Table of Contents 1. Introduction 2. Electrical Fundamentals Electron Theory Matter 4 MOLECULE

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1 Table of Contents 1. Introduction 3 2. Electrical Fundamentals 4 Electron Theory 4 Matter 4 MOLECULE 5 The atom 6 Atom construction 7 Electrical charges 11 Balanced atoms 12 Ions 13 Electron orbits 15 Free electrons 16 Insulators, Conductors, semiconductors 17 Electron Theory 20 Voltage 21 Voltmeter 22 Voltage Unites 22 Current 23 Ammeter 24 Amperage Unites 24 Current Flow Affects 25 Resistance 26 Ohmmeter 27 Resistance Unites 27 Resistance Factors 28 Types of Electricity 29 Static electricity 30 DC Electricity 32 AC Electricity 32 Sources of Electricity Electrical Circuits 34 Electric Circuit 34 Electric Circuit Requirements 34 Electric Circuit Construction 35 Loads 36 Automotive Electric Circuit 37 Ohm s Law 38 Ohm s Law Formula 39 Ohm s Law Shortcut 40 Application of Ohm s Law 41 Types of Circuits 44 Series Circuit 45 Parallel Circuit 52 Series-Parallel Circuits 60 Power 66

2 4. Magnetism Introduction to AC 73 AC sine wave 73 AC Generators 75 Frequency 78 Voltage and Current 79 Inductance 82 Capacitance 86 Inductive and Capacitive Reactance 90 Seriese R-L-C Circuit 97 Parallel R-L-C Circuit 99 Resistive Loads 101 Reactive Loads 102 Inductive Reactance 103 Capacitive Reactance 105 Combination- Resistive & Reactance. 107 Voltage Drop 108 Power and Power Factor in an AC Circuit Transformers Control Devices 134 Switches 136 Relays 141 Solenoids Circuit Protection 144 Fuses 146 Circuit Breakers Resistors 151 Carbon Resistors 152 Variable Resistors Understanding Logic Gates Lockout Procedure Summary Review Questions Sample Questions 190

3 Introduction Electricity is a manufactured product. It is not something you pump out of the ground, mine, or collect from the sun or wind. Electric power is manufactured from a rotating machine that we call an electrical generator. After it is generated, (manufactured) it is then delivered through copper wires to where it is utilized Electricity - most people don't understand what it is. They just turn on the light switch, start the appliance, or push the button and something works. It's only when there is no electric power available that we start to consider the importance of it in our daily personal and working lives. But the invention of the machine to generate power is right next to the invention of the printing press in the list of major contributions to the advancement of human civilization. Without it, we would be burning wood and coal to heat our homes and businesses and using oil and candles to light our way in the dark. That is the way it was for humans civilization for countless centuries. Only since the invention of the electric generator, have humans been able to advance in every aspect of modern life. In fact, modern living is defined by electric power. Upon completion of Basics of Electricity you will be able to: Explain the difference between conductors and insulators Use Ohm s Law to calculate current, voltage, and resistance Calculate equivalent resistance for series, parallel, or series-parallel circuits Calculate voltage drop across a resistor Calculate power given other basic values Identify factors that determine the strength and polarity of a current-carrying coil s magnetic field Determine peak, instantaneous, and effective values of an AC sine wave Identify factors that effect inductive reactance and capacitive reactance in an AC circuit Calculate total impedance of an AC circuit Explain the difference between real power and apparent power in an AC circuit Calculate primary and secondary voltages of single-phase and three-phase transformers Calculate kva of a transformer 3

4 Electrical Fundamentals 1 of 30 Electron Theory Electron Proton Nucleus MATTER everything in the world is made of matter. Matter is anything that has mass (weight) and occupies space. In order to understand how electricity is created and works it is necessary to look at how all matter is structured. All matter is made up of molecules that have a certain number of atoms, for example one molecule of water is made up of two atoms of hydrogen and one of oxygen giving a symbol of H 2 O. All other matter also has a symbol like this and is made up of atoms. To be able to understand electricity however, the atom must be broken down even further into a nucleus, neutrons, protons and electrons. The nucleus is made up of positively charged protons and neutrally charged neutrons that generally balance the number of negatively charged electrons, which are moving around the nucleus in a similar manner to the planets circling the sun. Group of atoms form a molecule. Group of molecules form compounds. a single atom that still maintaining the properties of the original material called elements. Matter has three states: Solid, Liquid, and Vapor. 4

5 Electrical Fundamentals 2 of 30 MOLECULE EXAMPLE Imagine a lake. Now imagine taking the smallest particle or piece of water from the lake. You would have a single molecule of water, H 2 O, which is made up of two hydrogen atoms and one oxygen atom. Not all materials are made up of molecules. Copper, for example, is made up of a single copper atom. These are called elements. Each element is a type of matter that has certain individual characteristics. 5

6 Electrical Fundamentals 3 of 30 THE ATOM One of the basic building blocks in the universe for matter is the atom. All matter - gas, liquid, or solid - is made up of molecules or atoms joined together. These atoms are the smallest particle into which an element or substance can be divided without losing its property. A single atom consists of three basic components: a proton, a neutron, and an electron. Within the atom there is a Nucleus. The Nucleus contains the protons and neutrons. Orbiting around the nucleus are the electrons. An atom is similar to a miniature solar system. As with the sun in the center of the universe, the nucleus is in the center of the atom. Protons and Neutrons are contained inside the nucleus. Orbiting around the nucleus are the electrons. 6

7 Electrical Fundamentals 4 of 30 ATOM CONSTRUCTION An atom is similar to a miniature solar system. As the sun is in the center of the solar system, so is the nucleus is in the center of the atom. Protons and neutrons are contained within the nucleus. Electrons orbit around the nucleus, which would be similar to planets orbiting around the sun. 7

8 Electrical Fundamentals 5 of 30 NUCLEUS The Nucleus is located in the center of the atom (shown in red). The Nucleus contains the protons and neutrons. Orbiting around the nucleus are the electrons. 8

9 Electrical Fundamentals 6 of 30 PROTONS Protons are located within the nucleus of the atom (shown in blue).protons are positively (+) charged. NEUTRONS Neutrons add atomic weight to an atom (shown in green).neutrons have no electrical charge. ELECTRONS Electrons orbit around the nucleus of the atom (shown in yellow).electrons are negatively (-) charged. 9

10 Electrical Fundamentals 7 of 30 Since electrons are lighter than protons and are outside the nucleus, they can be easily moved from atom to atom to form a flow of electrons. Normally electrons are prevented from being pulled into the atom by the forward momentum of their rotation. Electrons are also prevented from flying away because of the magnetic attraction of the protons inside the nucleus, the same type of force that keeps the planets orbiting around the sun. 10

11 Electrical Fundamentals 8 of 30 ELECTRICAL CHARGES Opposite electrical charges always attract each other. So these particles with opposite charges will tend to move toward each other. Like electrical charges always repel. So particles with like charges will move away from each other. Remember: Opposite s charges attract Like charges, repel Unlike Charges Attract Like Charges Repel Atoms always try to remain electrically balanced. 11

12 Electrical Fundamentals 9 of 30 BALANCED ATOMS Atoms normally have an equal number of electrons and protons. Atoms have no electrical charge. They are neither positive nor negative. They are electrically neutral or BALANCED. The negative charge of the electrons will cancel the positive charge of the protons, thus balancing the charge of the atom. This cancellation of charges creates a natural attraction or bonding between the positive proton and the negative electron. 12

13 Electrical Fundamentals 10 of 30 ION PARTICLES When an atom loses or gains an electron, an imbalance occurs. The atom becomes either a positively or negatively charged particle called an ION. ION is positively or negatively charged atom. IONs will take or release an electron to become balanced again, this process is responsible for electron flow ( electricity ). 13

14 Electrical Fundamentals 11 of 30 ION CHARGE A positive (+) ION has one less electron than it has protons. A negative (-) ION has one more electron than it has protons. The positive ION attracts a negative ION to become balanced. This attraction or difference in electrical potential causes electron flow. 14

15 Electrical Fundamentals 12 of 30 ELECTRON ORBITS Electrons rotate around the atom at different orbits called Rings, Orbits, or Shells. BOUND ELECTRONS orbit the nucleus on the inner rings. Bound electrons have a strong magnetic attraction to the nucleus. FREE ELECTRONS orbit on the outermost ring which is known as the VALANCE RING. 15

16 Electrical Fundamentals 13 of 30 FREE ELECTRONS Only the FREE ELECTRONS in the outermost shell (Valance Ring) are free to move from atom to atom. This movement is called ELECTRON FLOW. These FREE ELECTRONS are loosely held and can easily be moved to another atom or ion. Because of their distance from the nucleus, free electrons have a weak magnetic attraction. Since this attraction is not as strong to the nucleus as the bound electrons on the inner orbits, the electrons move easily from atom to atom. 16

17 Electrical Fundamentals 14 of 30 INSULATORS An INSULATOR is any material that inhibits (stops) the flow of electrons (electricity). An insulator is any material with 5 to 8 free electrons in the outer ring. Because, atoms with 5 to 8 electrons in the outer ring are held (bound) tightly to the atom, they CANNOT be easily moved to another atom nor make room for more electrons. Insulator material includes glass, rubber, and plastic. 17

18 Electrical Fundamentals 15 of 30 CONDUCTORS A CONDUCTOR is any material that easily allows electrons (electricity) to flow. A CONDUCTOR has 1 to 3 free electrons in the outer ring. Because atoms with 1 to 3 electrons in the outer ring are held (bound) loosely to the atom, they can easily move to another atom or make room for more electrons. Conductor material includes copper and gold. 18

19 Electrical Fundamentals 16 of 30 SEMICONDUCTORS Any material with exactly 4 free electrons in the outer orbit is called SEMICONDUCTORS. A semiconductor is neither a conductor or insulator. semiconductor material includes carbon, silicon, and germanium. These materials are be used in the manufacturer of diodes, transistors, and integrated circuit chips. 19

20 Electrical Fundamentals 17 of 30 Two Current Flow theories exist. The first is: ELECTRON THEORY The Electron Theory states that current flows from NEGATIVE to POSITIVE. Electrons move from atom to atom as they move through the conductor towards positive. The second Current Flow theory is: CONVENTIONAL THEORY Conventional theory, also known as HOLE THEORY, states that current flows from POSITIVE to NEGATIVE. Protons or the lack of electrons (the holes) moves towards the negative. (Current flow direction in Hole Theory is the opposite of that in Electron Theory.) 20

21 Electrical Fundamentals 18 of 30 VOLTAGE Voltage is the electrical force that moves electrons through a conductor. Voltage is electrical pressure also known as EMF (Electro Motive Force) that pushes electrons. The greater the difference in electrical potential push (difference between positive and negative), the greater the voltage force potential. How to measure voltage The instrument used to measure voltage, difference potential or electromotive force is called voltmeter. Steps for voltage measurement: Connect a small light bulb to a dry cell. A voltmeter is wired in parallel with the light bulb to measure voltage across the light bulb. Connect positive terminal (+) of voltmeter to positive terminal (+) of a dry cell and connect negative terminal (-) of voltmeter to negative terminal (-) of a dry cell (see figure). Safety instructions for measuring voltage: 1. Estimate voltage that required measuring then choose a suitable voltmeter, since each voltmeter is designed with the limit of voltage measurement. 2. Be sure that the connecting of positive terminal (+) and negative terminal (-) of voltmeter are correct. 21

22 Electrical Fundamentals 19 of 30 A VOLTMETER measures the voltage potential across the circuit. Voltmeters are placed in parallel. The Voltmeter measures the amount of electrical pressure difference between two points being measured. Voltage can exist between two points without electron flow. VOLTAGE UNITS Voltage is measured in units called VOLTS. Voltage measurements can use different value prefixes such as millivolt, volt, Kilovolt, and Megavolt. VOLTAGE LESS THAN BASE UNIT BASIC UNIT LARGER THAN BASE UNIT Symbol mv V kv Pronounced millivolt Volt Kilovolt Multiplier ,000 22

23 Electrical Fundamentals 20 of 30 CURRENT (AMPERES) CURRENT is the quantity or flow rate of electrons moving past a point within one second. Current flow is also known as amperage, or amps for short. Higher voltage will produce higher current flow, and lower voltage will produce lower current flow. How to measure current The instrument used to measure current is called ampere meter or ammeter. Steps for current measurement: Connect a small light bulb to a dry cell. Measure current that passes through light bulb by connecting positive terminal (+) of ammeter to negative terminal (- ) of a dry cell (see figure) Safety instructions for current measurement: 1. Estimate current that required measuring then choose a suitable ammeter, since each ammeter has different limit of current measurement. 2. Be sure that the connection to positive terminal (+) and negative terminal (-) of ammeter are correct. 3. Do not directly connect ammeter terminals to dry cell terminals. Since it can damage the meter. 23

24 Electrical Fundamentals 21 of 30 An AMMETER measures the quantity of current flow. Ammeters are placed in series (inline) to count the electrons passing through it. Example: A water meter counts the gallons of water flowing through it. AMPERAGE UNITS Current flow is measured in units called Amperes or AMPS. Amperage measurements can use different value prefixes, such as micro amp, milliamp, and Amp. AMPERAGE Symbol Pronounced Multiplier LESS THAN LESS THAN BASE UNIT BASE UNIT µa ma Micro amp milliamp BASIC UNIT A Amp 1 24

25 Electrical Fundamentals 22 of 30 AFFECTS OF CURRENT FLOW Two common effects of current flow are Heat Generation Electromagnetism. HEAT: When current flows, heat will be generated. The higher the current flow the greater the heat generated. An example would be a light bulb. If enough current flows across the filament, it will glow white-hot and illuminate to produce light. ELECTROMAGNETISM : When current flows, a small magnetic field is created. The higher the current flow, the stronger the magnetic field. An example: Electromagnetism principles are used in alternators, ignition systems, and other electronic devices. 25

26 Electrical Fundamentals 23 of 30 RESISTANCE Resistance is the force that reduces or stops the flow of electrons. It opposes voltage. Higher resistance will decrease the flow of electrons and lower resistance will allow more electrons to flow. How to measure resistance The instrument used to measure resistance is called Ohmmeter or Multi meter. The Multi meter or test meter is used to make various electrical measurements such as current, voltage and resistance. It combines the functions of ammeter, voltmeter and ohmmeter. Steps for resistance measurement: Turn the face dial to a position for required measuring, resistance, then touch both of terminals of multi meter (see figure 1) and adjust the meter range to 0 Ω. Touch both of terminals of meter to a resistance and take the reading (see figure 2). 26

27 Electrical Fundamentals 24 of 30 An OHMMETER measures the resistance of an electrical circuit or component. No voltage can be applied while the ohmmeter is connected, or damage to the meter will occur. Example: Water flows through a garden hose, and someone steps on the hose. The greater the pressure placed on the hose, the greater the hose restriction and the less water flows. RESISTANCE UNITS Resistance is measured in units called OHMS. Resistance measurements can use different value prefixes, such as Kilo ohm and Mega ohms. AMPERAGE Symbol Pronounced Multiplier MORE MORE BASIC THAN THAN UNIT BASE BASE UNIT UNIT K M Ohm Kilo ohm Mega ohm 1 1,000 1,000,000 27

28 Electrical Fundamentals 25 of 30 RESISTANCE FACTORS Various factors can affect the resistance. These include: LENGTH of the conductor. The longer the conductor, the higher the resistance. DIAMETER of the conductor. The narrower the conductor, the higher the resistance. TEMPERATURE of the material. Depending on the material, most will increase resistance as temperature increases. PHYSICAL CONDITION (DAMAGE) to the material. Any damage will increase resistance. TYPE of MATERIAL used. Various materials have a wide range of resistances. 28

