. When used on an individual component part, the voltage across that part is equal to the current (I) times the resistance (R) of that part. For the circuit shown in the figure below, the voltage can be determined as shown. V1 = IR1 V2 = IR2 V3 = IR3 VT = V1 + V2 + V3 VT = 10 volts + 24 volts + 36 volts VT = 70 volts Figure: Voltage Total in a Series Circuit To find the total voltage across a series circuit, multiply the current by the total resistance as shown below. ππ = πΌπ π Where: VT = total voltage I = current RT = total resistance The voltages of V1, V2, and V3 are termed voltage drops or IR drops. Their effect is to reduce the available voltage that is available across the other circuit components. The sum of the voltage drops in any series circuit is always equal to the applied voltage. 62 Rev 1 Resistance in Parallel Circuits The table below provides instructions for calculating resistance in parallel circuits. Step Action 1. Determine the type of circuit (series, parallel, or compound). 2. If it is a parallel circuit, continue. If not, go to the appropriate section for guidance. 3. Determine the current in each branch. (πΌ = π ) 4. Determine the Total Resistance. (π π = ) 5. The Total (Equivalent) Resistance for resistors in parallel calculated above is always less than the smallest of the individual resistances. π π πΌπ Parallel Currents The sum of the currents flowing through each branch of a parallel circuit is equal to the total current flow in the circuit. Using Ohmβs Law, the branch current for a three-branch circuit shown in the figure below equals the applied voltage divided by the resistance as shown in the equations below. π π Branch 1: πΌ1 = π 1 = π 1 π 1 π Branch 2: πΌ2 = π 2 = π 2 2 π3 π 3 3 Branch 3: πΌ3 = π = π Figure: Current in a Parallel Circuit In this example: πΌ1 = π 120 = = 8A π 1 15 Rev 1 63 πΌ2 = π 120 = = 6π΄ π 2 20 π°π = π½ πππ = = πππ¨ πΉπ ππ Parallel Currents Example A circuit includes two resistors, each drawing 3A, and a third resistor, drawing 2A, connected in parallel across a 115-volt source shown in the figure above. What is total current (IT)? Solution: πΌπ = πΌ1 + πΌ2 + πΌ3 πΌπ = 3π΄ + 3π΄ + 2π΄ πΌπ = 8π΄ Resistance in Parallel To determine total resistance in a parallel circuit, apply Ohmβs Law. Divide the voltage across the parallel resistance by the total line current as shown. π π = π πΌπ Figure: Resistance in a Parallel Circuit Solution You can also find the total resistance in a parallel circuit by using the equation below: 1 1 1 1 1 = + + +. . . . π π π 1 π 2 π 3 π π 64 Rev 1 Resistance in Parallel Example Find the total resistance of a 4Ξ©, an 8Ξ©, and a 16Ξ© resistor in parallel. Step 1. 1 1 1 1 = + + π π π 1 π 2 π 3 2. 1 1 1 1 = + + π π 4 8 16 3. 1 4 2 1 7 = + + = π π 16 16 16 16 4. π π = 16 = 2.29 πβππ 7 Whenever resistors are in parallel, the total resistance is always smaller than any single branch. Note Equal Resistors in Parallel Total resistance of equal resistors in a parallel circuit is equal to the resistance of one resistor divided by the number of resistors. π π Where: π π = RT = total resistance R = resistance of one resistor N = number of resistors Equal Resistors in Parallel Example Step 1. Five lamps, each with a resistance of 40Ξ©, are connected in parallel. Find the total resistance. π π = π 1 π 2 π 3 π 4 π 5 40πΊ = = = = = π π π π π π 2. π = 5 3. π π = π /π = 40/5 = 8 πβππ Rev 1 65 When any two resistors are unequal in a parallel circuit, it is easier to calculate RT by multiplying the two resistances and then dividing the product by the sum, as shown in the figure below. This approach is valid when there are only two resistors in parallel. π π = π 1 π 2 π 1 + π 2 Figure: Parallel Circuit Step What value of resistance must be added, in parallel, with an 8Ξ© resistor to provide a total resistance of 6Ξ© (See above figure)? 1. π π = 2. 3. 6 = π 1 π 2 π 1 + π 2 8π π 8 + π π 6(8 + π π ) = 8π π 48 + 6 π π = 8 π π 4. 5. 48 = 2 π π 6. π π = 24 πβππ Resistance in Compound Circuits The table below provides instructions for analyzing compound circuits. Step Action 1. Determine the type of circuit (series, parallel, or compound). 2. If it is a compound circuit, continue. If not, go to the appropriate section for guidance. 66 Rev 1 Step Action 3. Identify parallel circuits within the compound circuit. Solve them for RT, until you have an equivalent series circuit. 4. Solve the equivalent series circuit for I and for voltage drops across each resistance or equivalent resistance. 5. Solve each parallel portion for I through each resistor. 6. Check the solution. Series Circuit Demonstration A series circuit has a 50Ξ©, a 75Ξ©, and a 100Ξ© resistor in series as shown in the figure below. Find the voltage necessary to produce a current of 0.5 amps. Figure: Series Circuit Example Step Action Result 1. Find circuit current. As we already know, current is the same throughout a series circuit, which equals 0.5 amps. 2. Find RT. π π = π 1 + π 2 + π 3 π π = 50 πΊ + 75 πΊ + 100 πΊ π π = 225 πΊ 3. Find VT. Use Ohmβs law. ππ = πΌπ π ππ = (0.5 ππππ )(225 πΊ) ππ = 112.5 π£πππ‘π Rev 1 67 Parallel Circuit Demonstration Two branches, R1 and R2, are across a 120 V power source, as shown in the figure below. The total current flow is 30 A. Branch R1 takes 22 amps. What is the current flow in branch R2, the resistance provided by R1 and R2, and the equivalent resistance for the circuit? Figure: Parallel Circuit Example Step 1. 2. 3. 4. Solution πΌπ = πΌ2 = πΌ2 = πΌ2 = πΌ1 + πΌ2 πΌπ β πΌ1 30 ππππ β 22 ππππ 8 ππππ π 1 = π πΌ1 π 1 = 120 = 5.5 πβππ 22 π πΌ2 120 π 2 = = 15 πβππ 8 π 2 = π πΌπ 120 π π = = 4 πβππ 30 π π = Compound Circuit Demonstration Given the following: 68 Rev 1 ο· ο· The voltage source is 12 V. A = 6 ohms B = 24 ohms C = 12 ohms Find the current flow through each resistor and the equivalent resistance for resistors B and C, shown in the figure below. Figure: Compound Circuit Step 1. Action Result First, find the equivalent Resistance for resistors B and C. (π π΅ )(π πΆ ) (π π΅ + π πΆ ) (24)(12) = (24 + 12) π ππ = π ππ π ππ = 8 πβππ 2. Next, use Req to find total current (IT) which is also the current through resistor A. 3. Use IT and RA to find the voltage drop across RA, and then subtract that from V to find the voltage drop across RB and RC. 4. Finally, Use VB (VC) and RB and RC to determine the current through resistances B and C. Rev 1 πΌπ = π π π π π π΄ + π ππ 12 πΌπ = (6 + 8) 12 πΌπ = = 0.86 ππππ 14 πΌπ = ππ΄ = (πΌπ )(π π΄ ) ππ΄ = (0.86ππππ )(6πβππ ) = 5.16π ππ΅ = ππΆ = ππ β 5.16 ππ΅ = ππΆ = 12 β 5.16 = 6.84π πΌπ΅ = ππ΅ π π΅ πΌπ΅ = 6.84π = 0.29ππππ 24πβππ 69 Step Action Result πΌπΆ = πΌπΆ = ππΆ π πΆ 6.84π = 0.57ππππ 12πβππ Knowledge Check A 120 V battery connects in series with three resistors: 40Ξ©, 60Ξ©, and 100Ξ©, as shown in the figure below. Find the voltage across each resistor. 70 A. V1 = 24 volts, V2 = 36 volts, V3 = 60 volts B. V1 = 40 volts, V2 = 60 volts, V3 = 100 volts C. V1 = 30 volts, V2 = 30 volts, V3 = 60 volts D. V1 = 20 volts, V2 = 40 volts, V3 = 60 volts Rev 1 Knowledge Check A parallel circuit consists of R1 = 15Ξ©, R2 = 20Ξ© and R3 =10Ξ©, with an applied voltage of 120 V, shown in the figure below. What current will flow through each branch, and what is the equivalent resistance (RT) for the circuit? A. I1 = 8 amps, I2 = 6 amps, I3 = 12 amps, RT = 4.6 ohms B. I1 = 6 amps, I2 =8 amps, I3 = 10 amps, RT = 5.0 ohms C. I1 =6 amps, I2 =8 amps, I3 = 12 amps, RT = 5.0 ohms D. I1 = 8 amps, I2 = 6 amps, I3 = 10 amps, RT = 4.6 ohms Knowledge Check Given the following circuit shown in the figure below: ο· ο· ο· ο· Rev 1 The voltage source is 24 VDC. Resistors A, D, and E are each 4 ohms. Resistor B and C are each 8 ohms. Find the current through each resistor. A. IA = - 2.86 amps, IB = - 1.28 amps, IC = - 1.58 amps, ID = IE = - 0.64 amps B. IA = 2.86 amps, IB = 1.43 amps, IC = 1.43 amps, ID = IE = 0.71 amps C. IA = 2.86 amps, IB = 1.28 amps, IC = 1.58 amps, ID = IE = 0.64 amps D. IA = - 2.86 amps, IB = - 1.43 amps, IC = - 1.43 amps, ID = IE = - 0.71 amps 71 ELO 5.2 Voltage and Current Dividers Introduction In this section, you will learn how voltage and current dividers work. Voltage Divider When it is necessary to obtain different values of voltage from a single energy source, a circuit includes a voltage divider, or voltage network. The figure below shows a simple voltage divider. In this circuit, 24 volts acts on three resistors in series. The total resistance limits the current through the circuit to one ampere. Calculate individual voltages as follows. Figure: Voltage Divider Individual Voltages Total current: Solutions πΌ = π 24 24 = = = 1 πππ (4 + 8 + 12) π 24 Voltage drop across AB: π = πΌπ π = (1)(4) π = 4 π£πππ‘π Voltage drop across BC: π = πΌπ π = (1)(8) π = 8 π£πππ‘π Voltage drop across CD: π = πΌπ π = (1)(12) π = 12 π£πππ‘π Voltage drop across AC: π = πΌπ π = (1)(8 + 4) π = 12 π£πππ‘π 72 Rev 1 Current Divider Sometimes it is necessary to find the individual branch currents in a parallel circuit, knowing only resistance and total current. When only two branches are involved, the current in one branch will be some fraction of IT. Use the resistance in each circuit to divide the total current into fractional currents in each branch. This process is current division. πΌ1 = (π 2 )(πΌπ ) π 1 + π 2 πΌ2 = (π 1 )(πΌπ ) π 1 + π 2 Note that the equation for each branch current has the opposite R in the numerator. This is because the current in each branch is inversely proportional to the branch resistance. The figure below shows an example current divider. Figure: Current Divider Rev 1 73 Current Divider Example Step 1. 