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Basic Electricity
Part 1
Student Guide
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ii
Table of Contents
INTRODUCTION ............................................................................................1
TLO 1 ELECTRICAL PRINCIPLES OF OPERATION ..........................................2
Overview .................................................................................................2
ELO 1.1 Composition of an Atom and Electron Flow ...........................3
ELO 1.2 Electrical Terms and Characteristics ........................................6
ELO 1.3 Electrical Terms .....................................................................10
ELO 1.4 Electrical Parameters ..............................................................13
ELO 1.5 Applying Ohm's Law .............................................................16
TLO 1 Summary ...................................................................................18
TLO 2 MAGNETISM ...................................................................................19
Overview ...............................................................................................19
ELO 2.1 Electron Domains and Law of Magnetism.............................19
ELO 2.2 Magnetic Terms .....................................................................21
ELO 2.3 Magnetic Materials.................................................................24
ELO 2.4 Left-Hand Rule for Current Carrying Conductors .................25
ELO 2.5 Left-Hand Rule for Coils .......................................................26
ELO 2.6 Hysteresis Losses and Magnetic Circuits ...............................28
ELO 2.7 Faraday's Law of Induced Voltage .........................................30
TLO 2 Summary ...................................................................................33
TLO 3 ELECTRICAL DRAWINGS .................................................................33
Overview ...............................................................................................33
ELO 3.1 Electrical Symbols .................................................................33
ELO 3.2 Types of Drawings .................................................................35
ELO 3.3 Circuit Terminology ...............................................................38
ELO 3.4 Circuit Protection Devices .....................................................43
TLO 3 Summary ...................................................................................46
TLO 4 BATTERIES......................................................................................46
Overview ...............................................................................................46
ELO 4.1 Battery Terminology ..............................................................46
ELO 4.2 Simple Voltaic Cell ................................................................50
ELO 4.3 Chemistry of a Lead-Acid Battery .........................................51
ELO 4.4 Series and Parallel Connected Batteries .................................53
ELO 4.5 Types of Battery Materials .....................................................55
ELO 4.6 Battery Hazards ......................................................................56
TLO 4 Summary ...................................................................................58
TLO 5 DC CIRCUIT ANALYSIS...................................................................58
Overview ...............................................................................................58
ELO 5.1 Total Resistance .....................................................................58
ELO 5.2 Voltage and Current Dividers ................................................72
ELO 5.3 Polarity of Voltage Drops ......................................................75
ELO 5.4 Kirchhoff's Laws ....................................................................77
ELO 5.5 Applying Kirchhoff's Laws ....................................................78
TLO 5 Summary ...................................................................................84
TLO 6 DC MOTORS ...................................................................................85
Overview ...............................................................................................85
ELO 6.1 Current Carrying Conductors .................................................85
iii
ELO 6.2 Right-Hand Rule for Motors ................................................. 87
ELO 6.3 Torque in DC Motors ............................................................ 89
ELO 6.4 Counter-Electromotive Force (CEMF) in DC Motors .......... 91
ELO 6.5 DC Motor Control ................................................................. 92
ELO 6.6 Starting DC Motors ............................................................... 93
ELO 6.7 DC Motor Ratings ................................................................. 95
TLO 6 Summary................................................................................... 96
TLO 7 PRODUCING DC VOLTAGE ............................................................. 96
Overview .............................................................................................. 96
ELO 7.1 Methods of Producing DC Voltage ....................................... 97
ELO 7.2 Rectifiers .............................................................................. 103
ELO 7.3 Commutation ....................................................................... 107
ELO 7.4 DC Machine Components ................................................... 109
ELO 7.5 Conditions for Inducing Voltage ......................................... 111
ELO 7.6 Left-Hand Rule for Generators ............................................ 113
ELO 7.7 Terminal Voltage ................................................................. 115
ELO 7.8 DC Generator Ratings ......................................................... 117
TLO 7 Summary................................................................................. 118
BASIC ELECTRICITY PART 1 SUMMARY................................................... 119
iv
Basic Electricity Part 1
Revision History
Revision
Date
Version
Number
Purpose for Revision
Performed
By
11/6/2014
0
New Module
OGF Team
12/9/2014
1
Added signature of OGF
Working Group Chair
OGF Team
Introduction
In this module, you will learn electrical terminology, laws of electricity,
laws of magnetism, and how key power plant electrical components work.