29 Electrical Fundamentals 26 of 30 TYPES OF ELECTRICITY Two basic types of Electricity classifications: STATIC ELECTRICITY is electricity that is standing still. Voltage potential with NO electron flow. DYNAMIC ELECTRICITY is electricity that is in motion. Voltage potential WITH electron flow. Two types of Dynamic electricity exist: Direct Current (DC) Electron Flow is in only one direction. Alternating Current (AC) Electron flow alternates and flows in both directions (back and forth). 29

30 Electrical Fundamentals 27 of 30 STATIC ELECTRICITY Voltage potential with NO electron flow. Example: By rubbing a silk cloth on a glass rod, you physically remove electrons from the glass rod and place them on the cloth. The cloth now has a surplus of electrons (negatively charged), and the rod now has a deficiency of electrons (positively charged). Another example: Rub your shoes on a rug and then touch a metal table or chair... Zap!! The shock you felt was the static electricity dissipating through your body. 30

31 Electrical Fundamentals 28 of 30 DYNAMIC ELECTRICITY is electricity in motion, meaning you have electrons flowing, in other words voltage potential WITH electron flow. Two types of dynamic electricity exists: Direct Current (DC) Alternating Current (AC) 31

32 Electrical Fundamentals 29 of 30 DIRECT CURRENT (DC) Electricity with electrons flowing in only one direction is called Direct Current or DC. DC electrical systems are used in cars. ALTERNATING CURRENT (AC) Electricity with electrons flowing back and forth, negative - positive- negative, is called Alternating Current, or AC. The electrical appliances in your home use AC power. 32

33 Electrical Fundamentals 30 of 30 SOURCES OF ELECTRICITY Electricity can be created by several means: Friction Heat Light Pressure Chemical Action Magnetic Action. The battery produces electricity through chemical action, and the alternator produces electricity through magnetic action. Friction creates static electricity. Heat can act upon a device called a thermo couple to create DC. Light applied to photoelectric materials will produce DC electricity. Pressure applied to a piezoelectric material will produce DC electricity. Chemical Action of certain chemicals will create electricity. 33

34 Electrical Circuits 1 of 35 AN ELECTRICAL CIRCUIT The circuit shown below has a power source, fuse, switch, two lamps and wires connecting each into a loop or circle. When the connection is complete, current flows from the positive terminal of the battery through the wire, the fuse, the switch, another wire, the lamps, a wire and to the negative terminal of the battery. The route along which the electricity flows is called an electrical circuit. ELECTRICAL CIRCUIT REQUIREMENTS A complete Electrical Circuit is required in order to make electricity practical. Electrons must flow from and return to the power source. There are three different circuit types, all require the same basic components: 1. Power Source is needed to supply the flow of electrons (electricity). 2. Protection Device prevents damage to the circuit in the event of a short. 3. Load Device converts the electricity into work. 4. Control Device allows the user control to turn the circuit on or off 5. Conductors provide an electrical path to and from the power source. 34

35 Electrical Circuits 2 of 35 BASIC CIRCUIT CONSTRUCTION 1. Power Source (Battery, Alternator, Generator, etc.) 2. Protection Device (Fuse, Fusible Link, or Circuit Breaker) 3. Load Device (Lamp, Motor, Winding, Resistor, etc.) 4. Control (Switch, Relay, or Transistor) 5. Conductors (A Return Path, Wiring to Ground) 35

36 Electrical Circuits 3 of 35 LOADS The illustration below has a horn in place of the lamp. Any device such as a lamp, horn, wiper motor, or rear window defogger that consumes electricity is called a load. In an electrical circuit, all loads are regarded as resistance. Loads use up voltage and control the amount of current flowing in a circuit. Loads with high resistance cause less current to flow while those with lower resistance allow high current rates to flow. 36

37 Electrical Circuits 4 of 35 AUTOMOTIVE ELECTRICAL CIRCUITS In an automotive electrical circuit, one end of the wire from each load returning to the battery is connected to the vehicle body or frame. Therefore, the vehicle body or frame itself functions as a conductor, allowing current to flow though the body or frame and back to the battery. The body or frame is then referred to as the body ground (or earth) of the circuit (meaning that part of the circuit that returns the current to the battery). 37

38 Electrical Circuits 5 of 35 WHAT IS OHM'S LAW? A simple relationship exists between voltage, current, and resistance in electrical circuits. Understanding this relationship is important for fast, accurate electrical problem diagnosis and repair. OHM'S LAW Ohm's Law says: The current in a circuit is directly proportional to the applied voltage and inversely proportional to the amount of resistance. This means that if the voltage goes up, the current flow will go up, and vice versa. In addition, as the resistance goes up, the current goes down, and vice versa. Ohm's Law can be put to good use in electrical troubleshooting. However, calculating precise values for voltage, current, and resistance is not always practical... nor, needed. A more practical, less timeconsuming use of Ohm's Law would be to simply apply the concepts involved: SOURCE VOLTAGE is not affected by either current or resistance. It is either too low, normal, or too high. If it is too low, current will be low. If it is normal, current will be high if resistance is low, or current will be low if resistance is high. If voltage is too high, current will be high. CURRENT is affected by either voltage or resistance. If the voltage is high or the resistance is low, current will be high. If the voltage is low or the resistance is high, current will be low. RESISTANCE is not affected by either voltage or current. It is either too low, okay, or too high. If resistance is too low, current will be high at any voltage. If resistance is too high, current will be low if voltage is okay. NOTE: When the voltage stays the same, such as in an Automotive Circuit... current goes up as resistance goes down, and current goes down as resistance goes up. Bypassed devices reduce resistance, causing high current. Loose connections increase resistance, causing low current. 38

39 Electrical Circuits 6 of 35 OHM'S LAW FORMULA When voltage is applied to an electrical circuit, current flows in the circuit. The following special relationship exists among the voltage, current and resistance within the circuit: the size of the current that flows in a circuit varies in proportion to the voltage, which is applied to the circuit, and in inverse proportion to the resistance through which it must pass. This relationship is called Ohm's law, and can be expressed as follows: E = I R Voltage = Current x Resistance E Voltage applied to the circuit, in volts (V) I Current flowing in the circuit, in amperes (A) R Resistance in the circuit, in ohms In practical terms "V = I x R" which means "Voltage = Current x Resistance". 1 volt will push one amp through 1 ohm of resistance. NOTE: I = E R E = I x R R = E I are all variations of the same formula. How you learned Ohm's law will determine which one you will use. Personal preference is the only difference; anyone will get you the correct answer. 39

40 Electrical Circuits 7 of 35 OHM'S LAW SYMBOL SHORTCUT Mathematical formulas can be difficult for many who don't use them regularly. Most people can remember a picture easier than a mathematical formula. By using the Ohms law symbol below, anyone can remember the correct formula to use. By knowing any two values you can figure out the third. Simply put your finger over the portion of the symbol you are trying to figure out and you have your formula. 40

41 Electrical Circuits 8 of 35 APPLICATIONS OF OHM'S LAW As an application of Ohm's law, any voltage V, current I or resistance R in an electrical circuit can be determined without actually measuring it if the two others values are known. This law can be used to determine the amount of current I flowing in the circuit when voltage V is applied to resistance R. As stated previously, Ohm's law is: Current = Voltage / Resistance. In the following circuit, assume that resistance R is 2 and voltage V that is applied to it is 12 V. Then, current I flowing in the circuit can be determined as follows: 41

42 Electrical Circuits 9 of 35 This law can also be used to determine the voltage V that is needed to permit current I to pass through resistance R: V = I x R Voltage= Current x Resistance In the following circuit, assume that resistance R is 4 ohms. The voltage V that is necessary to permit a current I of 3 A to pass through the resistance can be determined as follows: 42

43 Electrical Circuits 10 of 35 Still another application of the law can be used to determine the resistance R when the voltage V which is applied to the circuit and current I flowing in the circuit are already known: Resistance = Voltage / Current In the following circuit, assume that a voltage V of 12 V is applied to the circuit and current I of 4 A flows in it. Then, the resistance value R of the resistance or load can be determined as follows: 43

44 Electrical Circuits 11 of 35 TYPES OF CIRCUITS Individual electrical circuits normally combine one or more resistance or load devices. The design of the automotive electrical circuit will determine which type of circuit is used. There are three basic types of circuits: Series Circuit + _ R 1 R 2 R 3 R 4 Parallel Circuit + _ R 1 R 2 Series-Parallel Circuit Parallel Branches + _ 44

45 Electrical Circuits 12 of 35 SERIES CIRCUITS A series circuit is the simplest circuit. The conductors, control and protection devices, loads, and power source are connected with only one path to ground for current flow. The resistance of each device can be different. The same amount of current will flow through each. The voltage across each will be different. If the path is broken, no current flows and no part of the circuit works. Christmas tree lights are a good example; when one light goes out the entire string stops working. A Series Circuit has only one path to ground, so electrons must go through each component to get back to ground. All loads are placed in series. Therefore: 1. An open in the circuit will disable the entire circuit. 2. The voltage divides (shared) between the loads. 3. The current flow is the same throughout the circuit. 4. The resistance of each load can be different. 45

46 Electrical Circuits 13 of 35 SERIES CIRCUIT CALCULATIONS If, for example, two or more lamps (resistances R1 and R2, etc.) are connected in a circuit as follows, there is only one route that the current can take. This type of connection is called a series connection. The value of current I is always the same at any point in a series circuit. The combined resistance RO in this circuit is equal to the sum of individual resistance R1 and R2. In other words: The total resistance(ro) is equal to the sum of all resistances (R1 + R2 + R3 +...) Therefore, the strength of current (I) flowing in the circuit can be found as follows: 46

47 Electrical Circuits 14 of 35 Resistance R0 (a combination of resistances R1 and R2, which are connected in series in the circuit as illustrated) and current I flowing in this circuit can be determined as follows: In this example, the circuit includes 4 series resistors. R t = R 1 + R 2 + R 3 + R 4 R t = R t = 10 Ω > I = 1.2 Amps 5 Ω 1 Ω 2 Ω 2 Ω 10 Ω + _ R 1 R 2 R 3 R 4 12 Volts R t 12 Volts Original Circuit Equivalent Circuit 47

48 Electrical Circuits 15 of 35 VOLTAGE DROP A voltage drop is the amount of voltage or electrical pressure that is used or given up as electrons pass through a resistance (load). All voltage will be used up in the circuit. The sum of the voltage drops will equal source voltage. A voltage drop measurement is done by measuring the voltage before entering the load and the voltage as it leaves the load. The difference between these two voltage readings is the voltage drop. VOLTAGE DROP TOTAL When more than one load exists in a circuit, the voltage divides and will be shared among the loads. The sum of the voltage drops equal source voltage. The higher the resistance the higher the voltage drop. Depending on the resistance, each load will have a different voltage drop. 0V + 5V + 7V + 0V = 12V 48

49 Electrical Circuits 16 of 35 VOLTAGE DROP CALCULATION When current flows in a circuit, the presence of a resistance in that circuit will cause the voltage to fall or drop as it passes through the resistance. The resultant difference in the voltage on each side of the resistance is called a voltage drop. When current (I) flows in the following circuit, voltage drops V1 and V2 across resistances R1 and R2 can be determined as follows from Ohm's law. (The value of current I is the same for both R1 and R2 since they are connected in series.) The sum of the voltage drops across all resistances is equal to the voltage of the power source (VT): 49

50 Electrical Circuits 17 of 35 The voltage drop across resistances R1 and R2 in the following circuit can be determined as follows: 50

51 Electrical Circuits 18 of 35 Example 2 12 V 3 V 3 V 3 V 3 V 1.5 Ω 1.5 Ω 1.5 Ω 1.5 Ω R 1 R 2 R 3 R 4 12 Volt Battery First, solve for total resistance: R t = R 1 + R 2 + R 3 + R 4 R t = R t = 6 Ω Second, solve for current: I = E R I = 12 6 E = 2 Amps Third, solve for voltage across any resistor: E = I x R E = 2 x 1.5 E = 3 Volts 51

52 Electrical Circuits 19 of 35 PARALLEL CIRCUIT A parallel circuit has more than one path for current flow. The same voltage is applied across each branch. If the load resistance in each branch is the same, the current in each branch will be the same. If the load resistance in each branch is different, the current in each branch will be different. If one branch is broken, current will continue flowing to the other branches. A Parallel Circuit has multiple paths or branches to ground. Therefore: In the event of an open in the circuit in one of the branches, current will continue to flow through the remaining. Each branch receives source voltage. Current flow through each branch can be different. The resistance of each branch can be different. 52

53 Electrical Circuits 20 of 35 PARALLEL CIRCUIT In parallel connection, two or more resistances (R1, R2, etc.) are connected in a circuit as follows, with one end of each resistance connected to the high (positive) side of the circuit, and one end connected to the low (negative) side. Full battery voltage is applied to all resistances within a circuit having a parallel connection. 53

54 Electrical Circuits 21 of 35 Resistance R0 (a combination of resistances R1 and R2) in a parallel connection can be determined as follows: From the above, the total current I flowing in this circuit can be determined from Ohm's law as follows: The total current I is also equal to the sum of currents I1 and I2 flowing through individual resistances R1 and R2 Since battery voltage V is applied equally to all resistances, the strength of currents I1 and I2 can be determined from Ohm's law as follows: 54

55 Electrical Circuits 22 of 35 Resistance RO (a combination of resistances R1 and R2, which are connected in parallel in the circuit as shown below), the total current I flowing in the circuit, and currents I1 and I2 flowing through resistances R1 and R2, can be determined respectively as follows: 55

56 Electrical Circuits 23 of 35 To determine the total resistance when resistors are of equal value in a parallel circuit, use the following formula: R t = Value of any one Resistor Number of Resistors In the following illustration there are three 15 W resistors. The total resistance is: R t = Value of any one Resistor Number of Resistors R t =3 Ω R 1 R 2 R 3 15 Ω 15 Ω 15 Ω There are two formulas to determine total resistance for resistors of any value in a parallel circuit. The first formula is used when there are any number of resistors = R t R 1 R R 3 1 R n In the following illustration, there are three resistors, each of different value. Solve for the total resistance as follows: 1 = R t R 1 R 2 R 3 Insert Values for the Resistors Find the Lowest Common Denominator Add the Numerators Invert Both Sides of the Equation 1 R t 1 R t 1 R t R t 1 R t = = = = = 2.86 Ω R 1 R 2 R 3 5 Ω 10 Ω 20 Ω 56

57 Electrical Circuits 24 of 35 The second formula is used when there are only two resistors. R t = R 1 x R 2 R 1 + R 2 In the following illustration there are two resistors, each of different value. The total resistance is: R t R t R t R t = = = R 1 x R 2 R 1 + R 2 5 x = 3.33 Ω + _ R 1 R 2 5 Ω 10 Ω When resistors are placed in parallel across a voltage source, the voltage is the same across each resistor. In the following illustration three resistors are placed in parallel across a 12 volt battery. Each resistor has 12 volts available to it. 12 Volt Battery + 12 V _ R 1 R 2 R 3 12V 12 V 57

58 Electrical Circuits 25 of 35 Current flowing through a parallel circuit divides and flows through each branch of the circuit. I t _ + R 1 R 2 R 3 I 1 I 2 I 3 I t Total current in a parallel circuit is equal to the sum of the current in each branch. The following formula applies to current in a parallel circuit. I t = I 1 + I 2 + I I n When equal resistances are placed in a parallel circuit, opposition to current flow is the same in each branch. In the following circuit R 1 and R 2 are of equal value. If total current (I t ) is 10 amps, then 5 amps would flow through R 1 and 5 amps would flow through R 2. I t = 10 Amps _ + R 1 R 2 I 1 = I 2 = 5 Amps 5 Amps I t = 10 Amps I t = I 1 + I 2 I t = 5 Amps + 5 Amps I t = 10 Amps 58