2. 3. Find branch current for I1 and I2 for the circuit shown above. πΌ1 = (π 2 )(πΌπ ) (8)(24) (8)(24) = = = 13.7 ππππ (6 + 8) π 1 + π 2 14 πΌ2 = (π 1 )(πΌπ ) (6)(24) (6)(24) = = = 10.3 ππππ (6 + 8) π 1 + π 2 14 Since we know I1 and IT, we could have also simply subtracted I1 from IT to find I2. Knowledge Check Given the following properties for the figure below: The voltage source is 24 VDC. RA = 12 ohms. RB = 12 ohms. RC = 6 ohms. What is the voltage drop across RC? 74 A. 8.0 volts B. 9.6 volts C. 24 volts D. 4.8 volts Rev 1 Knowledge Check Given the following for the figure shown below: ο· ο· ο· ο· IT = 10 amps. RA = 10 ohms. RB = 20 ohms. RC = 50 ohms. Determine the current through resistor C. A. 1.18 amps B. 2.0 amps C. 2.95 amps D. 5.9 amps ELO 5.3 Polarity of Voltage Drops Introduction In this section, you will learn to determine the polarity of voltages in DC circuits. Polarity of Voltage Drops Step Action 1. Determine the direction of electron flow through the circuit. 2. Where the electron flow enters each circuit component is the negative end of that component. Label that end as negative. 3. Label the opposite end of each component as positive. 4. Check the solution. Polarity in DC Circuits All voltages and currents have polarity as well as magnitude. In a series DC circuit, there is only one current, and its polarity is from the negative battery terminal through the rest of the circuit to the positive battery terminal. Voltage drops across loads also have polarities. The easiest way to find these polarities is to use the direction of the electron current as a basis. Rev 1 75 Then, where the electron current enters the load, the voltage is negative. This holds true regardless of the number or type of loads in the circuit. The drop across the load is opposite to that of the source, as shown in the figure below. The voltage drops oppose the source voltage and reduce it for the other loads. This is because each load uses energy, leaving less energy for other loads. Figure: DC Circuit Voltage Polarity Knowledge Check The negative poles in the circuit shown are found at_________________. 76 A. The left end of resistor A and the left end of resistor C. B. The right end of resistor A and the left end of resistor C. C. The bottom end of resistor B and the right end of resistor A. D. The left end of resistor A and the right end of resistor C. Rev 1 ELO 5.4 Kirchhoff's Laws Introduction In this module, we will review Kirchhoff's laws for determining voltage and current in a circuit. In all of the circuits examined so far, Ohmβs Law described the relationship between current, voltage, and resistance. These circuits have been relatively simple in nature. Many circuits are so complex that solving them with Ohmβs Law is impossible. These circuits have many power sources and branches, which would make the use of Ohmβs Law impractical or impossible. Through experimentation, in 1857 the German physicist Gustav Kirchhoff developed methods to solve complex circuits. Kirchhoff developed two conclusions, known today as Kirchhoffβs Laws. Kirchhoffβs two laws reveal a unique relationship between current, voltage, and resistance in electrical circuits that is vital to performing and understanding electrical circuit analysis. Kirchhoff's First Law (Voltage) Kirchhoffβs first law describes voltage in closed loop (circuit). It states that the sum of the voltage drops around a closed loop (circuit) is equal to the sum of the voltage sources of that loop (circuit). Another way of stating this law is that the algebraic sum of the voltage sources and voltage drops in a closed loop (circuit) must always be equal to zero. Kirchhoff's Second Law (Current) Kirchhoffβs second law describes current in a closed loop (circuit). It states that the current arriving at any junction point in a circuit is equal to the current leaving that junction. In other words, the current going into a junction equals the current going out of a junction (the sum of the goes-ins equals the sum of the goes-outs). Kirchhoffβs two laws may seem obvious based on what we already know about circuit theory. Even though they may seem very simple, they are powerful tools in solving complex and difficult circuits. Conservation of Energy and Charge We can relate Kirchhoffβs laws to conservation of energy and charge if we look at a circuit with one load and source. Since the load consumes all of the power provided from the source, there is conservation of energy and charge. Since we can relate voltage and current to energy and charge, then Kirchhoffβs laws are simply restating the laws governing energy and charge conservation. Rev 1 77 Knowledge Check Kirchhoff's Voltage Law states that the sum of currents entering a junction must equal the sum of currents exiting that junction. A. True B. False ELO 5.5 Applying Kirchhoff's Laws Introduction In this section, you will learn to use Kirchhoff's laws in DC circuit analysis. Applying Kirchhoff's Laws The table below gives instructions for using Kirchhoffβs voltage law. Step Action 1. Determine the sum of all voltage sources in the circuit. 2. Simplify the circuit, if necessary, by determining equivalent resistances for any parallel sections. 3. Determine the current in the simplified series circuit. 4. Determine the voltage drop across each resistance or equivalent resistance in the simplified series circuit. 5. Ensure the sum of the voltage sources equals the sum of the voltage drops. 6. Determine the current in parallel branches, if necessary. The table below gives instructions for using Kirchhoffβs current law. Step Action 1. Label the current in each flow path in the circuit (I1, I2, etc.), and include direction. Currents can be negative if the chosen direction goes against current flow. Choosing directions will not impede problem solution. 2. For each junction, incoming current equals outgoing current. 78 Rev 1 Step Action 3. Write an equation for the current at each junction. (Current in equals current out) 4. Solve the equations until determining all currents. 5. Check the solution. Kirchhoff's Voltage Law Demonstration Kirchhoffβs first law is sometimes termed his voltage law. The voltage law gives the relationship between the voltage drops around any closed loop in a circuit, and the voltage sources in that loop. The total of these two quantities is always equal. In equation form: πΈπ ππ’πππ = πΈ1 + πΈ2 + πΈ3 + ππ‘π. = πΌ1 π 1 + πΌ2 π 2 + πΌ3 π 3 + ππ‘π. π΄πΈπ ππ’πππ = π΄πΌπ Where the Greek symbol Ξ£ (the Greek letter sigma) means we apply the sum of Kirchhoffβs voltage law only to closed loops. A closed loop must meet two conditions: 1. It must have one or more voltage sources. 2. It must have a complete path for current flow from any point, around the loop, and back to that point. Simple Voltage Source Recall that in a simple series circuit, the sum of the voltage drops around the circuit is equal to the applied voltage. Actually, this is Kirchhoffβs voltage law applied to the simplest case, that is, where there is only one loop and one voltage source, as shown in the figure below. Figure: Using Kirchhoff's Voltage Law For a simple series circuit, Kirchhoffβs voltage law corresponds to Ohmβs Law. To find the current in the circuit above by using Kirchhoffβs voltage law, use the equation below. Rev 1 79 π΄πΈπ ππ’πππ = π΄πΌπ Solution: 80 = 20(πΌ) + 10(πΌ) 0 = 30(πΌ) 80 πΌ = = 2.66 πππππππ 30 Kirchhoff's Voltage Law Demonstration In the problem above, we knew the direction of current flow before solving the problem. When there is more than one voltage source, we may or may now know the direction of current flow. In such a case, we must assume a direction of current flow in the beginning of the problem. All the sources that would aid the current in the assumed direction of current flow are then positive, and all that would oppose current flow are negative. If the assumed direction is correct, the answer will be positive. The answer would be negative if the direction assumed was wrong. In any case, we will compute the correct magnitude. For example, what is the current flow in the figure below? Assume that the current is flowing in the direction shown. Figure: Kirchhoff's Voltage Law Solution Using Kirchhoffβs Voltage Law: π΄πΈπ ππ’πππ = π΄πΌπ 50 β 70 = 30πΌ + 10πΌ β20 = 40πΌ πΌ = β0.5 The result is negative, indicating that the assumed flow direction is incorrect. The current is actually 0.5 ampere in the opposite direction to that assumed. Kirchhoff's Current Law Demonstration Kirchhoffβs second law states: "At any junction point in a circuit, the current arriving is equal to the current leaving." Thus, if 15 amperes of 80 Rev 1 current arrives at a junction that has two paths leading away from it, 