Power plants use electrical generators to produce and distribute electrical
power throughout the station and to the grid for distribution and eventual
sale (this is our product). Understanding how they work and how to
monitor and control them is central to the plant operator.
Rev 1
1
Objectives
At the completion of this training session, the trainee will demonstrate
mastery of this topic by passing a written exam with a grade of 80 percent
or higher on the following Terminal Learning Objectives (TLOs):
1. Describe basic electrical theory principles of operation.
2. Describe the magnetic properties of materials and the use of
magnetism in electrical applications.
3. Differentiate between types of electrical symbols, drawings, and
diagrams.
4. Describe the operating characteristics, terminology, and hazards of a
lead-acid battery and voltaic cell.
5. Analyze various DC circuits to find resistances, currents, and voltages
at any given point within the circuit.
6. Describe the principles of operation, control, and characteristics of
DC motors.
7. Explain how a DC generator produces DC voltage.
TLO 1 Electrical Principles of Operation
Overview
In this section, you will learn basic electrical terms and how to use Ohm's
Law.
Understanding the relationships of basic electrical circuits is necessary for
an operator to monitor and control plant electrical equipment.
Objectives
Upon completion of this lesson, you will be able to do the following:
1. Describe the basic composition of an atom and the concept of electron
flow.
2. Define the following terms and their characteristics: electrostatic
force, potential difference, electromotive force, ion charge, and
Coulomb's Law.
3. Define the following electrical terms: conductor, insulator, resistor,
voltage, current, electron, and conventional current flow, direct and
alternating current, and real and ideal sources.
4. Describe the following electrical parameters, including the unit of
measurement and the relationship to other parameters: voltage,
current, resistance, conductance, power, inductance, capacitance, and
frequency.
5. Given any two of the three component values of Ohm’s Law, solve
for the unknown component value.
2
Rev 1
ELO 1.1 Composition of an Atom and Electron Flow
Introduction
Electricity is the flow of electrons through materials and devices. Tiny
particles called electrons and protons produce electricity. These particles
are not visible, but exist as subatomic particles in the atom.
The Atom
Elements are the basic building blocks of all matter. Atoms are the smallest
components of matter that retain the identifying properties of an element.
An atom consists of a positively charged nucleus surrounded by negatively
charged electrons, so that the atom as a whole is normally electrically
neutral. The figure below depicts a carbon atom with its components.
Figure: The Atom
The nucleus is composed of two kinds of subatomic particles, protons, and
neutrons, as shown in the figure above. The proton carries a single positive
charge equal in magnitude to the electron charge. The neutron is slightly
heavier than the proton and is electrically neutral. Various combinations of
these two particles exist in atoms, depending upon the element.
The electron is the fundamental negative charge (-) of electricity and
revolves around the nucleus, or center, of the atom in concentric orbits, or
shells. The proton is the fundamental positive charge (+) of electricity and
is located in the nucleus. The number of protons in the nucleus of any atom
specifies the atomic number of that atom or element. For example, the
carbon atom contains six protons in its nucleus; therefore, the atomic
number for carbon is six. In its natural state, an atom of any element
contains an equal number of electrons and protons. The negative charge (-)
of each electron is equal in magnitude to the positive charge (+) of each
proton; therefore, the two equal and opposite charges offset each other, and
the atom is electrically neutral.
Electron Transfer
Some atoms can lose electrons and others can gain electrons, so it is
possible to transfer electrons from one object to another. When this occurs,
the equal distribution of negative and positive charges in the atoms no
Rev 1
3
longer exists. One object will contain atoms with an excess of electrons and
become negatively charged. The other object will contain atoms that are
deficient in electrons and become positively charged. These objects, which
contain billions of atoms, will then follow the same law of electrostatics as
the electron and proton previously discussed.
Free Electrons
Free electrons are the electrons that can move around within an object. The
greater the number of free electrons, the greater the object’s negative
electric charge. Thus, the amount electric charge is a measure of free
electrons.
Valence Electrons
Valence electrons are the electrons in the outermost shell. When external
energy, such as heat, light, or electrical energy, act on certain materials, the
electrons in the individual atoms gain energy, become excited, and may
move to a higher energy level.