59 Electrical Circuits 26 of 35 When unequal value resistors are placed in a parallel circuit, opposition to current flow is not the same in every circuit branch. Current is greater through the path of least resistance. In the following circuit R 1 is 40 W and R 2 is 20 W. Small values of resistance means less opposition to current flow. More current will flow through R 2 than R 1. _ 12 Volts + I t = 0.9 Amps R 1 R 2 40 Ω 20 Ω I 1 = I 2 = 0.3 Amps 0.6 Amps Using Ohm s Law, the total current for each circuit can be calculated. Or 59

60 Electrical Circuits 27 of 35 SERIES PARALLEL CIRCUIT A series-parallel circuit has some components in series and others in parallel. The power source and control or protection devices are usually in series; the loads are usually in parallel. The same current flows in the series portion, different currents in the parallel portion. The same voltage is applied to parallel devices, different voltages to series devices. If the series portion is broken, current stops flowing in the entire circuit. If a parallel branch is broken, current continues flowing in the series portion and the remaining branches. 60

61 Electrical Circuits 28 of 35 SERIES-PARALLEL CIRCUIT A resistance and lamps may be connected in a circuit as illustrated below. This type of connecting method is called series-parallel connection, and is a combination of series and parallel connections. The interior dash board lights are a good example. By adjusting the rheostat, you can increase or decrease the brilliance of the lights. 61

62 Electrical Circuits 29 of 35 The combined resistance R02 in this series-parallel connection can be determined in the following order: a. Determine combined resistance R01, which is a combination of resistances R2 and R3 connected in parallel. b. Then, determine resistance R02, which is a combination of resistance R1 and combined resistance R01 connected in series. Total current I flowing in the circuit can be determined from Ohm's law as follows: The voltage applied to R2 and R3 can be found by the following formula: 62

63 Electrical Circuits 30 of 35 Currents I1, I2 and I flowing through resistances R1, R2 and R3 in the series-parallel connection, as shown below, can be determined as follows: 63

64 Electrical Circuits 31 of 35 R 3 10 Ω R 1 10 Ω R 2 10 Ω First, use the formula to determine total resistance of parallel circuit to find the total resistance of R 1 and R 2. When the resistors in a parallel circuit are equal, the following formula is used: R R R = = = Value of any One Resistor Number of Resistors 10 Ω 2 5 Ω Second, redraw the circuit showing the equivalent values. The result is a simple series circuit which uses already learned equations and methods of problem solving. R 3 10Ω R 3 5Ω + _ In the following illustration R 1 and R 2 are in series with each other. R 3 is in parallel with the series circuit of R 1 and R 2. + _ R 1 10Ω R 3 20Ω R 2 10Ω First, use the formula to determine total resistance of a series circuit to find the total resistance of R 1 and R 2. The following formula is used: R = R 1 + R 2 R = 10 Ω + 10 Ω R = 20 Ω 64

65 Electrical Circuits 32 of 35 Second, redraw the circuit showing the equivalent values. The result is a simple parallel circuit which uses already learned equations and methods of problem solving. + _ R = 20 Ω R 3 = 20 Ω + _ R t = 10 Ω 65

66 Electrical Circuits 33 of 35 Power Work Whenever a force of any kind causes motion, work is accomplished. In the illustration below work is done when a mechanical force is used to lift a weight. If a force were exerted without causing motion, then no work is done. Electric Power In an electrical circuit, voltage applied to a conductor will cause electrons to flow. Voltage is the force and electron flow is the motion. The rate at which work is done is called power and is represented by the symbol P Power is measured in watts, represented by the symbol W In a direct current circuit, one watt is the rate work is done in a circuit when 1 amp flows with 1 volt applied... Power Formulas In a DC circuit, power is the product of voltage times current. Later in this course, you will learn a slightly different version of this relationship for an alternating current (AC) circuit. P = E x I or P = EI Two other power equations can be derived from this formula by substituting other components of Ohm s Law. P = I 2 R and P= E 2 R 66

67 Electrical Circuits 34 of 35 DC Circuit Example In the following illustration, power can be calculated using any of the power formulas. I = 2 Amps R = 6 Ω P = EI P = 12 Volts x 2 Amps P = 24 Watts P = I 2 R P = (2 Amps) 2 x 6 Ω P = 24 Watts + _ 12 Volts P= P = P = E 2 R (12 Volts) 6 Ω 2 P = 24 Watts Additional Calculations Electrical equipment often has a power rating expressed in watts. This rating is an indication of the rate at which electrical equipment converts electrical energy into some other form of energy, such as heat or mechanical energy. If the power associated with a device and its operating voltage are known, other quantities can be easily calculated. For example, a common household lamp may be rated for 120 volts and 100 watts. Using Ohm s Law, the rated value of resistance of thelamp can be calculated. P= E 2 R which can be transposed to R= E 2 P R= (120 Volts) Watts R = 144 Ω Using the basic Ohm s Law formula, the amount of current flow for the 120 volt, 100 watt lamp can be calculated. I = E R I = 120 Volts 144 Ω I = Amps 67

68 Electrical Circuits 35 of 35 By comparison, a lamp rated for 120 volts and 75 watts has aresistance of 192 W and a current of amps would flow if the lamp had the rated voltage applied to it. R= R= E 2 P (120 Volts) 2 75 Watts R= 192 Ω I = I = E R 120 Volts 192 Ω I = Amps 68

69 Magnetism 1 of 4 The principles of magnetism are an integral part of electricity. In fact, magnetism can be used to produce electric current and vice versa. Types of Magnets When we think of a permanent magnet, we often envision a horse-shoe or bar magnet or a compass needle, but permanent magnets come in many shapes. However, all magnets have two characteristics. They attract iron and, if free to move (like the compass needle), a magnet will assume a north-south orientation. Magnetic Lines of Flux Every magnet has two poles, one north pole and one south pole. Invisible magnetic lines of flux leave the north pole and enter the south pole. While the lines of flux are invisible, the effects of magnetic fields can be made visible. When a sheet of paper is placed on a magnet and iron filings loosely scattered over it, the filings will arrange themselves along the invisible lines of flux. By drawing lines the way the iron filings have arranged themselves, the following picture is obtained. Broken lines indicate the paths of magnetic flux lines. The field lines exist outside and inside the magnet. The magnetic lines of flux always form closed loops. Magnetic lines of flux leave the north pole and enter the south pole, returning to the north pole through the magnet. 69

70 Magnetism 2 of 4 Interaction between Two Magnets When two magnets are brought together, the magnetic flux field around the magnets causes some form of interaction. Two unlike poles brought together cause the magnets to attract each other. Two like poles brought together cause the magnets to repel each other. 70

71 Magnetism 3 of 4 Electromagnetism Left-Hand Rule for Conductors An electromagnetic field is a magnetic field generated by current flow in a conductor. Every electric current generates a magnetic field and a relationship exists between the direction of current flow and the direction of the magnetic field. The left-hand rule for conductors demonstrates this relationship. If a current-carrying conductor is grasped with the left hand with the thumb pointing in the direction of electron flow, the fingers will point in the direction of the magnetic lines of flux. Current-Carrying Coil A coil of wire carrying a current, acts like a magnet. Individual loops of wire act as small magnets. The individual fields add together to form one magnet. The strength of the field can be increased by adding more turns to the coil, increasing the amount of current, or winding the coil around a material such asiron that conducts magnetic flux more easily than air. 71

72 Magnetism 4 of 4 Left-Hand Rule for Coils A left-hand rule exists for coils to determine the direction of the magnetic field. The fingers of the left hand are wrapped around the coil in the direction of electron flow. The thumb points to the north pole of the coil. Electromagnets An electromagnet is composed of a coil of wire wound arounda core. The core is made of soft iron or some other material that easily conducts magnetic lines of force. When current is passed through the coil, the core becomes magnetized. The ability to control the strength and direction of the magnetic force makes electromagnets useful. As with permanent magnets, opposite poles attract. An electromagnet can be made to control the strength of its field which controls the strength of the magnetic poles. A large variety of electrical devices such as motors, circuit breakers, contactors, relays and motor starters use electromagnetic principles. 72

73 Introduction to AC 1 of 56 The supply of current for electrical devices may come from a direct current (DC) source, or an alternating current (AC) source. In a direct current circuit, electrons flow continuously in one direction from the source of power through a conductor to a load and back to the source of power. Voltage in direct current remains constant. DC power sources include batteries and DC generators. By contrast, an AC generator makes electrons flow first in one direction then in another. In fact, an AC generator reverses its terminal polarities many times a second, causing current to change direction with each reversal. AC Sine Wave Alternating voltage and current vary continuously. The graphic representation for AC is a sine wave. A sine wave can represent current or voltage. There are two axes. The vertical axis represents the direction and magnitude of current or voltage. The horizontal axis represents time. + Direction 0 Time - Direction 73

74 Introduction to AC 2 of 56 When the waveform is above the time axis, current is flowing in one direction. This is referred to as the positive direction. When the waveform is below the time axis, current is flowing in the opposite direction. This is referred to as the negative direction. A sine wave moves through a complete rotation of 360 degrees, which is referred to as one cycle. Alternating current goes through many of these cycles each second. Single-Phase and Three-Phase AC Power Alternating current is divided into single-phase and three-three-phase AC Power phase types. Single-phase power is used for small electrical demands such as found in the home. Three-phase power is used where large blocks of power are required, such as found in commercial applications and industrial plants. Single-phase power is shown in the above illustration. Three-phase power, as shown in the following illustration, is a continuous series of three overlapping AC cycles. Each wave represents a phase, and is offset by 120 electrical degrees. + Phase 1 Phase 2 Phase

75 Introduction to AC 3 of 56 AC Generators Basic Generator A basic generator consists of a magnetic field, an armature,slip rings, brushes and a resistive load. In a commercial generator, the magnetic field is created by an electromagnet, but, for this simple generator, permanent magnets are used. An armature is any number of conductive wires wound in loops which rotates through the magnetic field. For simplicity, one loop is shown. When a conductor is moved through a magnetic field, a voltage is induced in the conductor. As the armature rotates through the magnetic field, a voltage is generated in the armature which causes current to flow. Slip rings are attached to the armature and rotate with it. Carbon brushes ride against the slip rings to conduct current from the armature to a resistive load. Pole Piece Magnetic Field Armature Brush R 1 Slip Ring Basic Generator Operation An armature rotates through the magnetic field. At an initial position of zero degrees, the armature conductors are moving parallel to the magnetic field and not cutting through any magnetic lines of flux. No voltage is induced. R 1 75

76 Introduction to AC 4 of 56 Generator Operation from Zero to 90 Degrees As the armature rotates from zero to 90 degrees, the conductors cut through more and more lines of flux, building up to a maximum induced voltage in the positive direction. 90 Degrees R 1 Generator Operation from 90 to 180 Degrees The armature continues to rotate from 90 to 180 degrees, cutting fewer lines of flux. The induced voltage decreases from a maximum positive value to zero. S 180 Degrees R 1 Generator Operation from 180 to 270 Degrees As the armature continues to rotate from 180 degrees to 270 degrees, the conductors cut more lines of flux, but in the opposite direction, and voltage is induced in the negative direction, building up to a maximum at 270 degrees. 270 Degrees R 1 76

77 Introduction to AC 5 of 56 Generator Operation from 270 to 360 Degrees As the armature continues to rotate from 270 to 360 degrees, induced voltage decreases from a maximum negative value to zero. This completes one cycle. The armature continues to rotate at a constant speed causing the cycle to repeat as long as the armature rotates. S 360 Degrees One Revolution R 1 77

78 Introduction to AC 6 of 56 Frequency The number of cycles per second of voltage induced in the armature is the frequency of the generator. If the armature rotates at a speed of 60 revolutions per second, the generated voltage will be 60 cycles per second. The recognized unit for frequency is hertz, abbreviated Hz 1 Hz is equal to 1 cycle per second. Power companies generate and distribute electricity at very low frequencies. The standard power line frequency in the United States and many other countries is 60 Hz. 50 Hz is also a common power line frequency used throughout the world. The following illustration shows 15 cycles in 1/4 second which is equivalent to 60 Hz. 1/4 Second Four-Pole AC Generator The frequency is the same as the number of rotations per second if the magnetic field is produced by only two poles. An increase in the number of poles, would cause an increase in the number of cycles completed in a revolution. A two-pole generator would complete one cycle per revolution and a four-pole generator would complete two cycles per revolution. An AC generator produces one cycle per revolution for each pair ofpoles. One Revolution R 1 78

79 Introduction to AC 7 of 56 Voltage and Current Peak Value Voltage and current in an AC circuit rise and fall over time in apattern referred to as a sine wave. The peak value of a sine wave occurs twice each cycle, once at the positive maximum value and once at the negative maximum value. + Peak Value 0 Time - Peak Value Peak-to-Peak Value The value of the voltage or current between the peak positive and peak negative values is called the peak-to-peak value. + 0 Time Peak-to-Peak Value - Instantaneous Value The instantaneous value is the value at any one point in the sine wave. + Instantaneous Value Time - 79

80 Introduction to AC 8 of 56 Calculating Instantaneous Voltage The voltage waveform produced as the armature rotates through 360 degrees rotation is called a sine wave because the instantaneous voltage (e) is related to the sine trigonometric function. The sine of an angle is represented symbolically as sin q, where the Greek letter theta (q) represents the angle. The sine curve is a graph of the following equation for values of q from 0 to 360 degrees: e = E peak x sin θ Instantaneous voltage is equal to the peak voltage times the sine of the angle of the generator armature. The sine value is obtained from trigonometric tables. The following table shows selected instantaneous values. Angle Si θ Angle Si θ 30Degrees Degrees Degrees 90Degrees 120Degrees 150Degrees Degrees Degrees Degrees Degrees Degrees Degrees 0 The following example illustrates instantaneous values at 90,150, and 240 degrees. The peak voltage is equal to 100 volts. By substituting the sine at the instantaneous angle value, the instantaneous voltage can be calculated = +100 Volts 150 = +50 Volts = Volts 80

81 Introduction to AC 9 of 56 Any instantaneous value can be calculated. For example: 240 e = 100 x e = volts Effective Value of an AC Sine Wave The instantaneous value of an alternating voltage and current are constantly changing values. However, there is a method for translating the varying values into an equivalent constant value, referred to at the effective value of voltage or current. This is also known as the RMS value. RMS is an abbreviation of the mathematical term root-mean-square. For example, a common voltage used in many applications is 120 volts, this is an RMS value, which is equal to the peak value times Peak Value Volts 0 - The effective value of AC is defined in terms of an equivalent heating effect when compared to DC. One RMS ampere of current flowing through a resistance will produce heat at the same rate as one DC ampere. It is sometimes necessary to know the peak value of an AC voltage or current when the RMS value is known. To calculate the peak value, multiply the effective value by For example, if the effective value is 100 volts, the peak value is 141 volts. 81