15 amperes will divide between the two branches, but a total of 15 amperes must leave the junction. We are already familiar with Kirchhoffβs current law from parallel circuits, that is, the sum of the branch currents is equal to the total current entering the branches, as well as the total current leaving the branches. The figure below illustrates Kirchhoffβs Current Law graphically. Figure: Kirchhoff's Current Law In equation form, we can express Kirchhoffβs current law as follows: πΌπΌπ β πΌπππ = 0 or πΌπΌπ = πΌπππ Normally Kirchhoffβs current law is not used by itself, but with the voltage law, in solving a problem. Kirchhoff's Laws Demonstration Find I2 in the circuit shown in the figure below using Kirchhoffβs voltage and current laws. Figure: Using Kirchhoff's Laws Rev 1 81 Step 1. Action First, apply Kirchhoffβs voltage law to both loops. Result Loop ABCDEF: πΌπ = πΈπ ππ’πππ 2πΊ πΌπ‘ππ‘ππ + 6πΊ πΌ1 = 6π Loop ABGHEF: πΌπ = πΈπ ππ’πππ 2πΊ πΌπ‘ππ‘ππ + 3πΊ πΌ2 = 6π 2. Since Kirchhoffβs current law states πΌπ‘ππ‘ππ = πΌ1 + πΌ2 , substitute (I1 + I2) in the place of Itotal in both loop equations and simplify. Loop ABCDEF 2πΊ(πΌ1 + πΌ2 ) + 6πΊπΌ1 = 6π 2πΊπΌ1 + 2πΌ2 + 6πΊπΌ1 = 6π 8πΊπΌ1 + 2πΊπΌ2 = 6π Loop ABGHEF 2πΊ(πΌ1 + πΌ2 ) + 3πΊπΌ2 = 6π 2πΊπΌ1 + 2πΊπΌ2 + 3πΊπΌ2 = 6π 2πΊπΌ1 + 5πΊπΌ2 = 6π 3. We now have two equations and two unknowns and must eliminate I1 to find I2. One way is to multiply Loop ABGHEF equation by four, and subtract Loop ABCDEF equation from the result. Multiply loop ABGHEF by 4: 4(2πΊπΌ1 + 5πΊπΌ2 = 6π) 8πΊπΌ1 + 20πΊπΌ2 = 24π 4. 82 Now we have an equation with only I2, which is the current we are looking for. Subtract Loop ABCDEF from Loop ABGHEF. 18 πΌ2 = 18 Rev 1 Knowledge Check Given the following properties of the circuit shown in the figure below: A = 20 V B = 12 V C = 15 ohms D = 12 ohms Find the current in this loop. Rev 1 A. 10.7 amps B. 1.2 amps C. 2.7 amps D. 0.3 amps 83 Knowledge Check Given the following properties of the circuit shown in the figure below: A = 24 V B = 12 V C = 6 ohms D = 12 ohms E = 6 ohms Find the current through each resistor. A. IC = - 3.6 amps, ID = - 1.2 amps, IE = - 2.4 amps B. IC = -1.2 amps, ID = -0.4 amps, IE = -0.8 amps C. IC = 1.2 amps, ID = 0.4 amps, IE = 0.8 amps D. IC = 3.6 amps, ID = 1.2 amps, IE = 2.4 amps TLO 5 Summary In this section, you learned the tools for DC circuit analysis. Now that you have completed this lesson, you should be able to: 1. Calculate total resistance for a series or parallel circuit. 2. Explain the terms voltage divider and current divider. 3. Given a DC electrical circuit, identify the polarity of the voltage drops in the circuit. 4. State Kirchhoffβs voltage law and current law. 5. Solve problems for voltage and current using Kirchhoffβs laws. 84 Rev 1 TLO 6 DC Motors Overview In this section, you will learn how DC motors operate. Many special applications in a nuclear facility use DC motors; operators must know how they work to monitor and control them. Objectives Upon completion of this lesson, you will be able to do the following: 1. Describe the action of a current carrying conductor in a magnetic field. 2. Using the right-hand rule for motors, determine the direction of the magnetic field, direction of current flow, or force on a conductor. 3. State the function of torque in a direct current motor and how it is developed. 4. Describe how counter-electromotive force (CEMF) is developed, and the affect it has on a DC motor. 5. Describe how the speed of a DC motor is adjusted, the relationship between field current and induced voltage, and the relationship between armature current and torque produced in a DC motor. 6. Describe why starting resistors are necessary for large DC motors. 7. List the four nameplate ratings for a DC motor. ELO 6.1 Current Carrying Conductors Introduction In this section, we will review the forces applied to a current carrying conductor positioned in a magnetic field. Two conditions are necessary to produce a force on a conductor: 1. The conductor must be carrying current. 2. The conductor must be within a magnetic field. When these two conditions exist, the conductor will experience a force, which will attempt to move the conductor in a direction perpendicular to the magnetic field. This is the basic theory by which all DC motors operate. Current Carrying Conductor in a Magnetic Field Every current-carrying conductor has a magnetic field around it. The lefthand rule for current-carrying conductors shows the direction of this magnetic field. When the left thumb points in the direction of current flow, the fingers will point in the direction of the magnetic field produced, as shown in the figure below. Rev 1 85 Figure: Left-Hand Rule for Current Carrying Conductors If a current-carrying conductor is in a magnetic field, the combined fields will be similar to those shown in the figure below. The direction of current flow through the conductor is indicated with an X or a β’ βdot,β similar to how an arrow would look in a drawing, either going away from you as an X, or coming toward you as a β’. The X indicates the current flow is away from the reader, or into the page. The β’ indicates the current flow is towards the reader, or out of the page. Figure: Current Carrying Conductor in a Magnetic Field Below the conductor on the left, the field caused by the conductor is in the same direction as the main field, and therefore, aids the main field. The net result is that above the left conductor, the main field is weaker, or flux density decreases; below the conductor, the main field strengthens, or flux density increases. A force develops on the conductor that moves the conductor in the direction of the weakened field (upward). Above the conductor on the right, the field caused by the conductor is in the same direction as the main field, and therefore, aids the main field. Below the conductor on the right, the field caused by the conductor is in the opposite direction of the main field, and therefore, opposes the main field. The net result is that above the right conductor, the main field strengthens, or flux density is increased, and below the conductor, the main field is weaker, or flux density decreases. A force develops on the conductor that moves the conductor in the direction of the weakened field (downward). 86 Rev 1 Knowledge Check The left-hand rule for current carrying conductors states that _____________________. A. when the thumb points in the direction of electron flow, it is also pointing in the direction of the induced North magnetic pole B. when the thumb points in the direction of electron flow, the fingers will wrap around the conductor in the direction of the magnetic lines of force (South to North) C. when the thumb points in the direction of conventional current flow, the fingers will wrap around the conductor in the direction of the magnetic lines of force (North to South) D. when the thumb points in the direction of electron flow, the fingers will wrap around the conductor in the direction of the magnetic lines of force (North to South) ELO 6.2 Right-Hand Rule for Motors Introduction In this section, we will cover the right-hand rule for motors and the forces applied to a current carrying conductor positioned in a magnetic field. A DC motor uses a conductor formed in a loop such that two parts of the conductor are in the magnetic field at the same time. The effects of the magnetic fields created by current flow through both parts of the conductor distort the main magnetic field and produce a force on each part of the conductor. When the conductor is on a rotor, the force exerted on both parts of the conductor will cause the rotor to rotate clockwise, as shown in the figure below. Figure: DC Motor Action Rev 1 87 You can think of these magnetic lines of force as rubber bands that are always trying to straighten themselves. The lines of force above the conductor exert a downward force due to the magnetic lines of force trying to straighten themselves. Right-Hand Rule for Motors The explanation of how a force develops on a conductor uses a fundamental principle of physics: a current carrying conductor in a magnetic field tends to move at right angles to that field. Another way to show the relationship between the current carrying conductor, magnetic field, and motion is the right-hand rule for motors, shown in the figure below. Figure: Right-Hand Rule for Motors The right-hand rule for motors shows the direction in which a currentcarrying conductor moves in a magnetic field. When the forefinger points in the direction of the magnetic field lines, and the middle finger is pointed in the direction of current flow, the thumb will point in the direction of force (motion). The table below gives instructions for using the right-hand rule for motors. Step Action 1. Use the right-hand rule for motors with electron flow in a conductor. 2. Hold your right hand with the thumb, index finger, and middle finger all at right angles to each other. 3. Point the forefinger in the direction of the magnetic field (North to South), and the middle finger in the direction of electron flow. 88 Rev 1 Step Action 4. The thumb will be pointing in the direction of motion. 