If enough energy acts on the atom, some of the valence electrons will leave
the atom, as shown in the figure below. These electrons are free electrons.
Figure: Free Electrons
When the outer shell of an atom contains eight electrons, the atom becomes
very stable, and very resistant to changes in its structure. This also means
that atoms with one or two electrons in their outer shell can lose electrons
much more easily than atoms with full outer shells.
Note
Note
The movement of free electrons provides electric
current flow in a metal conductor.
Electrons are in rapid motion around the nucleus. While the electrostatic
force is trying to pull the nucleus and the electron together, the electron is in
4
Rev 1
motion and trying to pull away from the nucleus. The unbalanced force
keeps the electron in orbit around the nucleus.
Electron Shells
The electrons in an atom exist in different energy levels. The energy level
of an electron is proportional to its distance from the nucleus. Higher
energy level electrons exist in orbits, or shells, that are farther away from
the nucleus. These shells nest inside one another and surround the nucleus.
The nucleus is the center of all the shells.
Letters identify the shells, beginning with the shell nearest the nucleus: as
K, L, M, N, O, P, and Q. Each shell has a maximum number of electrons it
can hold. For example, the K shell holds a maximum of two electrons and
the L shell holds a maximum of eight electrons. As shown in the figure
below, each shell has a specific number of electrons that it will hold for a
particular atom.
Figure: Energy Shells and Electron Quota
There are two rules concerning electron shells that make it possible to
predict the electron distribution of any element:
1. The maximum number of electrons that can fit in the outermost shell
of any atom is eight.
2. The maximum number of electrons that can fit in the next-tooutermost shell of any atom is 18.
Rev 1
5
Knowledge Check
Electrons located in the outermost shell of an atom are
called:
A.
free electrons.
B.
positrons.
C.
valence electrons.
D.
K shell electrons.
ELO 1.2 Electrical Terms and Characteristics
Introduction
In this section, you will learn about electrostatic and electromotive forces
within an atom.
One characteristic of an atom is that the electron and the nucleus attract
each other. Electrostatic force is the name of this attraction. Electrostatic
force holds the electron in orbit. The lines in the figure below show this
force.
Figure: Electrostatic Force
Without this electrostatic force, the electron, which is traveling at high
speed, would not remain in its orbit (it would fly away). Bodies that attract
each other in this way are termed charged bodies. The electron has a
negative charge, and the nucleus (due to the proton) has a positive charge.
First Law of Electrostatics
The First Law of Electrostatics (also known as the Law of Electrical
Charges) states that unlike charges attract and like charges repel. This law
is a vital concept in the understanding of electricity.
This force is present within every charged object and is the result of an
electrostatic field that exists around each charged particle or object. Lines
called "lines of force" as shown in the figure below illustrate this
electrostatic field, and the force it creates.
6
Rev 1
The negative charge of the electron is equal and opposite of the positive
charge of the proton. Electrostatic charge refers to these charges. Polarity
refers to the charge sign (either positive or negative).
Unlike charges attract each other, and like charges repel each other.
Figure: Electrostatic Field
Opposite Charges
Charged objects repel or attract each other because of the way these
electrostatic fields interact. When two objects of opposite charge are near
one another, the electrostatic field is concentrated in the area between them,
as shown in the figure below.
Figure: Electrostatic Field between Opposite Charges
When two objects of like charge are near one another, the lines of force
repel each other, as shown in the figure below.
Figure: Electrostatic Field Between Like Charges
Potential Difference
Potential difference is the term used to describe the size of the electrostatic
force between two charged objects. If there are two objects with a potential
Rev 1
7
difference, with a charged body between them, the charged body will try to
move in one direction, depending upon the polarity of the charged body.
The figure below shows the electrostatic force lines between three such
charged objects.
Figure: Potential Difference between Two Charged Objects
If an electron is between a negatively charged body and a positively charged
body, the potential difference will push the electron toward the positively
charged object. The negatively charged object will repel the negatively
charged electron; the positively charged object will attract the negatively
charged electron, as shown in the figure above.