82 Introduction to AC 10 of 56 Inductance The circuits studied to this point have been resistive. Resistance and voltage are not the only circuit properties that effect current flow, however. Inductance is the property of an electric circuit that opposes any change in electric current. Resistance opposes current flow, inductance opposes change in current flow. Inductance is designated by the letter L.. The unit of measurement for inductance is the henry (h). Current Flow and Field Strength Current flow produces a magnetic field in a conductor. The amount of current determines the strength of the magnetic field. As current flow increases, field strength increases, and as current flow decreases, field strength decreases. 0 Degrees 30 Degrees 90 Degrees No Current Increasing Maximum Current Current Any change in current causes a corresponding change in the magnetic field surrounding the conductor. Current is constant for a regulated DC source, except when the circuit is turned on and off, or when there is a load change. However, alternating current is constantly changing, and inductance is continually opposing the change. A change in the magnetic field surrounding the conductor induces a voltage in the conductor. This self-induced voltage opposes the change in current. This is known as counter emf. This opposition causes a delay in the time it takes current to attain its new steady value. If current increases, inductance tries to hold it down. If current decreases, inductance tries to hold it up. Inductance is somewhat like mechanical inertia which must be overcome to get a mechanical object moving or to stop a mechanical object from moving. A vehicle, for example, takes a few moments to accelerate to a desired speed, or decelerate to a stop. Inductors All conductors have inductance, but inductors are coils of wire wound for a specific inductance. For some applications, inductors are wound around a metal core to further concentrate the inductance. The inductance of a coil is determined by the number of turns in the coil, the coil diameter and length, and the core material. An inductor is usually indicated symbolically on an electrical drawing as a curled line or a filled rectangle. 82

83 Introduction to AC 11 of 56 Simple Inductive Circuit In a resistive circuit, current change is considered instantaneous. If an inductor is used, the current does not change as quickly. For the purpose of explanation, a DC circuit is used here to describe the operation of an inductor. There will always be some amount of resistance and inductance in any circuit. The electrical wire used in the circuit has some resistance and inductance. In addition, inductors also have resistance. However, to simplify examples in this book, the resistance and inductance of the wiring and the resistance of inductors are not considered. In the following circuit, initially the switch is in position 2, and there is no current flowing through the ammeter (A). When the switch is moved to position 1, current will rise rapidly at first, then more slowly as the maximum value is approached. + _ 1 2 A R 1 L 1 Inductive Time Constant The time required for the current to rise to its maximum value is determined by the ratio of inductance (in henrys) to resistance (in ohms). This ratio is called the time constant of the inductive circuit. A time constant is the time (in seconds) required for the circuit current to rise to 63.2% of its maximum value. When the switch is closed in the previous circuit, current will begin to flow. During the first time constant current rises to 63.2% of its maximum value. During the second time constant, current rises to 63.2% of the remaining 36.8%, or a total of 86.4%. It takes about five time constants for current to reach its maximum value % 98.1% 94.9% 86.4% 63.2% First Time Second Time Third Time Fourth Time Fifth Time Constant Constant Constant Constant Constant 83

84 Introduction to AC 12 of 56 Similarly, when the switch in the previous circuit is returned to position 2, the magnetic field around the inductor will begin to collapse, returning stored energy to the circuit, and it will take about five time constants for current to reach zero % First Time Second Time Third Time Fourth Time Fifth Time Constant Constant Constant Constant Constant 36.8% 13.6% 5.1% 1.9% 0% Calculating the Time Constant of an Inductive Circuit The time constant is designated by the symbol t To determine the time constant of an. inductive circuit use one of the following formulas: τ (in seconds) = L (henrys) R (ohms) τ (in milliseconds) = τ (in microseconds) = L (millihenrys) R (ohms) L (microhenrys) R (ohms) In the following illustration, L 1 is equal to 15 millihenrys and R 1 is equal to 5 W. When the switch is closed, it will take 3 milliseconds for current to rise from zero to 63.2% of its maximum value and approximately 15 milliseconds for full current to be reached. + _ L 1 15 mh R 1 5 Ω τ= 15 mh 5 Ω τ = 3 milliseconds 84

85 Introduction to AC 13 of 56 Formula for Series Inductors The same rules for calculating total resistance can be applied to calculating total inductance. In the following circuit, an AC generator is used to supply electrical power to four inductors.total inductance of series inductors is calculated using the following formula: L t = L 1 + L 2 + L L n 2 mh 2 mh 1 mh 1 mh L 1 L 2 L 3 L 4 AC Generator L t = L 1 + L 2 + L 3 + L 4 L t = 2 mh + 2 mh + 1 mh + 1 mh L t = 6 mh Formula for Parallel Inductors In the following circuit, an AC generator is used to supply electrical power to three inductors. Total inductance of parallel inductors is calculated using the following formula: = + + L L 2 L 3 1 L t L n L 1 5 mh L 2 10 mh L 3 20 mh 1 L t = L t = 7 20 L t L t = 20 7 = 2.86 mh 85

86 Introduction to AC 14 of 56 Capacitance Capacitance and Capacitors Capacitance is a measure of a circuit s ability to store an electrical charge. A device manufactured to have a specific amount of capacitance is called a capacitor. A capacitor is made up of a pair of conductive plates separated by a thin layer of insulating material. Another name for the insulating material is dielectric material. When a voltage is applied to the plates, electrons are forced onto one plate. That plate has an excess of electrons while the other plate has a deficiency of electrons. The plate with an excess of electrons is negatively charged. The plate with a deficiency of electrons is positively charged. Negative Plate Dielectric Material Positive Plate Direct current cannot flow through the dielectric material because it is an insulator; however, the electric field created when the capacitor is charged is felt through the dielectric. Capacitors are rated for the amount of charge they can hold. The capacitance of a capacitor depends on the area of the plates, the distance between the plates, and type of dielectric material used. The unit of measurement for capacitance is farads (F). However, the farad is a large unit and capacitors are often rated in microfarads (mf) or picofarads (pf). Capacitor Circuit Symbols Capacitance is usually indicated symbolically on an electrical drawing by a combination of a straight line with a curved line, or two straight lines. 86

87 Introduction to AC 15 of 56 Simple Capacitive Circuit For the purpose of explanation, a DC circuit is used here to describe the operation of an capacitor. The resistance of wiring and stray values of capacitance found in any circuit are not considered in this explanation. In a resistive circuit, voltage change is instantaneous. In a circuit with a resistor and capacitor in series, the voltage across the capacitor does not change as quickly. In the following circuit, initially the switch is in position 2 and no voltage is measured by the voltmeter (V). When the switch is moved to position 1, voltage across the capacitor will rise rapidly at first, then more slowly as the maximum value is approached. 1 + _ C R 1 V Capacitive Time Constant The time required for voltage across the capacitor in this simple circuit to rise to its maximum value is determined by the product of capacitance, in farads, times resistance, in ohms. This product is the time constant of a capacitive circuit. The time constant gives the time in seconds required for voltage across the capacitor to reach 63.2% of its maximum value. When the switch in the previous circuit is moved to position 1, the voltage measured by the voltmeter will begin to rise. During the first time constant, voltage will rise to 63.2% of its maximum value. During the second time constant, voltage will rise to 63.2% of the remaining 36.8%, or a total of 86.4%. It takes about five time constants for voltage across the capacitor to reach its maximum value % 98.1% 94.9% 86.4% 63.2% First Time Second Time Third Time Fourth Time Fifth Time Constant Constant Constant Constant Constant 87

88 Introduction to AC 16 of 56 The voltage across the capacitor will reach its maximum value when it is equal to the supply voltage. At that point, current flow will reach zero. When the switch in the previous circuit is returned to position 2, the capacitor will retain its charge because there is no path for current flow. When the switch is moved to position 3, the capacitor will begin to discharge, and it will take about five time constants for the voltage across the capacitor and the current through the resistor to reach zero % First Time Second Time Third Time Fourth Time Fifth Time Constant Constant Constant Constant Constant 36.8% 13.6% 5.1% 1.9% 0% Calculating the Time Constant of a Capacitive Circuit To determine the time constant of a capacitive circuit, use one of the following formulas: τ (in seconds) = R (megohms) x C (microfarads) τ (in microseconds) = R (megohms) x C (picofarads) τ (in microseconds) = R (ohms) x C (microfarads) In the following illustration, C 1 is equal to 2 mf, and R 1 is equal to 10 W. When the switch is closed, it will take 20 microseconds for voltage across the capacitor to rise from zero to 63.2% of its maximum value. It will take about five time constants, 100 microseconds, for this voltage to rise to its maximum value. + _ C 1 2µF R 1 10 Ω V τ = RC τ = 2µF x 10 Ω τ = 20 microseconds 88

89 Introduction to AC 17 of 56 Formula for Series Capacitors Connecting capacitors in series decreases total capacitance. The formula for series capacitors is similar to the formula for parallel resistors. In the following circuit, an AC generator supplies electrical power to three capacitors. Total capacitance is calculated using the following formula: 5µF 10µF 20µF C 1 C 2 C 3 Formula for Parallel Capacitors Adding capacitors in parallel increases circuit capacitance. In the following circuit, an AC generator is used to supply electrical power to three capacitors. Total capacitance is calculated usingthe following formula: C t = C 1 + C 2 + C C n C 1 C 2 C 3 10 µf 10 µf 20 µf C t = 5 µf + 10 µf + 20 µf C t = 35 µf 89

90 Introduction to AC 18 of 56 Inductive and Capacitive Reactance In a purely resistive AC circuit, resistance is the only opposition to current flow. In an AC circuit with only inductance, capacitance, or both inductance and capacitance, but no resistance, opposition to current flow is called reactance, designated. by the symbol X. Just like Total opposition to current flow in an AC circuit that contains both reactance and resistance is called impedance, designated by the symbol Z resistance, reactance and impedance are expressed in ohms. Inductive Reactance Inductance only affects current flow when the current is changing. Inductance produces a self-induced voltage (counter emf) that opposes changes in current. In an AC circuit, current is changing constantly. Inductance in an AC circuit, therefore, causes a continual opposition. This opposition to current flow is called inductive reactance and is designated by the symbol X L. Inductive reactance is proportional to both the inductance and the frequency applied. The formula for inductive reactance is: X L = 2πfL X L = 2 x 3.14 x frequency x inductance For a 60 hertz circuit containing a 10 mh inductor, the inductive reactance is: X L = 2πfL X L = 2 x 3.14 x 60 x X L = Ω For this example, the resistance is zero so the impedance is equal to the reactance. If the voltage is known, Ohm s Law can be used to calculate the current. If, for example, the voltage is 10 volts, the current is calculated as follows; I= I = E Z I = 2.65 Amps 90

91 Introduction to AC 19 of 56 Phase Relationship between Current and Voltage in an Inductive Circuit In a purely resistive circuit, current and voltage rise and fall at the same time. They are said to be in phase. In this circuit, there is no inductance. Resistance and impedance are the same. + Voltage Current 0 _ In a purely inductive circuit, current lags behind voltage by 90 degrees. Current and voltage are said to be out of phase In this circuit, impedance and inductive reactance are the same.. 90 Degrees + Voltage Current 0 _ In a circuit with both resistance and inductive reactance, AC current will lag the voltage by more than 0 degrees and less than 90 degrees. The exact amount of lag will depend upon the relative amounts of resistance and inductive reactance.the more resistive a circuit is, the closer it is to being in phase. The more reactive a circuit is, the more out of phase it is. In the following illustration, resistance and inductive reactance are equal. Current lags voltage by 45 degrees Degrees Voltage X L = 10 Ω Current 0 R = 10 Ω _ 91

92 Introduction to AC 20 of 56 Calculating Impedance in an Inductive Circuit When working with a circuit containing elements of inductance, capacitance, and resistance, impedance must be calculated. Because electrical concepts deal with trigonometric functions, this is not a simple matter of subtraction and addition. The following formula is used to calculate impedance in a circuit with resistance and inductive reactance: Z = R 2 + X L 2 In the previous example, resistance and inductive reactance are each 10 ohms. Impedance for this circuit can be calculated as follows: Z = Z = Z = Ω Capacitive Reactance Capacitance also opposes AC current flow. Capacitive reactance is designated by the symbol X C. The larger the capacitor, the smaller the capacitive reactance. Current flow in a capacitive AC circuit is also dependent on frequency. The following formula is used to calculate capacitive reactance: X C = 1 2πfC 92

93 Introduction to AC 21 of 56 The capacitive reactance for a 60 hertz circuit with a 10 microfarad capacitor is calculated as follows: X C = 1 2πfC X C = 1 2 x 3.14 x 60 x X C = Ω For this example, the resistance is zero so the impedance is equal to the reactance. If the voltage is known, Ohm s Law can be used to calculate the current. If, for example, the voltage is 10 volts, the current is calculated as follows: I = I = E Z I = Amps Phase Relationship between Current and Voltage The phase relationship between current and voltage are opposite to the phase relationship of an inductive circuit. In a purely capacitive circuit, current leads voltage by 90 degrees Degrees Voltage Current 0 _ 93

94 Introduction to AC 22 of 56 In a circuit with both resistance and capacitive reactance, AC current will lead the voltage by more than 0 degrees and less than 90 degrees. The exact amount of lead will depend upon the relative amounts of resistance and capacitive reactance. The more resistive a circuit is, the closer it is to being in phase.the more reactive a circuit is, the more out of phase it is. In the following illustration, resistance and capacitive reactance are equal. Current leads voltage by 45 degrees Degrees Voltage X C = 10 Ω Current 0 R = 10 Ω _ Calculating Impedance in a Capacitive Circuit The following formula is used to calculate impedance in acircuit with resistance and capacitive reactance: Z = R 2 + X C 2 In the previous example, resistance and capacitive reactance are each 10 ohms. Impedance for this circuit can be calculated as follows: Z= Z= Z = Ω Capacitive Reactance Capacitance also opposes AC current flow. Capacitive reactance is designated by the symbol X C. The larger the capacitor, the smaller the capacitive reactance. Current flow in a capacitive AC circuit is also dependent on frequency. The following formula is used to calculate capacitive reactance: X C 1 2πfC 94

95 Introduction to AC 23 of 56 The capacitive reactance for a 60 hertz circuit with a 10 microfarad capacitor is calculated as follows: X C = 1 2πfC X C = 1 2 x 3.14 x 60 x X C = Ω For this example, the resistance is zero so the impedance is equal to the reactance. If the voltage is known, Ohm s Law can be used to calculate the current. If, for example, the voltage is 10 volts, the current is calculated as follows: I= I = E Z I = Amps Phase Relationship between Current and Voltage The phase relationship between current and voltage are opposite to the phase relationship of an inductive circuit. In a purely capacitive circuit, current leads voltage by 90 degrees Degrees Voltage Current 0 _ In a circuit with both resistance and capacitive reactance, AC current will lead the voltage by more than 0 degrees and less than 90 degrees. The exact amount of lead will depend upon the relative amounts of resistance and capacitive reactance. The more resistive a circuit is, the closer it is to being in phase.the more reactive a circuit is, the more out of phase it is. 95

96 Introduction to AC 24 of 56 In the following illustration, resistance and capacitive reactance are equal. Current leads voltage by 45 degrees Degrees Voltage X C = 10 Ω Current 0 R = 10 Ω _ Calculating Impedance in a Capacitive Circuit The following formula is used to calculate impedance in a circuit with resistance and capacitive reactance: Z = R 2 + X C 2 In the previous example, resistance and capacitive reactance are each 10 ohms. Impedance for this circuit can be calculated as follows: Z= Z= Z = Ω 96

97 Introduction to AC 25 of 56 Series R-L-C Circuit Circuits often contain elements of resistance, inductance, and capacitance. In an inductive AC circuit, current lags voltage by 90 degrees. In a capacitive AC circuit, current leads voltage by 90 degrees. When represented in vector form, inductive and capacitive reactance are 180 degrees apart. As a result, the net reactance is determined by taking the difference between the two quantities. X L X C R An AC circuit is: Resistive if X L and X C are equal Inductive if X L is greater than X C Capacitive if X C is greater than X L Calculating Total Impedance in a Series R-L -C Circuit The following formula is used to calculate total impedance of a circuit containing resistance, capacitance, and inductance: Z = R 2 + (X L - X C )2 In the case where inductive reactance is greater than capacitive reactance, subtracting X C from X L results in a positive number. The positive phase angle is an indicator that the net circuit reactance is inductive, and current lags voltage. In the case where capacitive reactance is greater than inductive reactance, subtracting X C from X L results in a negative number. The negative phase angle is an indicator that the net circuit reactance is capacitive and current leads voltage. In either case, the value squared will result in a positive number. 97