5. This gives the direction of motion due to the force on the current carrying conductor. Knowledge Check The right-hand rule for motors states that_____________________________________. A. when the middle finger is pointed in the direction of the magnetic field lines, and the forefinger is pointed in the direction of current flow, the thumb will point in the direction of force (motion) B. when the middle finger is pointed in the direction of the magnetic field lines, and the thumb is pointed in the direction of current flow, the forefinger will point in the direction of force (motion) C. when the forefinger is pointed in the direction of the magnetic field lines, and the thumb is pointed in the direction of current flow, the middle finger will point in the direction of force (motion) D. when the forefinger is pointed in the direction of the magnetic field lines, and the middle finger is pointed in the direction of current flow, the thumb will point in the direction of force (motion) ELO 6.3 Torque in DC Motors Introduction In this section, you will learn how a DC motor develops torque. Torque Torque is that force which tends to produce and maintain rotation. The function of torque in a DC motor is to provide a mechanical output or drive a piece of equipment attached (coupled) to the motor, such as a pump, valve, etc. When a voltage acts on a motor, current will flow through the field winding, establishing a magnetic field. Current will also flow through the armature winding, from the negative brush to the positive brush as shown in the figure below. Rev 1 89 Figure: Armature Current in a Basic DC Motor Since the armature is a current-carrying conductor in a magnetic field, the conductor has a force exerted on it, tending to move it at right angles to that field. Using the left-hand rule for current-carrying conductors, you will see that the magnetic field on one side strengthens at the bottom, while it weakens on the other side. Using the right-hand rule for motors, we can see that there is a force exerted on the armature, which tends to turn the armature in the counter-clockwise direction. The sum of the forces, Newtons, multiplied by the radius of the armature, in meters, is equal to the torque developed by the motor in Newton-meters (N-m). Referring to the figure above, reversing the armature current while maintaining the magnetic field in the same direction will result in torque developing in the opposite direction. Likewise, reversing the field polarity and maintaining the armature current the same will result in torque developing in the opposite direction. The force developed on a conductor that is part of a DC motor armature is due to the combined action of the magnetic fields (main and armature). The force developed is directly proportional to the strength of the main field flux and the strength of the field around the armature conductor. As we know, the field strength around each armature conductor depends on the amount of current flowing through the armature conductor. Therefore, the torque developed by the motor can be determined using the following equation: π = πΎπ·πΌπ Where: T = torque, N-m K = a constant depending on physical size of motor Ξ¦ = field flux, number of lines of force per pole Ia = armature current, A 90 Rev 1 Knowledge Check Select all of the statements about DC motors that are correct. A. The physical dimensions of the motor do not influence torque. B. The magnitude of armature current does not influence torque. C. Torque is the product of the force exerted on the rotor and the radius of the rotor. D. The field strength, in part, determines force. ELO 6.4 Counter-Electromotive Force (CEMF) in DC Motors Introduction In this section, you will learn how counter-electromotive force (CEMF) is developed and how it affects DC motors. Counter-Electromotive Force Every motor develops a generator action (inducing a voltage). When a conductor cuts lines of force, the result is an induced EMF in that conductor. Current to start the armature turning will flow in the direction determined by the applied DC power source. After rotation starts, the conductor cuts lines of force. By applying the left-hand rule for generators, the induced EMF in the armature will produce a current in the opposite direction. The induced EMF that results from motor operation is counter-electromotive force, or CEMF, as illustrated in the figure below. Figure: Counter-Electromotive Force Rev 1 91 Since the action of the armature cutting lines of force generates the CEMF, the value of CEMF will depend on field strength and armature speed, as shown below. πΈπΆπΈππΉ = πΎπ·π Where: ECEMF = counter EMF K = constant Ξ¦ = field flux strength N = speed of the armature The CEMF opposes the applied voltage and functions to lower armature current. The effective voltage acting in the armature of a motor is the applied voltage, minus the CEMF. To calculate armature current, use Ohmβs law, as shown in the equation below. πΌπ = πΈπ‘ β πΈπΆπΈππΉ π π Where: Ia = armature current Et = terminal voltage ECEMF = counter EMF Ra = armature resistance Knowledge Check Select all of the statements that are true about CEMF. A. Counter-electromotive force always opposes the applied force. B. Hysteresis causes counter-electromotive force. C. Rotation of the current carrying conductor in the magnetic field causes counter-electromotive force. D. Counter-electromotive force exists when the rotor is stationary. ELO 6.5 DC Motor Control Introduction In this section, you will learn how to adjust the speed of a DC motor. DC Motor Speed Control External devices, usually field resistors vary the field of a DC motor. If a constant voltage is applied to the field (E), as the resistance of the field (RF) is lowered, the amount of current flow through the field (IF) increases, as shown by Ohmβs law. πΌπΉ = 92 πΈ π πΉ Rev 1 An increase in field current will cause field flux (Ξ¦F) to increase. Conversely, if the resistance of the field is increased, field current and field flux will decrease. If the field flux of a DC motor decreases, the motor speed will increase. The reduction of field strength reduces the CEMF of the motor, since the armature conductors, as shown in the equation below are cutting fewer lines of flux. β πΈπΆπΈππΉ = β β β πΎ Ξ¦πΉ π A reduction of counter EMF allows an increase in armature current as shown below. πΌπ = πΈπ‘ β πΈπΆπΈππΉ π π This increase in armature current causes a larger torque to be developed; the increase in armature current more than offsets the decrease in field flux as shown below. β β β βπ= πΎ Ξ¦πΉ πΌπ This increased torque causes the motor to increase in speed. βTβNβ This increase in speed will then proportionately increase the CEMF. The speed and CEMF will continue to increase until the armature current and torque decline to values just large enough to supply the load at a new constant speed. Knowledge Check Increasing field resistance will increase DC motor speed. A. True B. False ELO 6.6 Starting DC Motors Introduction In this section, you will learn the starting sequence for DC motors. Starting Current At the instant a DC motor is started the rotor (armature) is stationary and there is no generated counter EMF. The only component available to limit starting current is the resistance of the armature, which is really just a length of copper wire. In most DC motors, this resistance is very low (approximately one ohm or less). Rev 1 93 πΌπ = πΈπ‘ β πΈπΆπΈππΉ π π In order to reduce this very high starting current, there must be an external resistance in series with the armature during the starting period. To show why this is essential, let us consider a 10-hp motor with an armature resistance of 0.4 ohms. If a 260 VDC source supplies the motor, the resulting current would be as shown below. πΈπ‘ β πΈπΆπΈππΉ πΌπ = π π (260 β 0) = 650 ππππ 0.4 This large current is approximately twelve times greater than actual fullload current for this motor. This high current would likely cause severe damage to the brushes, commutator, or windings. Most motor designs incorporate starting resistors to limit starting current to 125 to 200 percent of full load current. πΌπ = Starting Resistance The equation below shows how to calculate the amount of starting resistance necessary to limit starting current to a more desirable value: π π = πΈπ‘ β π π πΌπ Where: RS = starting resistance Et = terminal voltage IS = desired armature starting current Ra = armature resistance Example: If the full load current of the motor mentioned previously is 50 amps, and we want to limit starting current to 125% of this value, find the additional required resistance in series with the armature. Solution: πΈπ‘ β π π πΌπ (260π π·πΆ) π π = β 0.4 πβππ (50 ππππ )(125%) 260 π π = β 0.4 = 3.76 πβππ 62.5 Most DC motors use starting resistors in the motor control circuit to limit the starting current. These starting resistors insert a maximum amount of resistance when the motor is first started, since no CEMF exists in the armature. As the speed of the motor increases, CEMF will begin to increase, limiting armature current. The starting resistors are then βcut outβ, in