Electromotive Force
Due to the force of the electrostatic field, the electrical charges shown in the
figure above have the ability to do work by moving another charged particle
by attraction and/or repulsion. Potential refers to this ability to do work;
therefore, if one charge is different from another, there is a potential
difference between them. Electromotive force (EMF) is the sum of the
potential differences of all charged particles in the electrostatic field.
The basic unit of measure of potential difference is the volt. The symbol for
potential difference is V, indicating the ability to do the work of forcing
electrons to move.
Ion Charge
An atom that has lost or gained one or more electrons has an ion charge
(ionized). If the atom loses one or more electrons, it becomes positively
charged and is a positive ion. If an atom gains one or more electrons, it
becomes negatively charged and is a negative ion.
Coulomb's Law
The strength of the attraction or of the repulsion force between two charged
objects depends upon two factors:
1. the amount of charge on each object
2. the distance between the objects
A larger charge on the charged objects results in a greater electrostatic field
between the objects. A larger distance between the charged objects results
8
Rev 1
in a weaker electrostatic field between them. This leads us to the law of
electrostatic attraction, commonly referred to as Coulomb’s Law of
electrostatic charges.
Coulomb’s Law states that the force of electrostatic attraction (or repulsion
between two objects), is directly proportional to the product of the two
charges and inversely proportional to the square of the distance between
them as shown in the equation below:
𝑞1 𝑞2
𝐹=𝐾 2
𝑑
Where:
F = force of electrostatic attraction or repulsion (Newtons)
K = constant of proportionality (N-m2/cm2)
q1 = charge of first particle (Coulombs)
q2 = charge of second particle (Coulombs)
d = distance between two particles (meters)
If q1 and q2 are both positively charged, or negatively charged, the force is
repulsive. If q1 and q2 are opposite in polarity or charge, the force is
attractive.
Knowledge Check
The force that holds electrons in their orbits is called:
A.
Electrostatic force
B.
Coulomb force
C.
Electromotive force
D.
Voltage
Knowledge Check
Select all that are correct:
According to Coulomb's Law, the force between two
charged objects...
Rev 1
A.
decreases as distance between the objects increases.
B.
increases as the distance between the objects increases.
C.
increases as the magnitude of either charge increase.
D.
is independent of the magnitude of charge on the objects.
9
ELO 1.3 Electrical Terms
Introduction
In this section, you will learn about commonly used electrical terms.
Conductors
Conductors are materials with electrons that are loosely bound to their
atoms. Conductors permit free motion of a large number of electrons.
Atoms with only one valence electron, such as copper, silver, and gold, are
examples of good conductors. Of these three, copper is most common in
conducting wire construction. Most metals are good conductors.
Insulators
Insulators, or nonconductors, are materials with electrons that are tightly
bound to their atoms and require large amounts of energy to free the
electrons from the influence of the nucleus. The atoms of good insulators
have their valence shells filled with eight electrons. Any energy applied to
such an atom distributes among a relatively large number of electrons,
minimizing the energy applied to any one electron. Examples of insulators
are rubber, plastics, glass, and dry wood.
Resistors
Resistors are made of materials that conduct electricity, but offer more
opposition to current flow than good conductors. Semiconductor is an
alternate term for these types of materials because they are neither good
conductors nor good insulators. Semiconductors have more than one or two
electrons in their valence shells, but less than seven or eight.
Carbon, silicon, germanium, tin, and lead are examples of semiconductors.
Each has four valence electrons.
Voltage
The volt (symbol V) is the basic unit of measure for potential difference.
Voltage indicates potential difference between charged objects.
The number of electrons that an object has gained or lost determines an
object’s electrical charge. The unit of an object’s electrical charge is the
coulomb. One coulomb equals 6.28 x 1018 (billion, billion) electrons. For
example, if an object gains one coulomb of negative charge, it has gained
6,280,000,000,000,000,000 extra electrons.
One volt is the potential difference that causes one coulomb of current to do
one joule of work. In addition, one volt is that amount of force required to
force one ampere of current through one ohm of resistance.
Current
The density of the atoms in copper wire is such that the valence orbits of the
individual atoms overlap, allowing the electrons to move easily from one
atom to the next. Free electrons can drift from one orbit to another in a
random direction. When a potential difference (voltage) is applied, the
direction of their movement is standardized. The strength of the potential
10
Rev 1
difference applied at each end of the wire determines how many electrons
change from a random motion to a directional path through the wire. The
movement or flow of these electrons is called electron current flow or
simply current.