98 Introduction to AC 26 of 56 Calculating Reactance and Impedance in a Series R-L -C Circuit In the following 120 volt, 60 hertz circuit, resistance is 1000 W, inductance is 5 mh, and capacitance is 2 mf. The following example shows the method for calculating impedance for this circuit. R = 1000 Ω L = 5 C = 2 X L = 2πfL X L = 6.28 x 60 x X L = Ω X C = X C = 1 2πfC x 60 x X C = 1,327 Ω Z = Z = Z = Z = Z = R 2 )2 + (X L - X C ( ,327 )2 1,000,000 + ( - 1, )2 1,000, ,755, ,755, Z = 1,660.1 Ω Given that the applied voltage is 120 volts, current can be calculated as follows: I= E Z I = 120 1,660.1 I = Amps 98

99 Introduction to AC 27 of 56 Parallel R-L-C Circuit Calculating Impedance in a Parallel R-L -C Circuit Total impedance (Z t ) can be calculated in a parallel R-L-C circuit if values of resistance and reactance are known. One method of calculating impedance involves first calculating total current, then using the following formula: Z t = E t I t Total current is the vector sum of current flowing through the resistance plus, the difference between inductive current and capacitive current. This is expressed in the following formula: I t = I R 2 + (I C - I L )2 In the following 120 volt, 60 hertz circuit, capacitive reactance is 25 W, inductive reactance is 50 W, and resistance is 1000 W. A simple application of Ohm s Law will find the branch currents. Remember, voltage is constant throughout a parallel circuit. 120 V R = 1000Ω X L = 50 Ω X C = 25 Ω I R = E R I L = E X L I C = E X C I R = I L = 120 I C = I R = 0.12 Amps I L = 2.4 Amps I C = 4.8 Amps Once the branch currents are known, total current can be calculated. I t = I t = I t = I t = I t = I 2 )2 R + (I C - I L ( ) Amps 99

100 Introduction to AC 28 of 56 Impedance can then be calculated as follows: Z t = E I t 120 Z t = Z t = Ω 100

101 Introduction to AC 29 of 56 Resistive Loads In AC and DC circuits containing purely resistive loads, like lights and heaters, Ohm's Law can be used to compute current, voltage and resistance in the circuit. Ohm's Law V = A x R where: V = voltage (volts) A = current (amps) R = resistance (ohms) For example, a current of 2 amps flowing through a resistance of 3 ohms is said to produce a voltage "across" that resistance of 6 volts. Example: A wire with a resistance of 10 ohm's is connected to a 9-volt battery. To determine the current flow in the wire, use ohm's law and divide 9 volts by 10 ohm's. The current flow in the wire equals 0.9 amps. Replace the 9-volt battery with a 1.5 volt battery. Using the same wire the calculated current flow is 1.5 volts divided by 10 ohms, which produces a current flow of 0.15 amps. The larger voltage results in more pressure to force more current through the given resistance of 10 ohms. 101

102 Introduction to AC 30 of 56 Reactive Loads The current and voltage in AC circuits that contain inductors, capacitors, or both, behave much differently than in a purely resistive circuit. We cannot measure resistance directly in these circuits. We measure what's known as "reactance." Inductors and capacitors react to current flow in ways that oppose, or impede, changes in the flow of current, but they do it in a different fashion than a pure resistor. Each device has its own characteristics which creates an impeding force. Whenever there is an inductor, or coil, in a circuit, we call its impeding force to current flow "inductive reactance." For a circuit with a capacitor, the impeding force is called "capacitive reactance." We treat both resistance and reactance as impedance, that is, any opposition to changes in the flow of current. 102

103 Introduction to AC 31 of 5 Inductive Reactance An inductor is simply a coil of wire. When current passes through the coil, an electrical field is generated. The field has been "induced." The bigger the coil or the greater the number of turns, the greater the induced field. This phenomenon is called "inductance." Inductive reactance is the name given to the opposition to a changing current flow. This impedance is measured in ohms, just like resistance. In inductors, voltage leads current by 90 degrees. The formula for calculating the inductive reactance of a coil is: inductive reactance, or X L, is the product of 2 times p (pi), or 6.28, the frequency of the ac current, in hertz, and the inductance of the coil, in henries. X L =2 p x f x L. Where: X L = inductive reactance measured in ohms 2 = a constant (2 x = 6.28) f = the AC frequency of the electrical supply in hertz L = the inductance value of the coil in henries. 103

104 Introduction to AC 32 of 56 Example: A coil with an inductance of 0.3 henries is connected to a 120 volt, 60-hertz AC circuit. To determine the current flow in the wire, first find the inductive reactance of the coil. The inductive reactance equals 6.28 times 60 hertz times 0.3 henries, which equals ohms. Now use Ohm's Law and divide 120 volts by ohms, which equals 1.06 amps. Remember the current will lag the voltage by 90 degrees so the current flow is 90 degrees behind the voltage sine wave. 104

105 Introduction to AC 33 of 56 Capacitive Reactance In the very first instant that current flows, there is a surge of electrons to one plate. They are following the natural laws of attraction. Once this plate becomes saturated, the plate is fully charged. The amount of charging a capacitor can achieve is called capacitance and is measured in Farads, or microfarads, µf. The opposition to the flow of alternating current due to capacitance is called "capacitive reactance." It is measured in ohms just like resistance and inductive reactance. In capacitors, the current leads voltage by 90 degrees The formula for calculating the Capacitive Reactance, or impedance of a capacitor is: Capacitive reactance, denoted as x sub c (X C ), is equal to the constant one million (or 106) divided by the product of 2 p ( or 6.28) times frequency times the capacitance. 105

106 Introduction to AC 34 of 56 Where: X C = Capacitive reactance measured in ohms. f = is the AC frequency in Hertz. C = is the capacitance in microfarads. Example: A capacitor with a capacitance of microfarads is connected to a 120 volt, 60 hertz AC circuit. To determine the current flow in the wire, first find the capacitive reactance of the capacitor. The capacitive reactance equals 1,000,000 divided by 6.28 times 60 hertz times microfarads which equals 25 ohms. Now use ohm's law and divide 120 volts by 25 ohms which equals 4.8 amps. Remember the current will lead the voltage by 90 degrees so the current flow is 90 degrees ahead of the voltage sine wave. 106

107 Introduction to AC 35 of 56 Combinations-Resistive & Reactive A resistive circuit opposes current directly. A reactive circuit transforms current and creates opposition to current flow in the process. For example, when current flows through an inductor, each winding creates an electromagnetic field. These electromagnetic fields interact with one another, creating an overall induced field that we can observe as measurable voltage. This interchange of energies between the windings of the coil creates an opposition to the flow of current called "inductive reactance." Similarly, a capacitive circuit will create an opposition to current flow. The capacitor reacts to current flow and creates an electric field that is measurable as voltage. The resultant opposition to current flow is called "capacitive reactance." When a circuit has a combination of these element, resistors, capacitors, and inductors, the calculation of the total impedance to current flow is calculated by the formula: Where: Z = total impedance in ohms R = resistance of the circuit in ohms XC = Capacitive reactance of circuit in ohms XL= Inductive reactance of circuit in ohms Example: Find the current flowing to an electric motor operated at 240 volts that has an electrical resistance of 80 ohms, an inductive reactance from the motor windings of 90 ohms, and a capacitive reactance from a connected capacitor of 30 ohms. You cannot find the total impedance by adding the resistance and reactance together since they are not in phase. Use the equation for calculating the total impedance. The square root of 80 squared + ( 30 squared - 90 squared equals a total impedance of 100 ohms. Use ohms law to find the current flow by dividing 240 volts by 100 ohms and the current flow equals 2.4 amps. 107

108 Introduction to AC 36 of 56 Voltage Drop Definition Wires carrying current always have inherent resistance, or impedance, to current flow. Voltage drop is defined as the amount of voltage loss that occurs through all or part of a circuit due to impedance. A common analogy used to explain voltage, current and voltage drop is a garden hose. Voltage is analogous to the water pressure supplied to the hose. Current is analogous to the water flowing through the hose. And the inherent resistance of the hose is determined by the type and size of the hose - just like the type and size of an electrical wire determines its resistance. Excessive voltage drop in a circuit can cause lights to flicker or burn dimly, heaters to heat poorly, and motors to run hotter than normal and burn out. This condition causes the load to work harder with less voltage pushing the current. The National Electrical Code recommends limiting the voltage drop from the breaker box to the farthest outlet for power, heating, or lighting to 3 percent of the circuit voltage. This is done by selecting the right size of wire and is covered in more detail under "Voltage Drop Tables." If the circuit voltage is 115 volts, then 3 percent of 115 volts is 3.5 volts. This means that voltage lost from the wires in the circuit should not exceed 3.5 volts and the outlet should still have or volts to supply. Since most appliances require an extension cord to plug into an outlet, some voltage drop will occur in the extension cord as well. Some motors will not run correctly, and could even burn up, if the voltage at the motor falls too low. 108

109 Introduction to AC 37 of 56 Causes Resistance in the conductor or connections leading to the electrical load causes voltage drop. There are many causes of resistance in the conductor path. There are four fundamental causes of voltage drop: 1. Material - Copper is a better conductor than aluminum and will have less voltage drop than aluminum for a given length and wire size. 2. Wire Size - Larger wire sizes (diameter) will have less voltage drop than smaller wire sizes (diameters) of the same length. 3. Wire Length - Shorter wires will have less voltage drop than longer wires for the same wire size (diameter). 4. Current Being Carried - Voltage drop increases on a wire with an increase in the current flowing through the wire. Voltage Drop Limits The National Electric Code, Section (a), recommends limiting the voltage drop to 3% on a branch circuit to the farthest output for power, heating or lighting. The fine-print note to NEC Section 215-2(b) recommends limiting voltage drop on feeder conductors and the branch circuit to the farthest outlet should not exceed 5%. 109

110 Introduction to AC 38 of 56 Measuring Voltage Drop Voltage drop under typical operating conditions can easily be measured. If excessive voltage drop is suspected in a circuit, follow these steps: 1. Turn on all the electrical equipment which is normally in operation at the time excessive voltage drop is suspected to be a problem. 2. Measure the voltage at theservice panel that supplies the circuit in question. It should be 234 volts or more between hot conductors and 117 volts or more between hot and neutral of a 120/240 volt, single phase system (maximum of 3% voltage drop on service drop). If not, call the utility. 3. Measure the voltage at the service panel board with the problem circuit. It should be 227 volts or more between hot conductors and volts or more between hot and neutral of a 120/240-volt, single phase system (maximum of 3% voltage drop on feeders, 2% maximum recommended). 4. Measure the voltage at the problem piece of equipment. It should be 220 volts or greater between hot conductors of a 240-volt circuit or 110 volts or greater between hot and neutral of a 120-volt circuit (maximum of 3% voltage drop on the branch circuit back to the service panel board). Results If a problem with the voltage exists at the main service - call the utility. If voltage at main service was fine but low at service panel - check feeder from main service for problems. If voltage at service panel was fine but low at outlet or controller, check branch circuit for problems. Remember A 480 volt circuit should be a minimum of 480 volts at the transformer secondary and a minimum of 440 at the equipment outlet or controller. A 240 volt circuit should be a minimum of 240 volts at the transformer secondary and a minimum of 220 at the equipment outlet or controller. A 120 volt circuit should be a minimum of 120 volts at the transformer secondary and a minimum of 110 at the equipment outlet or controller. 110

111 Introduction to AC 39 of 56 Voltage Drop Formulas The size of conductor for any voltage drop can be determined readily by using mathematical formulas which calculate the voltage drop for given wires sizes, lengths, and types under load. These formulas may be used to determine any one of the four factors affecting voltage drop if the other three factors are known. Keep in mind there are separate formulas for single and three phase, and for copper and aluminum. Formulas For Copper Single Phase Circuits: Where: CM = Area of conductor in circular mills A = Single Phase line current in Amperes L = Length (one-way) of circuit in feet V = Voltage Drop (Volts) For Copper Three Phase Circuits: Where A3 = average three phase line current in amperes. For sizes of aluminum conductors, these formulas may be used and the results multiplied by 1.6 or the formulas may be modified as follows: Find the size of copper wire to carry a load of 40 amperes at 240 volts a distance of 500 feet with 2% voltage drop. Use the formula: Example 1 How far can No. 6 copper wire be used to carry a load of 30 amperes at 240 volts and keep within 1% voltage drop? 111

112 Introduction to AC 40 of 56 Voltage Flicker Starting motors with large loads causes voltage drop which is often evidenced by flickering lights. This flicker is objectionable only when the magnitude and frequency of the voltage drop exceed certain thresholds. This threshold of objection is shown on a Voltage-Flicker curve. If the magnitude of the voltage drop and the frequency of occurrence lie below the threshold of perception, people generally do not notice any flicker. Example: A five horsepower three phase motor is supplied by a 208 Volt feeder which also supplies 120 Volt lighting circuits. Assume that the feeder resistance = 0.06 ohms. For a 5 horsepower motor, the Full Load Amps (FLA) = 16 amps. The motor starting current = 16 amps x 6 = 96 amps. V drop = starting current x feeder resistance = 96 amps x 0.06 ohms = 6 Volts. The 6 Volt drop along the feeder is equal to 5% of the voltage on the 120 V lighting circuit, and it causes a noticeable flicker. If the motor is started once every hour, then the representative point, on the flicker curve is in the objectionable range. To correct this problem, supply the lighting circuits from a separate feeder, or reduce the voltage drop along the feeder. A reduced voltage starter often presents a very cost effective solution. Voltage Drop Tables A number of electrical reference books contain voltage drop tables which allow the correct wire size to be determined if the desired voltage drop limit, maximum current, and distance from the source to the load are known. These tables are very convenient and do not require the use of the mathematical formulas. They do require you to find the appropriate voltage, phase, conductor material, and voltage drop table in order to determine the correct answer. This requires a large number of tables. To use the tables, find the amperage in the left column and the length of run or distance between the source and load along the top of the table. If your number is between two of the table numbers, use the higher value. The row and column where they intersect on the table is the recommended wire size that will keep voltage drop within acceptable limits. Using Voltage Drop Tables Wire Type: There are different tables for Copper and Aluminum wire. + Amperage: The maximum amperage this table can be used for. D Voltage: The voltage rating for this table. There are different tables for each of the standard servicevoltages. Phase: There are different tables for Single and Three Phase power. l Percent Voltage Drop: The allowable voltage drop limits for table. There are tables with other values. Minimum Size of Conductor: * Copper, + Up to 200 Amperes, D Volts, 0 Single Phase, l Based on 3% Voltage Drop 112

113 Introduction to AC 41 of 56 Example: Find the size of copper wire to carry a load of 40 amperes at 120 volts a distance of 500 feet with 3% voltage drop. Use the Table: Note the column heading of the table: Copper, Single Phase, 120 volts, 3% voltage drop. Follow the first column "amperage" down to 40 amps. Find the 500 feet column in the table under length of run. Where the 40 amp row and 500 foot column cross, the wire size can be found. In this case, a 00 or 2 ought copper wire. This method of finding the correct wire size is simple when you have the right table. Procedure: Find the amperage in the left column and the length of run along the top of the table (if between two of the table values go to the higher value). Where the two intersect on the table is the recommended wire size that will keep voltage drop within acceptable limits. Compare the recommended value on the right side of the table to the value shown on left side (minimum NEC requirements for the insulation type to be used) and use the larger size. 113