successive steps, until the motor reaches full running speed and the starting resistors are no longer necessary. When running at full speed, CEMF limits armature current and circuitry bypasses the starting resistors. π π = 94 Rev 1 Knowledge Check Starting resistors are needed in DC motors to... (Select all that are correct) A. overcome the starting resistance. B. limit the voltage during a motor start. C. compensate for the high values of CEMF at startup. D. limit the current during a motor start. ELO 6.7 DC Motor Ratings Introduction In this section, we will review the nameplate ratings that a manufacturer provides for DC motor operation. Nameplate ratings of DC motor typically refer to conditions of voltage, current, speed, and power for which the manufacturer designed the motor; these conditions normally match motor operating conditions. Continuous Power The principal rating for a DC motor is known as the continuous rating; this is the rating described on the nameplate of a motor. The continuous power rating is a thermal rating. At this power, the motor will operate for long periods without a large rise in temperature and within temperature limits of the conductor insulating material, bearings and other components, which are temperature dependent. Speed The nameplate provides the speed rating of a DC motor. This speed is the upper limit for motor operation without sustaining mechanical damage. As with DC generators, the mechanical limitations of rotor construction determine the upper speed limit. Knowledge Check The common ratings for DC motors include _________________________. (Select all that are correct) Rev 1 A. speed B. ambient temperature C. starting current D. continuous power 95 TLO 6 Summary In this section you learned how DC motors work, including how torque and CEMF are developed, and how the different types of DC motors are used. Now that you have completed this lesson, you should be able to: 1. Describe the action of a current carrying conductor in a magnetic field. 2. Using the right-hand rule for motors, determine the direction of the magnetic field, direction of current flow, or force on a conductor. 3. State the function of torque in a direct current motor and how it is developed. 4. Describe how counter-electromotive force (CEMF) is developed, and the affect it has on a DC motor. 5. Describe how the speed of a DC motor is adjusted, the relationship between field current and induced voltage, and the relationship between armature current and torque produced in a DC motor. 6. Describe why starting resistors are necessary for large DC motors. 7. List the four nameplate ratings for a DC motor. TLO 7 Producing DC Voltage Overview In this section, we will explain production of DC voltage. Operators must understand the principles behind electrical machines to monitor their performance. Objectives Upon completion of this lesson, you will be able to do the following: 1. Describe the common methods for producing a DC voltage and give an example of each. 2. State the purpose of a rectifier and describe the outputs of rectifier circuits. 3. Describe the effects of commutation in a DC generator. 4. State the purpose of each of the components of a DC machine. 5. List the three conditions necessary to induce a voltage. 6. Using the left-hand rule of generators, determine the direction of the magnetic field, the motion of the conductor, or the direction of current induced into a conductor. 7. Define terminal voltage as it applies to DC generators and describe how terminal voltage of a DC generator is adjusted. 8. Identify the four categories and their bases for DC generator nameplate ratings. 96 Rev 1 ELO 7.1 Methods of Producing DC Voltage Introduction When most people think of DC electricity, they usually think of batteries. In addition to batteries, however, there are other means of producing DC voltage. Modern technology employs some of these methods. This chapter describes various methods for producing a DC voltage and some of the more common industrial applications. Electrochemistry When combined with specific metals, certain chemicals cause a chemical reaction that will transfer electrons to produce electrical energy. This process works on the electrochemistry principle. One example of this principle is the voltaic chemical cell. A chemical reaction produces and maintains opposite charges on two dissimilar metals that serve as the positive and negative terminals. The metals are in contact with an electrolyte solution. Connecting together more than one of these cells produces a battery. Chemical Cell The chemical cell is composed of two electrodes made of different types of metal or metallic compounds immersed in an electrolyte solution. The chemical actions that result vary, depending on the type of material used in cell construction. Some knowledge of the basic action of a simple cell will be helpful in understanding the operation of a chemical cell in general. In the cell, electrolyte ionizes to produce positive and negative ions as shown in the figure below. Simultaneously, chemical action causes the atoms within one of the electrodes to ionize. Figure: Basic Chemical Cell This action results in electron deposition on the electrode, and positive ions from the electrode pass into the electrolyte solution (Part B). This causes a negative charge on the electrode and leaves a positive charge in the area near the electrode (Part C). The positive ions, produced by ionization of the electrolyte, are repelled to the other electrode. At this electrode, these ions will combine with the electrons. Because this action causes removal of electrons from the electrode, it becomes positively charged. Rev 1 97 Batteries A battery consists of two or more chemical cells connected in series. The combination of materials inside a battery converts chemical energy into electrical energy. Static Electricity Atoms with the proper number of electrons in orbit around them are in a neutral state, or have a zero charge. A body of matter consisting of these atoms will neither attract nor repel other matter in its vicinity. Removal of electrons from the atoms in this body of matter, as happens due to friction when rubbing a glass rod with a silk cloth, results in the body becoming electrically positive as shown in the figure below. If this body of matter (e.g., glass rod) comes near, but not in contact with, another body having a normal charge, an electric force acts between them because of their unequal charges. The existence of this force is static electricity or electrostatic force. Figure: Static Electricity An example of static electricity producing a voltage occurs when someone walks across a carpet and receives a shock when touching a metal doorknob. The soles of the personβs shoes build up a charge by rubbing on the carpet, and this charge transfers to their body. Their body becomes positively charged and upon touching the zero-charged doorknob, electrons transfer to the personβs body until both the body and the doorknob are at equal charges. Magnetic Induction A generator is a machine that converts mechanical energy into electrical energy by using the principle of magnetic induction. Magnetic induction produces a voltage by rotating coils of wire through a stationary magnetic field, as shown in the figure below, or by rotating a magnetic field through stationary coils of wire. 98 Rev 1 Figure: Magnetic Induction DC Generator A simple DC generator consists of an armature coil with a single turn of wire. (When discussing motors and generators the term armature generally refers to the portion of the device where the voltage is induced.) The armature coil cuts across the magnetic field to produce a voltage output. As long as a complete path is present, current will flow through the circuit in the direction shown by the arrows in the figure below. As the armature rotates the first commutator segment contacts the first brush, while the second commutator segment is in contact with the second brush. Rotating the armature one-half turn in the clockwise direction causes reversal of the contacts between the commutator segments. Now, the first segment contacts the second brush and the second segment contacts the first brush. Figure: Basic DC Generator Due to this commutator action, the side of the armature coil that is in contact with either of the brushes is always cutting the magnetic field in the Rev 1 99 same direction. Both brushes and have a constant polarity, and pulsating DC results. Magnetic induction is one of the most widely employed methods of producing electrical power and will be discussed in more detail in later chapters of this lesson. Piezoelectric Effect By applying pressure to certain crystals (such as quartz or Rochelle salts) or ceramics (like barium titanate), it is possible to force electrons out of orbit in the direction of the force. Electrons leave one side of the material and accumulate on the other side, building up positive and negative charges on opposite sides, as shown in the figure below. Upon release of the pressure, the electrons return to their orbits. (Some materials will react to bending pressure, while others will respond