If two charged objects that have a potential difference have a copper wire
between them, all of the negatively charged free electrons will feel a force
pushing them from the negative charge to the positive charge. The figure
below depicts this force, which is opposite to the conventional direction of
the electrostatic lines of force.
To produce current, a potential difference must move the electrons. The
symbol for current is (I), and the basic unit for current is the ampere (A).
One ampere of current is the movement of one coulomb of charge past any
given point of a conductor during one second of time.
Figure: Electron Flow
Electron Flow and Conventional Current
The solid arrow shown in the figure below indicates the direction of
electron flow. The flow of electrons is from the negative (-) side of the
battery, through the wire, and back to the positive (+) side of the battery.
The direction of electron flow is from a point of negative potential to a
point of positive potential.
Figure: Conventional Current vs. Electron Flow
Rev 1
11
As electrons leave atoms during electron current flow, positively charged
atoms (holes) result. The flow of electrons in one direction causes a flow of
positive charges in the opposite direction. Conventional current is the term
for this flow of positive charges, denoted by a dashed arrow in the figure
above.
As electrons flow from negative to positive, or from a higher potential to a
lower potential, they create electrical effects. If there was a flow of positive
charges in the opposite direction, the electrical effects are the same.
Either electron flow or positive charge flow can describe the flow of
electrical current. The effects of both types of flow are essentially
equivalent. In this lesson, the effects of electrical current flow reflect
electron flow.
Direct Current and Alternating Current
There are two general types of electric current flow: direct current (DC) and
alternating current (AC). Direct current flows continuously in the same
direction. An alternating current periodically reverses direction. An
example of DC is the current flowing in an electrical circuit powered by a
battery. An example of AC is the current used in most industries and
households to power lights, motors, etc.
Real and Ideal Sources
An ideal source is a theoretical concept of an electric current or voltage
supply (such as a battery) that has no losses and is therefore a perfect
voltage or current supply. Analytical examples use ideal sources only since
they do not occur in real life applications.
A real source is a current or voltage supply that has some losses associated
with it such as a battery or electrical generator.
12
Rev 1
Knowledge Check
Match the following terms to their appropriate definitions.
1. Materials with electrons that are
loosely bound to their atoms, or
materials that permit free motion of a
large number of electrons
A. Conductor
2. Materials with electrons that are tightly
bound to their atoms and require large
amounts of energy to free them from
the influence of the nucleus
B. Resistor
3. Materials that conduct electricity, but
offer opposition to current flow
C. Insulator
4. Flow of positive charges (holes)
through a conductor
D. Conventional
current
ELO 1.4 Electrical Parameters
Introduction
The International (metric) System, also known as the SI System provides
the basis of electrical measurement units. Units of electrical measurement
include the following:
Ampere – unit used to measure electrical current
Volt – unit used to measure electrical potential difference
Hertz – unit used to measure frequency
Ohm – unit used to measure resistance to current flow
Siemens – unit used to measure a material’s ability to conduct current
flow
 Watt – unit used to measure power
 Henry – unit used to measure electrical inductance
 Farad – unit used to measure electrical capacitance





Voltage (Volt)
Voltage, electromotive force (EMF), or potential difference, is the pressure
or force that causes electrons to move in a conductor. In electrical formulas
and equations, you will see voltage symbolized with a capital E, while on
laboratory equipment or schematic diagrams, you will see voltage
symbolized with a capital V. Both symbols indicate voltage and are equal
representations.
Rev 1
13
Current (Ampere or Amp)
Electron current, or amperage, is the movement of free electrons through a
conductor. In electrical formulas, current is symbolized with a capital I,
while in the laboratory or on schematic diagrams, it is common to use a
capital A to indicate amps or amperage (amps).
Resistance (Ohm)
Now that we have discussed the concepts of voltage and current, we are
ready to discuss a third key concept called resistance. Resistance is the
opposition to current flow. The amount of opposition to current flow
produced by a material depends upon the amount of available free electrons
it contains and the types of obstacles the electrons encounter as they attempt
to move through the material. The symbol (R) represents resistance in
equations.