114 Introduction to AC 42 of 56 Series Circuits - Resistance There are three rules governing the simple series circuits of resistive elements. They are: 1. The current flow is the same through each element of the series circuit. 2. The combined resistance of the various loads in series is the sum of the separate resistances. 3. The voltage across the source or power supply is equal to the sum of the voltage drops across the separate loads in series. Solution: We can now determine the current flow through and voltage drop across each element of the circuit shown. Recalling that Ohm's Law can be applied to the whole circuit or any part of the circuit, we can determine the current flow in the circuit. First calculating the total resistance using Rule 2, Then applying Ohm's Law for the total circuit, we find Recalling Rule 1, we know the current in each resistor is We can find the voltage drop for each resistor by again applying Ohm's Law, this time to each of the resistors. Note we can check our calculations by using Rule 3: 114

115 Introduction to AC 43 of 56 Series Circuits - Inductance Inductance is the characteristic of an electrical circuit that opposes the starting, stopping, or changing of current flow. it really begins to show when you wrap wire into a coil where the current produces a strong magnetic field. Inductance is measured in units called "henries." The amount of actual power dissipation with current flow is called inductive reactance and is measured in units of ohms. The following formula is used to calculate the inductive reactance: Where; f = frequency in hertz (60 cycles in the US AC circuits) L = inductance in henries p = Voltage across and current through an inductor are described by Ohm's Law for inductors: Find the current flow in the circuit with the pure inductor shown at right: First finding the inductive reactance as: then applying Ohm's Law: 115

116 Introduction to AC 44 of 56 The total reactance of several inductances in series can be obtained by the following rule. For series circuits: For a series circuit with 3 inductive reactances of 10, 20, and 30 ohms, the total inductive reactance is calculated as follows: If the circuit voltage is 120 volts, then ohms law is used to find the total current flow in the circuit. 2 amps of current flows through each inductance in the series circuit. 116

117 Introduction to AC 45 of 56 Series Circuits - Capacitance Capacitors are essentially "voltage storage devices" commonly found in controls, motors and welding circuits, and many other places. They are "charged up" by another source and hold that charge even when the circuit is open, unlike typical resistance loads that lose their voltage as soon as the current goes to zero. Capacitors are essentially "static electricity storage devices" just as you are when you walk across a rug dragging your feet on a dry winter day. You discharge your capacitance when you touch a conductor such as a door knob. The simplest capacitor consists of two plates separated by a dielectric or non-conductive material. Materials such as air, paper, mica, and oil can be used as dielectrics. Capacitance is the amount of electrical charge that a capacitor can store for each volt of applied potential. Capacitance is measured in units of farads. The farad is a very large unit of capacitance. Practical devices are more often rated in terms of microfarads, where micro means 1 millionth. Current flow in a circuit "sees" a capacitor in an AC circuit similar to a resistor. The amount of opposition to current flow is quantified as the capacitive reactance. Capacitive reactance is measured in units of ohms and can be calculated from the frequency of the source and capacitance using the following formula: where; f = frequency in hertz C = capacitance in microfarads Ohm's law can be applied in the form E = IX C for capacitors. EXAMPLE ac Capacitor Current Find the current flow in the circuit shown. Find the capacitive reactance. 117

118 Introduction to AC 46 of 56 Applying Ohm's Law Therefore, the capacitor is an energy storing element and not a dissipative one like a resistor. Total capacitance of a number of capacitors in series can be found using the following rule: The total capacitive reactance of 3 capacitors in series with capacitive reactances of 10, 20 and 30 ohms would be calculated by: 118

119 Introduction to AC 47 of 56 Series Circuits Combinations Ohm's Law is used to solve circuit problems which may contain all three elements: resistors, inductors, and capacitors. These circuits are sometimes called R LC circuits using the symbol R for resistance, L for inductance and C for capacitance. The general form of Ohm's Law applied to R LC circuits states: Voltage = Current x Total Impedance, or V = A times R where; A = current in amps R = total impedance in ohms Total impedance is the result of combining the impedances of the resistance and inductive and capacitive reactance components of the circuit. This is not done by simple addition. EXAMPLE Series R LC AC Circuit Determine the total impedance and current flow for the circuit shown. Obtaining the total impedance through vector addition and power factor from the angle between total impedance and resistance: Determine the current flow. the power factor of the circuit can also be found by dividing the resistive component by the reactive component in the circuit. 119

120 Introduction to AC 48 of 56 Parallel Circuits - Resistive A simple parallel circuit is made up of a source and resistors connected in parallel across the source by "ideal conductors." This diagram shows two ways of drawing the same circuit. There are three rules governing simple parallel circuits of resistive elements: 1. Voltage across each resistor is the same as the voltage across the parallel combination. 2. The current flowing through the parallel combination is the sum of the current in the separate branches. 3. Summing resistance of a parallel circuit can be stated as follows: The reciprocal of the total resistance is equal to the sum of the reciprocals of each of the individual resistances. Kirchoff's Current Law which states that the sum of the current leaving a junction must equal the sum of the currents entering a junction. This can be expressed for the example as: 120

121 Introduction to AC 49 of 56 The total resistance in ohms is calculated by multiplying the resistances and dividing by the sum of the resistances. If the voltage produced by the source is 240 volts, then each load has 240 volts applied to it. Ohms Law allows us to calculate the total current (amps) flowing in the circuit. Since 8 amps is the total current flow through the circuit, the current through each load is equal to the circuit voltage divided by its resistance. 121

122 Introduction to AC 50 of 56 Parallel Circuits - Inductive Inductance is measured in units of "henries" and the amount of opposition to current flow the inductive reactance is measured in units of "ohms" The following formula is used to calculate the inductive reactance: f = frequency in hertz L = inductance in henries p = Voltage across and current through an inductor are described by Ohm's Law for inductors: Find the current flow in the circuit with the pure inductor shown. First finding the inductive reactance as: The total reactance of several inductances in parallel can be obtained by the following rule. For parallel circuits: For a parallel circuit with 3 inductive reactances of 10, 20, and 30 ohms, the total inductive reactance is calculated as follows: The total current flowing in the parallel inductive circuit is: 122

123 Introduction to AC 51 of 56 Parallel Circuits - Capacitive Capacitance is the amount of electrical charge that a capacitor can store for each volt of applied potential. Capacitance is measured in units of farads. The farad is a very large unit of capacitance. Practical devices are more often rated in terms of microfarads, where micro means 1 millionth. A capacitor in an ac circuit limits the current flow in a similar manner to a resistor. The amount of opposition to current flow is quantified as the capacitive reactance. Capacitive reactance is measured in units of ohms and can be calculated from the frequency of the source and capacitance using the following formula: where; f = frequency in hertz C = capacitance in microfarads EXAMPLE AC Capacitor Current Find the current flow in the circuit shown. Find the capacitive reactance. 123

124 Introduction to AC 52 of 56 The capacitor is an energy storing element and not a dissipative one like a resistor. Total capacitance of a number of capacitors in parallel can be found using the following rule: Parallel: C T = C 1 + C 2 + C The total capacitive reactance of a 120 volt circuit of 3 capacitors in parallel with capacitive reactances of 10, 20 and 30 ohms would be calculated by: T = C 1 + C 2 + C 3 = 10 ohms + 20 ohms + 30 ohms = 60 ohms The total current flowing in the parallel capacitive circuit is: 124

125 Introduction to AC 53 of 56 Parallel Circuits - Combinations Ohm's Law is used to solve circuit problems, which may contain all three elements: resistors, inductors, and capacitors. These circuits are sometimes called R LC circuits with R for resistance, L for inductance and C for capacitance. The general form of Ohm's Law applied to R LC circuits states: Voltage = Current x Total Impedance or E = I times R where; I = current in amps R = total impedance in ohms Total impedance is the result of combining impedances of the resistive, capacitive and inductive components of the circuit. However, remember, the resistance, inductance and capacitance are not in phase so they must be added vectorially. They cannot be added directly. When a circuit contains resistors, capacitors, and inductors in parallel, total current flow is obtained by vector addition of current flow for each element. Currents in this case add vectorially in the same orientation as the voltage in the series circuit. In this case, the angle between the current due to pure resistance, IR, and the total or source current, IS, is the phase shift angle, for the circuit. 125

126 Introduction to AC 54 of 56 For parallel R LC circuits, impedances do not add vectorially as in the series case. Total impedance must be obtained by dividing source voltage by total current. EXAMPLE 3.11 Parallel Combination R LC Circuit For the circuit shown, determine the current flow in each element, the source current, the true power, and the apparent power. Use Ohm's Law for each element of the parallel combination. (Note the voltage across each element is the same for parallel connected loads.) Determine the source current and phase angle by vector addition. To find the power factor, divide the amps flowing through the resistance by the total current in amps from the source: 126

127 Introduction to AC 55 of 56 Power and Power Factor in an AC Circuit Power consumed by a resistor is dissipated in heat and not returned to the source. This is called true power because it is the rate at which energy is used. Current in an AC circuit rises to peak values and diminishes to zero many times a second. The energy stored in the magnetic field of an inductor, or plates of a capacitor, is returned to the source when current changes direction. Although reactive components do not consume energy, they do increase the amount of energy that must be generated to do the same amount of work. The rate at which this non-working energy must be generated is called reactive power. If voltage and current are 90 degrees out of phase, as would be the case in a purely capacitive or purely inductive circuit, the average value of true power is equal to zero. There are high positive and negative peak values of power, but when added together the result is zero. Power in an AC circuit is the vector sum of true power and reactive power. This is called apparent power. True power is equal to apparent power in a purely resistive circuit because voltage and current are in phase. Voltage and current are also in phase in a circuit containing equal values of inductive reactance and capacitive reactance. In most circuits, however, apparent power is composed of both true power and reactive power. True Power and Apparent Power Formulas The formula for apparent power is: P = EI Apparent power is measured in volt-amps (VA). True power is calculated from another trigonometric function, the cosine of the phase angle(cosq). The formula for true power is: P = EI cos θ In a purely resistive circuit, current and voltage are in phase. There is a zero degree angle displacement between current and voltage. The cosine of zero is one. Multiplying a value by one does not change the value. Therefore, in a purely resistive circuit, the cosine of the angle is ignored. In a purely reactive circuit, either inductive or capacitive, current and voltage are 90 degrees out of phase. The cosine of 90 degrees is zero. Multiplying a value times zero results in a zero product. Therefore, no power is consumed in a purely reactive circuit. Calculating Apparent Power in a simple R-L -C Circuit In the following 120 volt circuit, current is equal to 84.9 ma. Inductive reactance is 100 W and capacitive reactance is 100 W.The phase angle is -45 degrees. By referring to a trigonometric table, the cosine of -45 degrees is found to be V R = 1000 Ω X L = 100 Ω X C = 1100 Ω 127

128 Introduction to AC 56 of 56 The apparent power consumed by the circuit is: P = EI P = 120 x P = 10.2 VA The true power consumed by the circuit is: P = EI cos θ P = 120 x x P = 7.2 Watts Another formula for true power is: P = I 2 R P = x 1000 P = 7.2 Watts Power Factor Power factor is the ratio of true power to apparent power in an AC circuit. Power factor is expressed in the following formula: PF = True Power Apparent Power Power factor can also be expressed using the formulas for true power and apparent power. The value of EI cancels out because it is the same in the numerator and denominator. Power factor is the cosine of the angle. PF = EI cos θ EI PF = cos θ In a purely resistive circuit, where current and voltage are in phase, there is no angle of displacement between current and voltage. The cosine of a zero degree angle is one. The power factor is one. This means that all energy delivered by the source is consumed by the circuit and dissipated in the form of heat. In a purely reactive circuit, voltage and current are 90 degrees apart. The cosine of a 90 degree angle is zero. The power factor is zero. This means the circuit returns all energy it receives from the source to the source. In a circuit where reactance and resistance are equal, voltage and current are displaced by 45 degrees. The cosine of a 45 degree angle is The power factor is This means the circuit uses approximately 70% of the energy supplied by the source and returns approximately 30%. 128

129 Transformers 1 of 5 Mutual Induction Transformers are electromagnetic devices that transfer electrical energy from one circuit to another by mutual induction. A single-phase transformer has two coils, a primary and a secondary. Mutual induction is the transfer of electrical energy from the primary to the secondary through magnetic fields. The following circuit illustrates mutual induction. The AC generator provides electrical power to the primary coil. The magnetic field produced by the primary induces a voltage into the secondary coil, which supplies power to a load. Primary Coil Secondary Coil Transformers are used to step a voltage up to a higher level, or down to a lower level. To understand the need to stepping up or down voltages, consider how electrical power is generated anddistributed. Generators used by power companies typically generate voltages of 30 KV or less. While this is a relatively high voltagecompared to the voltages used by power customers, it is more efficient for utilities to transmit this power at still higher voltages, up to as high at 765 KV. The electrical power is received at substation transformers many miles away where it is stepped down and distributed locally. When it arrives at the customer s location, it is further stepped down to the level needed for the type of customer. Even within a customer s facility, voltage may need to be stepped down further to meet requirements of some equipment. This process of stepping up or down the voltage throughout a power distribution system is most often accomplished using transformers. The size and ratings of the transformers vary, but the basic operation of these devices is the same. Coefficient of Coupling Mutual inductance between two coils depends on their flux linkage. Maximum coupling occurs when all the lines of flux from the primary coil cut through the secondary winding. The amount of coupling which takes place is referred to as coefficient of coupling. To maximize coefficient of coupling, both coils are often wound on an iron core which is used to provide a path 129

130 Transformers 2 of 5 for the lines of flux. The following discussion of step-up and step-down transformers applies to transformers with an iron core. Lines of Flux Confined to Iron Core Lines of Flux that don t Couple Voltage, Current, and the Number of Turns in a Coil There is a direct relationship between voltage, impedance, current, and the number of coil turns in a transformer. This relationship can be used to find either primary or secondary voltage, current, and the number of turns in each coil. It is the number of turns which determine if a transformer is a step up or step down transformer. The following rules-of-thumb apply to transformers: 1. If the primary coil has fewer turns than the secondary coil, the transformer is a step-up transformer. 2. If the primary coil has more turns than the secondary coil, the transformer is a step-down transformer. 3. When the number of turns on the primary and secondary coils of a transformer are equal, input voltage, impedance, and current are equal to output voltage, impedance, and current. 130

131 Transformers 3 of 5 Step-Up Transformer A step-up transformer is used when it is desirable to step voltage up in value. The following circuit illustrates a step-up transformer. The primary coil has fewer turns than the secondary coil. When the primary has fewer turns than the secondary, voltage and impedance are stepped up. In the circuit illustrated, The transformer secondary has twice as many turns as the primary and voltage is stepped up from 120 VAC to 240 VAC. Because impedance is also stepped up, current is stepped down from 10 amps to 5 amps. 1:2 Primary Coil Secondary Coil 900 Turns 1800 Turns 120 VAC Supply 240 VAC 10 Amps 5 Amps Step-Down Transformer A step-down transformer is used when it is desirable to step voltage down in value. The following circuit illustrates a step-down transformer. The primary coil has more turns than the secondary coil. The step-down ratio is 2:1. voltage and impedance are stepped down, current is stepped up. 2:1 Primary Coil Seconday Coil 1800 Turns 900 Turns 240 VAC Supply 120 VAC Out 5 Amps 10 Amp 131