to twisting pressure.) This generation of voltage is the piezoelectric effect. If external wires provide connectivity while pressure and voltage are present, electrons will flow and produce current. By holding the pressure constant, the current will flow until equalization of the potential difference. Upon removal of the force, the material decompresses and an electric force is created in the opposite direction. The power capacity of these materials is extremely small. However, these materials are very useful because of their extreme sensitivity to changes of mechanical force. Figure: Pressure Applied to Crystal Produces Electric Charge An example of the piezoelectric effect is the crystal phonograph cartridge that contains a Rochelle salt crystal. A phonograph needle attaches to the crystal. As the needle moves in the grooves of a record, it swings from side to side, applying compression and decompression to the crystal. This mechanical motion applied to the crystal generates a voltage signal that reproduces sound. Thermoelectricity Some materials readily give up their electrons and others readily accept electrons. For example, when joining two dissimilar metals like copper and zinc together, a transfer of electrons can take place. Electrons will leave the copper atoms and enter the zinc atoms. The zinc gains surplus electrons from the copper, and becomes negatively charged. The copper loses 100 Rev 1 electrons and takes on a positive charge. This creates a voltage potential across the junction of the two metals. The heat energy of normal room temperature is enough to make these metals release and gain electrons, causing a measurable voltage potential. Applying more heat energy to the junction causes release of more electrons, and the voltage potential increases. Upon removal of the heat, the junction cools, the charges dissipate, and the voltage potential decreases. This process is thermoelectricity. A thermocouple is an example of a device that relies on thermoelectricity to produce a voltage. Thermocouple A thermocouple is a device used to convert heat energy into a voltage output. The thermocouple consists of two different types of metal joined at a junction as shown in the figure below. As the junction is heated, the electrons in one of the metals gain enough energy to become free electrons. These free electrons then migrate across the junction and into the other metal. This displacement of electrons produces a voltage across the terminals of the thermocouple. The thermoelectric voltage produced by a thermocouple is dependent upon the heat energy applied to the junction of the two dissimilar metals. Thermocouples are widely used to measure temperature and as heat-sensing devices in automatic temperature controlled equipment. The voltage produced causes a current to flow through a meter; calibration of the meter correlates current with temperature. One advantage of thermocouples in power plants is that they can withstand higher temperatures than ordinary mercury or alcohol thermometers. Thermocouple power capacities are much smaller than some other sources, but are somewhat greater than those of piezoelectric crystals. The combinations used in the makeup of a thermocouple include iron and constantan; copper and constantan; antimony and bismuth; and chromel and alumel. Rev 1 101 Figure: Production of DC Voltage Using a Thermocouple Photoelectric Effect Light is a form of energy; many scientists consider light to consist of small particles of energy called photons. When the photons in a light beam strike the surface of a material, they release their energy and transfer it to the atomic electrons of the material. This energy transfer may dislodge electrons from their orbits around the surface of the substance. Upon losing electrons, the photosensitive (light sensitive) material becomes positively charged and an electric force is created, as shown in the figure below. Figure: Producing Electricity from Light Using a Photovoltaic Cell 102 Rev 1 Knowledge Check Match the following terms with the correct descriptions. 1. Electrochemistry A. Applying pressure to certain crystals (such as quartz or Rochelle salts) or certain ceramics (like barium titanate) forces electrons out of orbit in the direction of the force. 2. Piezoelectric effect B. Photons in a light beam strike the surface of a material and release their energy to the atomic electrons of the material. This energy transfer may dislodge electrons from their orbits around the surface of the substance. 3. Magnetic induction C. A chemical reaction produces and maintains opposite charges on two dissimilar metals that serve as the positive and negative terminals. 4. Photoelectric effect D. Producing a voltage by rotating coils of wire through a stationary magnetic field, or by rotating a magnetic field through stationary coils of wire. ELO 7.2 Rectifiers Introduction Most electrical power generating stations produce alternating current. AC power transmission results in significantly less power loss as compared to DC, however, many of todayβs devices operate only, or more efficiently, with DC. For example, transistors, and certain electronic control devices require DC for operation. In order to operate these devices from ordinary AC outlet receptacles, they must be equipped with rectifier units to convert AC to DC. Therefore, the purpose of a rectifier circuit is to convert AC power to DC. The most common type of solid-state diode rectifier is made of silicon. The diode acts as a gate, which allows current to pass in one direction and blocks current flow in the other direction. The polarity of the applied Rev 1 103 Duration ο§ 20 minutes Logistics ο§ Use PowerPoint slides 234β241 and the IG to present ELO 7.2. voltage determines if the diode will conduct. The two polarities are forward bias and reverse bias. Forward Bias A forward biased diode has the positive terminal of a voltage source connected to its anode, and the negative terminal connected to the cathode as shown in the figure below. The power sourceβs positive side will tend to repel the holes in the p-type material toward the negative side of the p-n junction. A hole is a vacancy in the electron structure of a material. Holes behave as positive charges. As the holes and the electrons reach the p-n junction, some of them break through it. Holes combine with electrons in the n-type material, and electrons combine with holes in the p-type material. Figure: Forward-Biased Diode When a hole combines with an electron, or an electron combines with a hole near the p-n junction, an electron from an electron-pair bond in the ptype material breaks its bond and enters the positive side of the source. Simultaneously, an electron from the negative side of the source enters the n-type material as shown in part C of the figure above. This produces a flow of electrons in the circuit. Reverse Bias Reverse biasing occurs when the diodeβs anode connects to the negative side of the source, and the cathode connects to the positive side of the source as shown in the figure below. The negative terminal attracts holes within the p-type material, and the positive terminal (part B) attracts electrons in the n-type material. This prevents the combination of electrons 104 Rev 1 and holes near the p-n junction, and therefore causes a high resistance to current flow. This resistance prevents current from flowing through the circuit. Figure: Reverse-Biased Diode Half-Wave Rectifier When a diode is connected to a source of alternating voltage, it will be alternately forward-biased, and then reverse-biased, during each cycle of the AC sine wave. When using a single diode in a rectifier circuit, current will flow through the circuit only during one-half of the input voltage cycle, when forward biased as shown in the figure below. For this reason, this type of rectifier circuit is a half-wave rectifier. The output of a half-wave rectifier circuit is pulsating DC. Figure: Half-Wave Rectifier Full-Wave Rectifier A full-wave rectifier circuit is a circuit that rectifies the entire cycle of the AC sine wave. A basic full-wave rectifier uses two diodes. The figure below shows the action of these diodes during each half cycle. Rev 1 105 Figure: Full-Wave Rectifier Full-Wave Rectifier Bridge Another type of full-wave rectifier circuit is the full-wave bridge rectifier. This circuit utilizes four diodes. The figure below shows these diodesβ actions during each half cycle of the applied AC input voltage. The output of this circuit is a pulsating DC, with rectification of all of the waves of the input AC. The output looks identical to that obtained from the full-wave rectifier. Figure: Full-Wave Rectifier Bridge Full-Wave Rectifier Output The figure below shows the output of a full-wave rectifier or full-wave rectifier bridge. 