One ohm is that amount of resistance that will limit the current in a
conductor to one ampere when the potential difference (voltage) applied to
the conductor is one volt.
The symbol for the ohm is the Greek letter capital omega (Ω).
If a voltage difference acts on a conductor, current flows. The amount of
current flow depends upon the resistance of the conductor: the lower the
resistance, the higher the current flow for a given amount of voltage; the
higher the resistance, the lower the current flow.
The relationship between these three parameters is referred to as Ohm’s
law, (𝐸 = 𝐼 × 𝑅) and will be covered in more detail later in the module.
Conductance (Siemens)
The opposite, or reciprocal, of resistance is conductance. Recall that
resistance is the opposition to current flow. Since resistance and
conductance are opposites, conductance is the ability to conduct current.
For example, if a wire has a high conductance, it will have low resistance,
and vice-versa. To calculate conductance, compute the reciprocal of the
resistance. Siemens is the unit used to specify conductance, named in honor
of German inventor Ernst Werner von Siemens. The symbol for electrical
conductance is capital letter S. When used in a formula, the letter G
represents conductance.
The equation below is the mathematical representation of conductance
obtained by relating the definition of conductance (1/R) to Ohm’s Law.
1
𝐼
=
𝑟𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑅
For example, if a resistor (R) has a value of five ohms; its conductance will
be 0.2 siemens.
𝐺=
14
Rev 1
Power (Watt)
Electricity generally performs work, such as turning a motor or generating
heat. Specifically, power is the rate of performing work, or the rate of heat
generation. The unit commonly used to specify electric power is the watt.
In equations, the capital letter P denotes power, and the capital letter W
denotes watts. Power is also described as the current (I) in a circuit
multiplied by the voltage (E) across the circuit. The equation below is a
mathematical representation of this concept.
𝑃 = 𝐼 × 𝐸 or 𝑃 = 𝐼𝐸
Using Ohm’s Law for the value of voltage (E), 𝐸 = 𝐼 × 𝑅 and using
substitution laws,
𝑃 = 𝐼 × (𝐼 × 𝑅)
Therefore, we can describe power as the current (I) in a circuit squared
multiplied by the resistance (R) of the circuit, or as the formula listed
below:
𝑃 = 𝐼2𝑅
Inductance (Henry)
Inductance is the ability of a coil to store energy, induce a voltage in itself,
and oppose changes in current flowing through it. The symbol used to
indicate inductance in electrical formulas and equations is a capital L.
Henries are the units of measurement for inductance.
The capital letter H denotes the henry. One henry is the amount of
inductance (L) that permits one volt to be induced (VL) when the current
through the coil changes at a rate of one ampere per second. The
mathematical representation of the rate of change in current through a coil
per unit time is:
∆𝐼
∆𝑡
The equation below is the mathematical representation for the voltage VL
induced in a coil with inductance L. The negative sign indicates that
voltage induced opposes the change in current through the coil per unit
time.
∆𝐼
∆𝑡
A later section in this lesson presents additional detail on inductance.
𝑉𝐿 = −𝐿
Capacitance (Farad)
Capacitance is the ability to store an electric charge, designated by the
capital letter C. Capacitance (C) units are farads; capacitance is equal to the
amount of charge (Q) that can be stored in a device or capacitor divided by
the voltage (E) applied across the device or capacitor plates when the charge
was stored. The equation below is the mathematical representation for
capacitance.
Rev 1
15
𝐶=
𝑄
𝐸
Frequency (Hertz)
Frequency (measured in hertz) is the number of alternating voltage or
current cycles completed per second.
Knowledge Check
Match the following terms to their appropriate definitions.
1. Henry
A.
Frequency
2. Farad
B.
Inductance
3. Siemen
C.
Capacitance
4. Hertz
D.
Conductance
ELO 1.5 Applying Ohm's Law
Introduction
In this section, you will practice applying Ohm’s law to solve problems.
In 1827, George Simon Ohm discovered that there was a definite
relationship between voltage, current, and resistance in an electrical circuit.
Ohm’s law defines this relationship, stated mathematically below.