132 Transformers 4 of 5 Single-Phase Transformer 120 or 240 VAC single-phase transformers are used to supply lighting, receptacle, and small appliance loads. A transformer with a 240 VAC secondary can be used to supply 240 VAC to larger appliances such as stoves, air conditioners and heaters. A 240 VAC secondary can be tapped in the center to provide two sources of 120 VAC power. Primary Primary 120 VAC 120 VAC 120 VAC Secondary Ground 240 VAC Secondary Formulas for Calculating the Number of Primary and Secondary Turns of a Transformer There are a number of useful formulas for calculating, voltage, current, and the number of turns between the primary and secondary of a transformer. These formulas can be used with either step-up or step-down transformers. The following legend applies to the transformer formulas: E S = secondary voltage E P = primary voltage I S = secondary current I P = primary current N S = turns in the secondary coil N P = turns in the primary coil To find voltage: E S = E x I P P I S E P = E S x I S I P To find current: I S = EP x IP E S I P = E S x I S E P 132

133 Transformers 5 of 5 To find the number of coil turns: N S = E S x N P E P N P = E P x N S E S Using the values for the step-down transformer in the example of the previous page, the secondary voltage can be verified. E S = E S = E = S E P x I P I S 240 Volts x 5 Amps 10 Amps E S = 120 Volts Transformer Ratings Transformers are rated for the amount of apparent power they can provide. Because values of apparent power are often large, the transformer rating is frequently given in kva (kilovolt-amps). The kva rating determines the current and voltage a transformer can deliver to its load without overheating. Given kva and volts, amps can be calculated. kva= Volts x Amps 1000 Amps = kva x 1000 Volts Using the illustrated step-down transformer, the kva rating can be calculated. The kva rating of a transformer is the same for both the primary and the secondary. Primary kva = 240 x Primary kva = 1.2 kva Secondary kva = 120 x Secondary kva = 1.2 kva T ransformer Losses Most of the electrical energy provided to the primary of a transformer is transferred to the secondary. Some energy, however, is lost in heat in the wiring or the core. Some losses in the core can be reduced by building the core of a number of flat sections called laminations. 133

134 Control Devices 1 of 10 Optional equipment that can be included in a circuit is of two kinds: Control devices Protective devices These devices are not required to make a circuit work. A control device is something that allows us to determine where and when electricity flows. Most control devices either open or close the path of the circuit. Light switches, thermostats, and time clocks are examples of common control devices found in circuits. A protective device is used to protect either the load or the path from excessive heat from overcurrent or overvoltage conditions. Most protective devices open the circuit path if excessive current is flowing in the circuit. Common examples of protective devices include fuses and circuit breakers. 134

135 Control Devices 2 of 10 Control devices are needed to start, stop, or redirect current flow in an electrical circuit. Control devices include a variety of 1. Switches Single Pole Single Throw (SPST) Single Pole Double Throw (SPDT) Momentary Contact Multiple Pole Multiple Throw (MPMT or Gang Switch) Mercury Temperature (Bimetal) Time Delay Flasher 2. Relays 3. solenoids Most switches require physical movement for operation Relays and Solenoids are operated with electromagnetism. 135

136 Control Devices 3 of 10 SWITCHES A switch is the most common circuit control device. Switches usually have two or more sets of contacts. Opening these contacts is called "break" or "open" the circuit, Closing the contacts is called "make" or "completing" the circuit. Switches are described by the number of Poles and Throws they have. "Poles" refer to the number of input circuit terminals "Throws" refer to the number of output circuit terminal. Switches are referred to as: SPST (single-pole, single-throw) SPDT (single-pole, double-throw) MPMT (multiple-pole, multiple-throw) 136

137 Control Devices 4 of 10 SINGLE POLE SINGLE THROW (SPST) The simplest type of switch is a "hinged pawl" or "knife blade" switch. It either "completes" (turn on) or "break" (turn off) the circuit in a single circuit. This switch has a single input pole and a single output throw. SINGLE POLE DOUBLE THROW (SPDT) A single-pole input, double-throw output switch has one wire going it and two wires coming out. A Headlamp dimmer switch is a good example of a single-pole double-throw switch. The switch sends current to either the high-beams or low-beams of the headlight circuit. 137

138 Control Devices 5 of 10 MULTIPLE POLE MULTIPLE THROW (MPMT) Multiple-Pole input, Multiple-Throw output switches, which are also known as "gang" switches, have movable contacts in wired in parallel. These switches move together to supply different sets of output contacts with current. An ignition switch is a good example of a multiple-pole multiple-throw switch. Each switch sends current from different source to different output circuits at the same time depending on position. The dotted line between the switches indicates they move together; one will not move without the other moving as well. MOMENTARY CONTACT The momentary contact switch has a spring-loaded contact that keeps it from making the circuit except when pressure is applied to the button. This is a "normally open" type (shown below). A horn switch is a good example of a momentary contact switch. Push the horn button and the hold sounds; release the button and the horn stops. A variation of this type is the normally closed (not shown) which works the opposite as described above. The spring holds the contacts closed except when the button is pressed. In other words the circuit is "ON" until the button is pushed to break the circuit. 138

139 Control Devices 6 of 10 MERCURY A mercury switch is made of a sealed capsule that is partially filled with mercury. In one end of the capsule are two electrical contacts. As the switch is rotated (moved from true vertical) the mercury flows to the opposite end of the capsule with the contacts, completing the circuit. Mercury switches are often be used to detect motion, such as the one used in the engine compartment on the light. Other uses include fuel cut off for roll-overs, and some air bag sensor applications. Mercury is a hazardous waste and should be handled with care. BI-METALLIC A temperature-sensitive switch, also known as a "bi-metallic" switch, usually contains a bimetal element that bends when heated to make contact completing a circuit or to break contact opening a circuit. In an engine coolant temperature switch, when the coolant reaches the temperature limit, the bimetal element bends causing the contacts in the switch to close. This completes the circuit and lights the warning indicator on the instrument panel. 139

140 Control Devices 7 of 10 TIME DELAY SWITCH The time delay switch contains a bimetal strip, contacts, and a heating element. The time delay switch is normally closed. As current flows through the switch, current flows through the heating element causing it to heat, which causes the bimetal strip to bend and open the contacts. As current continues to flows through the heating element, the bimetal strip is kept hot, keeping the switch contacts open. The amount of time delay before the contacts open is determined by the characteristics of the bimetal strip and the amount of heat produced by the heating element. When power to the switch is turned off, the heating element cools and the bimetal strip returns to the rest position and the contacts are closed. A common application for a time delay switch is the rear window defroster. FLASHER The flasher operates basically the same as the time delay switch; except when the contacts open, current stops flowing through the heating element. This causes the heating element and bimetal strip to cool. The bimetal strip returns to the rest position which closes the contacts, allowing current to flow through the contacts and heating element again. This cycle repeats over and over until power to the flasher is eliminated. Common uses for this type of switch are the turn signals or the four-way flasher (hazard lamps). 140

141 Control Devices 8 of 10 RELAYS A relay is simply a remote-control switch, which uses a small amount of current to control a large amount of current. A typical relay has both a: Control circuit Power circuit. Relay construction contains : iron core electromagnetic coil An armature (moveable contact set). There are two types of relays: normally open (shown below) normally closed (NOT shown). A Normally open (N.O.) relay has contacts that are "open" until the relay is energized while a normally closed (N.C.) relay has contacts that are "closed" until the relay is energized. 141

142 Control Devices 9 of 10 RELAY OPERATION Current flows through the control coil, which is wrapped around an iron core. The iron core intensifies the magnetic field. The magnetic field attracts the upper contact arm and pulls it down, closing the contacts and allowing power from the power source to go to the load. When the coil is not energized, the contacts are open, and no power goes to the load. When the control circuit switch is closed, however, current flows to the relay and energizes the coil. The resulting magnetic field pulls the armature down, closing the contacts and allowing power to the load. Many relays are used for controlling high current in one circuit with low current in another circuit. An example would be a computer, which controls a relay, and the relay controls a higher current circuit. 142

143 Control Devices 10 of 10 SOLENOIDS - PULLING TYPE A solenoid is an electromagnetic switch that converts current flow into mechanical movement. As current flows through the winding, a magnetic field is created. The magnetic field will pull the moveable iron core into the center of the winding. This type of solenoid is called a "pulling" type solenoid, as the magnetic field pulls the moveable iron core into the coil. A common use for pulling solenoids is in the starting system. The starter solenoid engages the starter with the flywheel. 143

144 Circuit Protection 1 of 7 CIRCUIT PROTECTION Circuit protection devices are used to protect wires and connectors from being damaged by excess current flow either caused by an over current or short-circuit. Excess current causes excess heat, which causes circuit protection to "open circuit". 144

145 Circuit Protection 2 of 7 CIRCUIT PROTECTION DEVICES Fuses and circuit breakers are used as circuit protection devices. Circuit protection devices are available in a variety of types, shapes, and specific current ratings. 145

146 Circuit Protection 3 of 7 FUSES A fuse is the most common protection device. A fuse is placed in an electrical circuit, so that when current flow exceeds the rating of the fuse it "blows" or "blows out". The element in the fuse melts, opening the circuit and preventing other components of the circuit from being damaged by the overcurrent. The size of the metal fuse element determines its rating. Remember, excessive current causes excess heat, and it's the heat and not the current that causes the circuit protector to open. Once a fuse "blows" it must be replaced with a new one. FUSE TYPES Fuses are classified into basic categories: blade type fuses or cartridge type fuses. Several variations of each are used. 146

147 Circuit Protection 4 of 7 BASIC CONSTRUCTION The blade type fuse is a compact design with a metal element and transparent insulating housing which is color-coded for each current rating. (Standard Auto shown below; however construction of both the mini and maxi fuses are the same.) 147

148 Circuit Protection 5 of 7 FUSE AMPERAGE COLOR RATING Fuse amperage color ratings for both the mini and standard ATO fuses are identical. However, the amperage color ratings of maxi fuses use a different color scheme. Color Ratings For STANDARD and MINI Fuses Fuse Amp Rating Identification Color 3 Violet 5 Tan 7.5 Brown 10 Red 15 Blue 20 Yellow 25 Colorless 30 Green MAXI STANDARD MINI Color Ratings For MAXI Fuses Fuse Amp Rating Identification Color 20 Yellow 30 Green 40 Amber 50 Red 60 Blue 70 Brown 80 Colorless 148

149 Circuit Protection 6 of 7 CIRCUIT BREAKERS Circuit breakers are used in place of fuses for the protection of complicated power circuits such as the power windows, sunroofs and heater circuits. Three types of circuit breakers exists: The manual reset type - mechanical, the automatic resetting type - mechanical, and the automatically reset solid state type - PTC. Circuit breakers are usually located in relay/fuse boxes; however, some components like power window motors have circuit breakers built in. CIRCUIT BREAKER CONSTRUCTION (MANUAL TYPE) A circuit breaker basically consists of a bimetal strip connected to two terminals and to a contact in between. Manual circuit breaker when tripped (current flow beyond its rating) will open and must be reset manually. These manual circuit breakers are called "non-cycling" circuit breakers. CIRCUIT BREAKER OPERATION (MANUAL TYPE) The circuit breaker contains a metal strip made of two different metals bonded together called a bimetal strip. This strip is in the shape of a disc and is concaved downward. When heat from the excessive current is higher than the circuit breaker current rating, the two metals change shape unevenly. The strip bends or warps upwards and the contacts open to stop current flow. The circuit breaker can be reset after it is tripped. 149

150 Circuit Protection 7 of 7 AUTOMATIC RESETTING TYPE MECHANICAL Circuit breakers that automatically reset are called "cycling" circuit breakers. This type of circuit breaker is used to protect high current circuits, such as power door locks, power windows, air conditioning, etc. The automatically resetting circuit breaker contains a bimetal strip. The bimetal strip will overheat and open from the excess current by an overcurrent condition and is automatically reset when the temperature of the bimetal strip cools. AUTO RESET CONSTRUCTION AND OPERATION A cycling circuit breaker contains a metal strip made of two different metals bonded together called a bimetal strip. When heat from the excessive current is higher than the circuit breaker current rating the two metals change shape unevenly. The strip bends upwards and a set of contacts open to stop current flow. With no current flowing the bimetal strip cools and returns to its normal shape, closing the contacts, and resuming the current flow. Automatically resetting circuit breakers are said to "cycle" because they cycle open and closed until the current returns to a normal level. 150

151 Variable Resistors 1 of 5 RESISTORS All electrical circuits require resistance to operate correctly. Resistors are sometimes added to an electrical circuit to limit current flow, create voltage drops, or provide different operating modes. All resistors are rated in both a fixed ohm value of resistance and a power rating in watts. (Watt = Volts X Amps) Three basic categories of resistors are used in automotive electrical systems: 1. Fixed 2. Variable Each has different characteristics and usage ranging from a simple fan circuit to a completed computer circuit. FIXED RESISTORS Fixed-value resistors are divided into two category types of resistors: Carbon / Metal Oxide and Wire-Wound. Carbon and Metal Oxide Film Fixed Resistor Electrical Symbol 151

152 Variable Resistors 2 of 5 CARBON RESISTORS Carbon resistors are commonly used in electronic systems. Carbon is mixed with binder; the more carbon, the lower the resistance. Carbon resistors have a fixed resistance value and are used to limit current flow. They are rated in watts and most have color-code bands to show the resistance value. A typical resistor has a watt rating from 0.125W to 2.0 W. Note: Metal-Oxide Film is sometimes used instead of carbon. While carbon is commonly used for ratings up to 0.5 watt, Metal-Oxide Film provide, better high-temperature satiability and is often used for watt resistors. Carbon Metal Oxide Film RESISTOR RATING COLOR BANDS The first two bands set the digit or number value of the resistor. The third band, also known as the multiplier band, is the number of zeros added to the number value. The last band is the Tolerance band. Example: +/- 10% 152

153 Variable Resistors 3 of 5 RESISTOR COLOR BAND CHART The chart below is used to interpret the color bands on the carbon resistor. Another chart is used to show the value of tolerance band colors (not shown). READING COLOR BANDS - RATING VALUE Using the illustration below: The first color band is Green with a value of "5". The second color band is Red with a value of "2". The third band is Black with a value of "0" zero. (No zeros are added) So the resistor has a base value of 52 ohms. 153

154 Variable Resistors 4 of 5 READING COLOR BANDS - TOLERANCE VALUE Resistors vary in tolerance (accuracy). Common tolerance values are 20%, 10%, 5%, 2%, or 1%, simply meaning the maximum percent allowable difference the resistor value actually is from the designed value rating. A 1% resistor is a higher quality resistor than one with a 20% rating. The tolerance band (last band) is silver with a value of 10%. So, the resistance value is "52 ohms plus or minus 5.2 ohms" (46.8 to 57.2 ohms) 154

155 Variable Resistors 5 of 5 VARIABLE RESISTORS Variable resistors provide an infinite amount of resistance values. Variable resistors are used by electrical circuits to provide information on temperature, position, or light source. Variable Resistors are used in the headlamp switch to dim or brighten dash panel lighting. Variable Resistors have two connections, one to the fixed end of a resistor and the other to a sliding contact on the resistor. Turning the control moves the sliding contact away from or toward the fixed end, increasing or decreasing the resistance. Variable Resistors control resistance, thus controlling current flow. Generic Variable Resistor Electrical Symbol Variable Resistors OPERATION As the wiper moves along the Variable Resistors it exposes more or less of the resistor. Moving the wiper towards the high places a small portion of the resistor in series with the light, causing the light to glow bright. Moving the wiper toward the low, places a larger portion of the resistor in series with the lamp; this increased resistance causes less current to flow lowering the intensity of the light. 155