106 Rev 1 Figure: Full-Wave Rectifier Output Knowledge Check Select all the statements that are true. A. A half-wave rectifier can be built with one diode. B. Rectifiers convert DC power into AC power. C. A full-wave rectifier can be built with one diode. D. A forward biased diode allows current flow with little resistance. ELO 7.3 Commutation Introduction Commutation is the positioning of the DC generator brushes so that the commutator segments change brushes at the same time the armature current changes direction. Simply stated, commutation is the mechanical conversion from AC to DC at the brushes of a DC machine, as shown in the figure below. Figure: Commutation Commutation The EMF induced in the rotor is actually an AC voltage. A commutator converts the AC voltage generated in the rotating loop into a DC voltage. The commutator also serves as a means of connecting the brushes to the rotating loop. The purpose of the brushes is to connect the generated voltage to an external circuit. In order to do this, each brush must make contact with one of the ends of the loop. Since the loop or armature rotates, a direct connection is impractical. Instead, the brushes contact the ends of the loop through the commutator. Rev 1 107 In a simple one-loop generator, the commutator is made up of two semicylindrical pieces of a smooth, conducting material, usually copper, separated by an insulating material, usually mica, as shown in the figure below. Each commutator segment is permanently attached to one end of the rotating loop, and the commutator rotates with the loop. The brushes, usually made of carbon, rest against the commutator and slide along the commutator as it rotates. Springs hold the brushes against the commutator, completing brush contact with each end of the loop. Figure: Commutator Segment and Brushes Each brush slides along one half of the commutator and then along the other half as the commutator rotates. The brushes are positioned on opposite sides of the commutator; they will pass from one commutator half to the other at the instant the loop reaches the point of rotation, where the induced voltage reverses the polarity. Every time the ends of the loop reverse polarity, the brushes switch from one commutator segment to the next. This means that one brush is always positive with respect to the other. The voltage between the brushes fluctuates in amplitude between zero and some maximum value, but is always of the same polarity, as shown in the figure below. Figure: Commutation in a DC Generator It is important to note that, as the brushes pass from one segment to the other, there is an instant when the brushes contact both segments at the same time. The induced voltage at this point is zero. If the induced voltage 108 Rev 1 at this point were not zero, the brushes would short the ends of the loop together, producing extremely high currents. The point at which the brushes contact both commutator segments, when the induced voltage is zero, is the neutral plane. Because commutators in DC generators convert AC to DC, they are sometimes referred to as mechanical rectifiers. Knowledge Check Commutation is... A. a means of increasing the voltage output of a DC generator. B. a means of increasing the total power output of a DC generator. C. the positioning of the DC generator brushes so that the commutator segments change brushes at the same time the armature current changes direction to convert from AC to DC at the brushes of a DC machine. D. the positioning of the DC generator brushes so that the commutator segments change brushes at the same time the armature current changes direction to convert from DC to AC at the brushes of a DC machine. ELO 7.4 DC Machine Components Introduction Direct current machines are energy transfer devices. These machines can function as either a motor or a generator. DC motors and generators have the same basic construction, differing primarily in the energy conversion. To understand the operation and construction of DC machines, we must define a few basic terms. Armature The purpose of the armature is to provide the energy conversion in a DC machine (refer to the figure below). In a DC generator, an external mechanical force, such as a steam turbine, rotates the armature. This rotation induces a voltage and current flow in the armature. Thus, the armature converts mechanical energy into electrical energy. In a DC motor, the armature receives voltage from an outside electrical source and converts electrical energy into mechanical energy in the form of torque. Rev 1 109 Figure: Basic DC Machine Components Rotor The purpose of the rotor is to provide the rotating element in a DC machine (refer to the figure above). In a DC generator, an external force rotates the rotor. In a DC motor, the rotor is the component that turns a piece of equipment. In both types of DC machines, the rotor is the armature. Stator The stator is the part of a motor or generator that is stationary (refer to the figure above). In DC machines, the purpose of the stator is to provide the magnetic field. The stator in the figure above has a magnetic field provided by a permanent magnet. Field The purpose of the field in a DC machine is to provide a magnetic field for producing either a voltage (generator) or a torque (motor) (refer to the figure above). A permanent magnet or an electromagnet provides the field in a DC machine. Normally, fields use electromagnets because they have increased magnetic strength, and the magnetic strength is more easily varied using external devices. In the figure above, the stator provides the field. 110 Rev 1 Knowledge Check Match the DC machine component to their appropriate definition. 1. The component that provide a magnetic field for producing either a voltage (generator) or a torque (motor). A. Field 2. The component that provides the energy conversion. In a generator, it is the component in which the voltage is induced. B. Stator 3. The stationary portion of the DC machine. C. Rotor 4. The rotating element of the DC machine. D. Armature ELO 7.5 Conditions for Inducing Voltage Introduction In this section, you will learn the conditions required to induce voltage in a conductor. Voltage Production (Generator Action) Recall that there are three conditions necessary to induce a voltage into a conductor: 1. A magnetic field 2. A conductor 3. Relative motion between the conductor and the magnetic field A DC generator provides these three conditions to produce a DC voltage output. Theory of Operation A basic DC generator has four parts: 1. 2. 3. 4. A magnetic field A single conductor, or loop A commutator Brushes Field As mentioned earlier, either a permanent magnet or an electromagnet may provide the magnetic field. This example will use a permanent magnet to describe a basic DC generator (see the figure below). Rev 1 111 Figure: Basic DC Generator Operation Voltage Induction A single conductor, shaped in the form of a loop, lies between the north and south poles of the magnet. As long as the loop is stationary, the magnetic field has no effect (there is no relative motion). If we rotate the loop, the loop cuts through the magnetic field, inducing an EMF (voltage) into the loop. When there is relative motion between a magnetic field and a conductor in that magnetic field, and the direction of rotation is such that the conductor cuts the lines of flux, the conductor gains an induced EMF. The magnitude of the induced EMF (voltage) depends on the strength of the magnetic field and the rate at which the conductor cuts the lines of flux. The stronger the field or the more lines of flux cut for a given period of time, the larger the induced EMF (voltage). πΈπ = πΎπ·π Where: Eg = generated voltage K = fixed constant Ξ¦ = magnetic flux strength N = speed of rotation in RPM Counter-Electromotive Force (CEMF) In a DC machine using a rotating armature, the conductors of the rotor cut the magnetic lines of force in the magnetic field and induce voltage in the armature conductors. This induced voltage opposes the applied voltage; it counteracts some of the applied voltage, which reduces the current flow through the armature. Since the induced voltage acts counter to the applied voltage, we call it counter-electromotive force (CEMF). Knowledge Check Relative motion between the conductor and the magnetic field is necessary to induce voltage. 112 A. True B. False Rev 1 Knowledge Check Select all the statements that are true. A. The counter-electromotive force always opposes the applied voltage. B. The counter-electromotive force always opposes current flow. C. The counter-electromotive force is induced if the rotor is not turning. D. The counter-electromotive force is induced only in rotating armature machines. ELO 7.6 Left-Hand Rule for Generators Introduction In this section, you will learn to apply the left-hand rule for generators. Left-Hand Rule for Generators The table below gives instructions for using the left-hand rule for generators. Step Action 1. Hold your left hand with the thumb, index finger, and middle finger at right angles to each other (see illustration below). 2. Point your thumb in the direction of motion of the conductor. 3. Point your index finger in the direction of magnetic flux (north to south). 4. Your middle finger will point in the direction of current flow (electron flow). 