𝐸 = 𝐼 × 𝑅 or 𝐸 = 𝐼𝑅
Applying Ohm's Law
Ohm's law states the relationship between voltage, current, and resistance.
It is possible to solve for any unknown value, given the other two values of
the formula. The table below gives the steps necessary to calculate the
unknown quantity.
Step
1.
Action
Determine the unknown and
choose the appropriate form of
Ohm's Law.
2.
Insert the known values into the
equation.
3.
Solve for the unknown quantity.
16
Result
𝐸 = 𝐼𝑅; 𝐼 =
𝐸
𝑅
𝐸
; 𝑜𝑟 𝑅 = 𝐼
Rev 1
Ohm's Law Demonstration 1
Given that I = 2 A, E = 12 V, find the circuit resistance.
Step
Action
Result
𝑅=
𝐸
𝐼
Insert the known values into the
equation.
𝑅=
12 𝑉
2𝐴
Solve for the unknown quantity.
𝑅 = 6 𝑂ℎ𝑚𝑠
1.
Determine the unknown and choose the
appropriate form of Ohm's Law. (𝐸 =
𝐸
𝐸
𝐼𝑅; 𝐼 = 𝑅; or 𝑅 = 𝐼 )
2.
3.
Ohm's Law Demonstration 2
Given that I = 4 A, R = 30 Ohms, find the circuit voltage.
Step
Action
Result
Determine the unknown and choose the
appropriate form of Ohm's Law. (𝐸 =
𝐸
𝐸
𝐼𝑅; 𝐼 = ; or 𝑅 = )
𝐸 =𝐼×𝑅
2.
Insert the known values into the
equation.
𝐸 = 4 𝐴 × 30 𝑂ℎ𝑚𝑠
3.
Solve for the unknown quantity.
𝐸 = 120 𝑣𝑜𝑙𝑡𝑠
1.
𝑅
Rev 1
𝐼
17
Knowledge Check
Given E = 260 V and R = 240 Ω, what current will
flow through a circuit?
A.
0.923 A
B.
0.923 V
C.
1.083 A
D.
1.083 V
Knowledge Check
How much current would a hot tub draw if it will run at
220 V and the resistance is 8 Ω?
A.
0.275 A
B.
3.63 A
C.
27.5 A
D.
36.6 A
TLO 1 Summary
In this section, you learned electrical terminology that you will use
throughout this course and your career. You also learned to apply Ohm's
law, which is one of the most useful tools in analyzing electrical circuits.
Now that you have completed this lesson, you should be able to:
1. Describe the basic composition of an atom and the concept of electron
flow.
2. Define the following terms and their characteristics: electrostatic
force, potential difference, electromotive force, ion charge, and
Coulomb's Law.
3. Define the following electrical terms: conductor, insulator, resistor,
voltage, current, electron, and conventional current flow, direct and
alternating current, and real and ideal sources.
4. Describe the following electrical parameters, including the unit of
measurement and the relationship to other parameters: voltage,
current, resistance, conductance, power, inductance, capacitance, and
frequency.
5. Given any two of the three component values of Ohm’s Law, solve
for the unknown component value.
18
Rev 1
TLO 2 Magnetism
Overview
Certain metals and metallic oxides have the ability to attract other metals.
This property is magnetism, and the materials that have this property are
termed magnets. Some magnets occur naturally; manufacturing processes
can produce others.
Understanding magnetism and its role in electrical generation is necessary
to monitor and operate electrical machines.
Objectives
Upon completion of this lesson, you will be able to do the following:
1. Describe the relationship between magnetic materials, electron
domains, and the law of magnetism.
2. Define the following magnetic terms: flux, flux density, permeability,
magnetomotive force, and reluctance.
3. Describe the following materials as they relate to permeability, giving
an example for each type of material: ferromagnetic, paramagnetic,
and diamagnetic.
4. Apply the Left-Hand Rule for current carrying conductors to
determine the direction of lines of magnetic flux.
5. Apply the Left-Hand Rule for coils to determine the polarity of a coil.
6. Describe the operation of a simple magnetic circuit including effects
of hysteresis.
7. Given Faraday’s Law of Induced Voltage, describe how varying
parameters affect induced voltage.
ELO 2.1 Electron Domains and Law of Magnetism
Introduction
In this section, you will learn how electron domains cause magnetic
attraction.