156 Understanding Logic Gates 1 of 11 LOGIC GATES Logic Gates are circuits made up of transistors, diodes, and resistors. Logic gates process one or more input signals in a logical fashion. Depending on the input value or voltage, the logic gate will either output a value of '1' for ON or a value of '0' for OFF. Logic Gates allow simplification of circuit operation. A basic understanding of logic gates will aid technicians in electrical diagnosis. The five common logic gates used in wiring diagrams are the: AND, OR, NOT, NAND, NOR A light switch in your house can be used as an example of a digital circuit. The light is either ON or OFF depending on the switch position. When the Light is ON the output value is '1'. When the Light is OFF the output value is '0'. The inputs are the position of the light switch. The switch is placed either in the ON or OFF position to activate the Light. 156

157 Understanding Logic Gates 2 of 11 BINARY CODE Logic gates are digital circuits and they utilize a binary numbering system known as binary code. Binary code is the same language used by computers that use only 1 or 0 as numbers. People use a base 10 numbering system, ones, tens, hundreds, etc. Example: 1,2,3,4,5,6,7,8,9,and 0. Once we get to zero, we expand to the tens place: 10, 11, etc. BINARY CODE EXAMPLE: = = = = = = = = = = 10 When the number place holder is empty, it has a zero in it. When full, there is a 1. Look at the first example, the number one. When we add a 1 to the number 1, the first place holder becomes a zero and we carry one place to the left. The zero (the second from the left) now becomes a 1. So a number 10 in the binary system equals a number 2 in the base 10 system. LOGIC SYMBOLS FOR THE FIVE COMMON LOGIC GATES 157

158 Understanding Logic Gates 3 of 11 HOW DOES THE "AND" GATE WORK? 'AND' gates are like two or more switches in series. All the switches have to be closed ( 'ON' or a value of '1') in order to make the lamp (output C) turn on. If all inputs are not "ON", the output is "OFF". TRUTH TABLE FOR THE "AND" GATE TRUTH TABLE Input Input Output A B C All input values to the AND gate must be a '1' in order for the output value to be '1'. Any other input combinations will result in a 'zero' as the output as shown in the truth table above. 158

159 Understanding Logic Gates 4 of 11 EXAMPLE OF "AND" GATE OPERATION A value of '1' is needed at all AND gate inputs to produce an output value of '1' from the AND gate, thus sending B+ to the lamp. EXAMPLE OF "AND" GATE OPERATION Unless all AND gate inputs receive a value of '1' the output value will be '0', thus preventing B+ to the lamp. 159

160 Understanding Logic Gates 5 of 11 HOW DOES THE "OR" GATE WORK? An 'OR' gate is like two or more switches in parallel. Only one switch needs to be closed ('ON' or a value of '1') in order to make the lamp (output C) turn 'ON' with a value of '1'. TRUTH TABLE FOR THE "OR" GATE TRUTH TABLE Input Input Output A B C A value of '1' applied to either or both inputs of the OR gate will result in an output value of '1'. A value of '0' applied to both inputs will result in an output value of '0'. 160

161 Understanding Logic Gates 6 of 11 EXAMPLE OF "OR" GATE OPERATION An input value of '1' at either of the OR gate inputs will result in an output value of '1' from the OR gate, thus sending B+ to the lamp. EXAMPLE OF "OR" GATE OPERATION Input values of '0' at all inputs to the OR gate will result in an output value of '0' from the OR gate, thus preventing B+ from going to the lamp. 161

162 Understanding Logic Gates 7 of 11 LOGIC SYMBOL FOR THE "NOT" GATE TRUTH TABLE FOR THE "NOT" GATE TRUTH TABLE Input Output A C NOT gates reverse the input signal value. If the input value is '1', the output value will be '0'. If the input value is '0', then the output value will be '1'. NOT gates can be referred to as inverters; whatever the input signal is the output is always the opposite. EXAMPLE OF "NOT" GATE OPERATION An input value of '0' at the NOT gate produces an output value of '1' from the NOT gate, thus sending B+ to the lamp (as shown above). An input value of '1' at the NOT gate produces an output value of '0' from the NOT gate, thus preventing B+ from going to the lamp. 162

163 Understanding Logic Gates 8 of 11 LOGIC SYMBOL FOR THE "NAND" GATE Notice the circle on output C. What could it be? TRUTH TABLE FOR THE "NAND" GATE TRUTH TABLE Input Input Output A B C A NAND gate is the combination of both an AND gate and a NOT gate. It operates the same as an AND gate but the output will be the opposite. Remember the NOT gate does not always have to be on the output leg; it could be used to invert an input signal also. 163

164 Understanding Logic Gates 9 of 11 EXAMPLE OF "NAND" GATE OPERATION If a value of '1' is sent to all inputs of the AND gate the result will be an output value of '1' from the AND gate. The NOT gate receives an input value of '1' and will invert the output value to '0'. EXAMPLE OF "NAND" GATE OPERATION If a value of '1' is applied to all the NAND gate inputs, an output value of '0' will result from the NAND gate, thus preventing B+ to the lamp. EXAMPLE OF "NAND" GATE OPERATION If a value of '0' is sent to all of the AND gate inputs, the output value of '0' will result from the AND gate. The NOT gate will receive an input value of '0', which is inverted to produce an output value of '1'. EXAMPLE OF "NAND" GATE OPERATION If a value of '0' is applied to all the NAND gate inputs, an output value of '1' will result from the NAND gate, thus sending B+ to the lamp. 164

165 Understanding Logic Gates 10 of 11 LOGIC SYMBOL FOR THE "NOR" GATE Notice the circle on output C TRUTH TABLE FOR THE "NOR" GATE TRUTH TABLE Input Input Output A B C A NOR gate is the combination of both an OR gate and a NOT gate. It operates the same as an OR gate, but the output will be the opposite. 165

166 Understanding Logic Gates 11 of 11 EXAMPLE OF "NOR" GATE OPERATION If a value of '1' is applied to either input of the OR gate, it will produce an output value of '1' from the OR gate. The NOT gate receives an input value of '1', which is inverted by the NOT gate to an output value of '0'. EXAMPLE OF "NOR" GATE OPERATION If a value of '1' is applied to either input of the NOR gate, an output value of '0' will result from the NOR gate, thus preventing B+ from going to the lamp. EXAMPLE OF "NOR" GATE OPERATION If a value of '0' is sent to all of the inputs of the NOR gate, the output value of '0' will result from the OR gate. The NOT gate will receive an input value of '0' which is inverted to an output value of '1'. EXAMPLE OF "NOR" GATE OPERATION If a value of '0' is applied to all the NOR gate inputs, an output value of '1' will result from the NOR gate, thus sending B+ to the lamp. 166

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168 Lockout/Tagout procedures There are nine steps involved in the lockout/tagout procedures. Following these steps will keep accidents from occurring while maintaining or repairing machinery. Keep in mind that any time a worker chooses, he or she may apply additional measures or apply a lock or tag to any or all of the electrical isolating devices. Let us review the nine steps: 1. Think, plan and check. Think through the entire procedure and identify all parts of any systems that need to be shutdown. 2. Communicate. Let other employees working on the equipment know when and why you are shutting down the system. 3. Locate all power sources. Locate all switches and other electrical sources that need to be locked out. 4. Neutralize all power at its sources. Lower any suspended parts, block any moveable parts, and disconnect the electricity. 5. Lockout all power sources. Used a lock designed for only this purpose and a lockout tag that includes your name, and the time, the date and department. 6. Test operating controls. Test the operating controls to make certain the power has been removed. 7. Turn the controls back off. Be sure to check each and every control is in the "OFF" position before beginning any necessary maintenance or repairs. 8. Perform any maintenance or repairs. 9. Remove locks and restore energy. Tools should be removed from equipment and machine guards put back in place. Notify other workers that the machines are working and back on. Restart equipment only after all workers are at a safe distance. FAQs What is Voltage What is Current What is Power What are the 5 characteristics of AC Power? What is a kwh or Kilowatt-hour? How much electricity does it take to kill a person? What should I do if I see a low or downed power line? Why is it important to keep electric appliances and tools away from water? Why can't all power lines be buried? Why are some electrical cords and wires fatter than others? What is the most common type of power plant? 168

169 What is Voltage Voltage is the electrical force that causes free electrons to move from one atom to another. Just as water needs some pressure to force it through a pipe, electrical current needs some force to make it flow. "Volts" is the measure of "electrical pressure" that causes current flow. Voltage is sometimes referred to as the measure of a potential difference between two points along a conductor. Voltage is typically supplied by either a generator or battery. Generators are analogous to a water pump in a water piping system, and batteries are similar to water towers. Both systems have a potential difference between the source of the power and someplace downstream from the source. The scientific symbol for voltage is an "E", dating to early days of electricity when it was called the "Electromotive force". Scientists and engineers use the "E" symbol for voltage, while electricians and wiring books use "V" as the voltage symbol. This can create some confusion, since either may be encountered. In this title, we'll use the practical symbol "V" for voltage. What is Current Current is a measure of the rate of electron flow through a material. Electrical current is measured in units of amperes or "amps" for short. This flow of electrical current develops when electrons are forced from one atom to another. One amp is defined as 6.28 x electrons per second. When current flows in a conductor, heat is produced. This happens because every conductor offers some resistance to current flowing. That is why the amperage flow in a circuit is important, since the more amps flowing, the more heat is produced. Most people notice this heating effect when the cord of any appliance or electrical device heats up after the device has been running for an extended period. Recognizing this heat production is important in specifying wire sizes. When a wire carries more amps than it can handle without overheating, we say it is "overloaded". Overloaded wires can melt the insulation and create shocks or even fires. 169

170 The scientific symbol for amperage is an "I", dating back to the early days of electricity. It is still used by scientists and engineers. Electricians and wiring guides use "A" as the amperage symbol. In this title, we'll use the practical symbol "A" for current flow in amps. What is Power The ability to do work. Watt is the standard unit in the metric system. 746 watts equals one horsepower in the English system of units. What are the 5 characteristics of AC Power? AC power is represented graphically by a sinusoidal or sine waveform. -- called sine wave for short. As you look at this sine wave, remember that this apparently stable picture changes 60 times every second. In doing so, we think in terms of averages of current, voltage and any changes in frequency. There are five characteristics of AC power; Amplitude, Cycles, Frequency, Peak to Peak, and RMS. Amplitute RMS Cycles Frequency Peak to Peak 170

171 Amplitute The first characteristic of AC power is its "amplitude". Amplitude is the maximum value of current or voltage. It is represented by either of the two peaks of the since wave. This voltage level is also referred to as the peak voltage, and can be either positive or negative. Positive and negative refer only to the direction of current flow. A negative number does not mean that the voltage or current flow are less than zero, only that the current flows in the opposite direction. RMS The second value of voltage is the actual useful voltage that is available and is called RMS. This stands for Root Mean Square and it is the standard way of measuring and reporting alternating current and voltage. It is not the peak; it is the average. The RMS is found by dividing the peak amplitude by the square root of 2 (approximately 1.414). This yields the actual, useable voltage. It is typically represented by a dotted line drawn across each peak near the 70 percent point. 171

172 Cycles A cycle is one complete repetition of the sine wave pattern. It is produced by one complete revolution (360 degrees) of the AC generator. Since the sine wave begins at zero, goes positive through the positive peak, then negative through zero and reaches the negative peak, and to zero, we say a full cycle has been completed. Frequency Peak to Peak There are two values of voltage that we must be familiar with. The first is "peak-to-peak" voltage. This is the voltage measured between the maximum positive and negative amplitudes on the sine wave. It is twice the amplitude. This value is the maximum voltage available, but is not all useable in practical applications. 172

173 What is a kwh or Kilowatt-hour? Electrical energy is the average amount of power used over a given time period and is commonly measured in "kilowatt-hours." Electric utility electric meters accurately measure the kilowatt-hour energy use by the customer, and may also measure peak power use during a specified time interval. Let's calculate the energy use for a blow dryer. Say the blow dryer is rated at 1,500 watts by the manufacturer. This is how much electric power it uses when it operates. If the blow dryer is operated for a total of 2 hours each month, the blow dryer consumes 1,500 watts x 2 hours = 3000 watt-hours. Since utility rates are based on kilowatt-hours, divide by 1,000 to get 3 kilowatt-hours. This shows how power consumption and operating time are important in determining energy use. How much electricity does it take to kill a person? At levels of current flow exceeding 1/10 of an amp or 100 milliamps, the heart stops. This is called fibrillation. A person may survive an electrocution if his or her heart can be started again. This is why CPR is such an important skill in the electrical industry. 173

174 What should I do if I see a low or downed power line? A downed power line is potentially hazardous. Always assume a fallen wire is "live" or "hot" even if it looks harmless. If the wire is energized or "live," it will electrically charge anything that comes into contact with it. Never touch anything the fallen wire has been in contact with. Stay clear, warn others around you to keep away and call the local utility company immediately. If someone is harmed by an outdoor wire, call an ambulance, notify the police or fire department, and call the local utility company immediately. Stay away from the wire and the person who was hurt. Do not touch them because they can still conduct electricity through you. If you see someone in a car with a fallen power line contacting it, do not approach the car and try to help the person out. If you touch the car, you complete the path for the electricity to flow into the ground through your body. Instead, tell the person to stay in the car and remain calm, and that you will contact and alert the necessary emergency people. If you're inside a car and a live wire comes in contact with your vehicle, stay inside where you are safe and wait for help. The tires of the car provide insulation between the car and ground, and should protect you against electrical shock while you remain inside the vehicle. If you touch the vehicle and the ground at the same time, you will complete the path for electricity to flow between the downed wire and the ground, right through your body. If you must get out, a method that can work well is to stand on the edge of the inside of the vehicle and leap as far from the car as possible onto the ground. 174

175 Why is it important to keep electric appliances and tools away from water? Remember this simple rule: water and electricity are a potentially lethal combination. Stay away from water when using electrical appliances -- standing in a tub of water or shower and using a blow dryer or curling iron could result in electrocution. Many consumer products such as hair dryers, electric power tools, TV sets, radios and small kitchen appliances can easily become electrical hazards if they come in contact with water. They are not designed to operate when wet. The best idea is not to use these appliances anywhere near basins, tubs or sinks that hold water. If an appliance does contact water, say the blow dryer drops into a sink full of water, do not reach into the sick of water after it. This could cause an electrocution. Unplug the blow dryer or turn the electricity off at the fuse or breaker box before you retrieve the blow dryer from the sink, even if the dryer is in the "off" position. Why can't all power lines be buried? Distribution lines may be located either overhead or underground. 175

176 The traditional method of distributing electricity to customers has been on wires attached to poles high above the ground, referred to as overhead distribution. Transformers and other equipment in the overhead system are mounted on poles or other supporting structures. Overhead distribution is still widely used despite recent advancements in wiring materials that have increased the popularity of underground systems. Overhead lines are less expensive to build and maintain, however they are subject to many weather related problems. Underground lines are protected from severe weather by their location, but are more expensive to build and maintain. There are some parts of the country where, because of earthen conditions, underground distribution is nearly impossible. Low-lying land, flood plains, and rock layers will always be strong candidates for overhead distribution. Even in ideal conditions, underground is still more expensive for utilities to install and maintain than overhead. Why are some electrical cords and wires fatter than others? The current carrying capacity of a particular wire is dictated by its "ampacity" - how many amps it can handle. Ampacity is a function of the cross section area or diameter of the wire and its material type. Larger diameter wires have larger cross section areas and can safely carry more electrical current without overheating. The maximum ampacity for different types of wires is reported in the electrical codes used throughout the industry. These tables are based on the size of the wire and the particular insulation type for the particular wire. Insulation Type is important since some insulation materials dissipate heat better than others. 176