5. Note that the other side of the conductor loop is traveling in the opposite direction, so you have to reverse your thumb. Doing so will demonstrate that current is induced to flow around the loop. Rev 1 113 Note Note that the left-hand rule gives the direction of electron flow. In some applications, conventional current is used instead of electron flow, and conventional current is opposite of electron flow. To determine conventional current flow, follow the same process using the right hand. Left-Hand Rule Demonstration The direction of the induced current flow resulting from the EMF induced in the rotor can be determined using the left-hand rule for generators. This rule states that if you point the index finger of your left hand in the direction of the magnetic field (from north to south) and point the thumb in the direction of motion of the conductor, the middle finger will point in the direction of current flow. In the generator shown below, the conductor closest to the north (N) pole is traveling upward across the field; therefore, the motion is to the left, upper corner. Applying the left-hand rule to both sides of the loop will show that current flows in a counter-clockwise direction in the loop. Figure: Left-hand Rule for Generators 114 Rev 1 Knowledge Check The left-hand rule for generators is used as follows: A. Point the index finger of your left hand in the direction of the magnetic field (from north to south) and point the thumb in the direction of motion of the conductor, the middle finger will point in the direction of electron flow. B. Point the index finger of your left hand in the direction of the magnetic field (from north to south) and point the thumb in the direction of motion of the conductor, the middle finger will point in the direction of conventional current flow. C. Point the thumb of your left hand in the direction of the magnetic field (from north to south) and point the index finger in the direction of motion of the conductor, the middle finger will point in the direction of electron flow. D. Point the thumb of your left hand in the direction of the magnetic field (from north to south) and point the index finger in the direction of motion of the conductor, the middle finger will point in the direction of conventional current flow. ELO 7.7 Terminal Voltage Introduction In this section, you will learn the meaning of terminal voltage as it applies to DC machines. Terminal Voltage Terminal voltage, as applied to DC generators, is the voltage measured at the output of the generator. Applied voltage is the voltage delivered across the load and should be the same as terminal voltage. However, various circuit characteristics, such as losses, may reduce the applied voltage from the terminal voltage value. Field Excitation Electromagnets commonly provide the magnetic fields in DC generators. A current must flow through the electromagnetβs conductors to produce a magnetic field. In order for a DC generator to operate properly, the magnetic field must always be in the same direction. Therefore, the current through the field winding must be direct current. This current is the field excitation current and the field winding receives the current in one of two ways. Rev 1 115 It can come from a separate DC source external to the generator (e.g., a separately excited generator). It can come directly from the output of the generator, in which case the generator is a self-excited generator. Self-Excited Generator In a self-excited generator, the field winding connects directly to the generator output. There are three orientations for connections between field and output. The field winding can be in series with the output, in parallel with the output, or in some combination of the two. Separately Excited Generator Separate excitation requires an external source, such as a battery or another DC generator. This type of generator is generally more expensive than a self-excited generator, and used only where a self-excited generator is not satisfactory. For example, instances where the generator must respond quickly to an external control source or where it is necessary to vary the generated voltage over a wide range during normal operations call for a separately excited generator. Regulating Terminal Voltage DC generator output voltage depends on three factors: 1. The number of conductor loops in series in the armature 2. Armature speed 3. Magnetic field strength In order to change the generator output, it is necessary to change one of these three factors. It is impossible to change the number of conductor loops in the armature of an operating generator, and it is usually impractical to change the speed at which the armature rotates. Varying the current through the field winding easily changes the magnetic field strength. This is the most widely used method for regulating the output voltage of DC generator. The figure below shows a simple voltage regulator circuit. Figure: Varying DC Generator Terminal Voltage 116 Rev 1 Knowledge Check Which of the following does not affect the magnitude of voltage generated? A. Speed of rotation of the armature B. Direction of rotation of the armature C. Number of current loops in the armature D. Magnetic field strength ELO 7.8 DC Generator Ratings Introduction There are generally four rating categories for DC Generators: voltage, current, power and speed. These ratings are based on limitations associated with the design and construction of the particular generator, and are normally provided by the manufacturer on a label plate attached to the machine. The engineering documentation associated with the generator will also include these ratings. Voltage The voltage rating of a machine depends on the insulation type and design of the machine. The voltage rating provides a measure of the insulationβs capability to prevent electrical grounds and short circuits from developing inside the machine. Current The current rating depends on the size of the conductors used in the armature and field of the machine and the internal heat dissipation capability of the generator. Power The power rating is based on the mechanical limitations of the device that is used to turn the generator (referred to as the prime mover) and on the thermal limits of conductors, bearings, and other components of the generator. Speed The upper limit on speed for a DC machine depends on the speed at which mechanical damage will occur to the machine. The maximum speed limitation usually depends on the mechanical construction of the generatorβs rotor. A rotor assembled from separate parts (shaft and pole pieces) connected or keyed together, will have a lower speed limit than a rotor machined as a single unit. The lower speed rating for a DC machine depends on the maximum field current limit (as speed decreases, it is necessary to apply a higher field to produce the same voltage output from the generator). Rev 1 117 Knowledge Check Match each DC generator rating with the limiting factor it is based on. Duration ο§ 30 minutes Logistics ο§ Use PowerPoint slides 270β271, Crossword activity and the IG to review TLO 7 material. Use directed and nondirected questions to students, check for understanding of ELO content, and review any material where student understanding of ELOs is inadequate. 1. Insulation type and design A. Speed 2. Size of conductors in the armature B. Power 3. Mechanical limits of the prime mover C. Current 4. Mechanical construction of the rotor D. Voltage TLO 7 Summary In this section, you learned the different means of producing a DC voltage, and you learned the basic workings of rectifiers and DC generators. Now that you have completed this lesson, you should be able to: 1. Describe the common methods for producing a DC voltage and give an example of each. 2. State the purpose of a rectifier and describe the outputs of rectifier circuits. 3. Describe the effects of commutation in a DC generator. 4. State the purpose of each of the components of a DC machine. 5. List the three conditions necessary to induce a voltage. 6. Using the left-hand rule of generators, determine the direction of the magnetic field, the motion of the conductor, or the direction of current induced into a conductor. 7. Define terminal voltage as it applies to DC generators and describe how terminal voltage of a DC generator is adjusted. 8. Identify the four categories and their bases for DC generator nameplate ratings. 118 Rev 1 Basic Electricity Part 1 Summary Now that you have completed this module, you should be able to demonstrate mastery of this topic by passing a written exam with a grade of 80 percent or higher on the following Terminal Learning Objectives (TLOs): 1. Describe basic electrical theory principles of operation. 2. Describe the magnetic properties of materials and the use of magnetism in electrical applications. 3. Differentiate between types of electrical symbols, drawings, and diagrams. 4. Describe the operating characteristics, terminology, and hazards of a lead-acid battery and voltaic cell. 5. Analyze various DC circuits to find resistances, currents, and voltages at any given point within the circuit. 6. Describe the principles of operation, control, and characteristics of DC motors. 7. Explain how a DC generator produces DC voltage. Rev 1 119 Duration ο§ 30 minutes Logistics ο§ Review PowerPoint slide 272.