Electron Domains
Magnetism is a result of electrons spinning on their axis around the nucleus
of an atom, as shown in the figure below.
Rev 1
19
Figure: Producing a Magnetic Field
In magnetic materials, the atoms have areas called domains that align in
such a way that their electrons tend to spin in the same direction as shown
in the figure below. When the domains align such that electrons spin in the
same direction, the object develops magnetic poles.
Figure: Magnetic Domains
Magnetism
Certain metals and metallic oxides have the ability to attract other metals.
Magnetism is the name for this property, and the materials that have this
property are called magnets. Some magnets occur naturally; manufacturing
processes can produce others.
Law of Magnetism
The alignment of atom domains results in the formation of magnetic poles
at each end of the magnet. These poles are the north magnetic pole and the
20
Rev 1
south magnetic pole. The law of magnetism states that like magnetic poles
repel and unlike magnetic poles attract, as shown in the figure below.
Figure: Magnetic Attraction and Repulsion
Knowledge Check
The alignment of electrons spinning around their nuclei
creates magnetic fields.
A.
True
B.
False
Knowledge Check
Select all that are true. According to the Law of
Magnetism...
A.
unlike magnetic poles attract.
B.
like magnetic poles repel.
C.
magnets can be made of any kind of material.
D.
magnetism is caused by metal forging and does not
occur naturally.
ELO 2.2 Magnetic Terms
Introduction
In this section, you will learn common magnetic terms.
Rev 1
21
Magnetic Flux
Magnetic flux is the group of magnetic field lines emitted outward from the
north pole of a magnet. The symbol for magnetic flux is the Greek letter Φ
(phi).
The weber (Wb) is the SI unit for magnetic flux. One weber is equal to 1 x
108 magnetic field lines.
Magnetic Flux Density
Magnetic flux density (B) is the amount of magnetic flux that passes
through a certain area, perpendicular to the direction of magnetic flow, also
commonly called magnetic induction. The figure below depicts magnetic
flux density. The flux density units are Weber/meter2 in SI or in Tesla in
CGS units.
Figure: Flux Density
Permeability
Permeability is a measure of the ability of a material to support the
formation of a magnetic field within itself; or the degree of magnetization
that a material obtains in response to an applied magnetic field. The Greek
letter μ represents magnetic permeability. Permeability (µ) refers to the
ability of a material to concentrate magnetic lines of flux. The higher
permeability, the greater the material’s ability to concentrate magnetic flux;
this increases the material’s probability of becoming magnetized.
Magnetomotive Force
Magnetomotive force (MMF) is the strength of a magnetic field in a coil of
wire. The amount of current flowing in the turns of the coil determines the
MMF: the more current, the stronger the magnetic field; the more turns of
wire, the more concentrated the lines of force.
Reluctance
Reluctance is the opposition to the production of flux in a material,
corresponding to resistance. Reluctance is inversely proportional to
permeability. Iron cores have high permeability and, therefore, low
22
Rev 1
reluctance. Air has a low permeability and, therefore, a high reluctance.
The figure below shows four arrangements with varying reluctance.
Figure: Different Physical Forms of Electromagnets
Generally, different types of materials have different values of reluctance as
shown in the figure above. The air gap is the air space between two poles
of a magnet. Air is nonmagnetic and does not concentrate magnetic lines of
flux. Since air has a very high reluctance, the size of the air gap affects the
value of reluctance: the shorter the air gap, the stronger the field in the gap.
A larger air gap provides space for the magnetic lines to spread out.
Knowledge Check
Match the following terms to their appropriate definitions.
1. Opposition to the production of flux in
a material
A. Reluctance
2. The ability of a material to concentrate
magnetic lines of flux
B. Magnetic flux
3. The group of magnetic field lines
emitted outward from the north pole of
a magnet
C. Permeability
4. The strength of a magnetic field in a
coil of wire
D. Magnetomotive
force
Rev 1
23
ELO 2.3 Magnetic Materials
Introduction
Magnetic materials have the ability to be magnetized, and are those
materials that can be either attracted or repelled by a magnet. The most
commonly used magnetic materials are iron and steel.
A permanent magnet is made of a very hard magnetic material, such as
cobalt steel, that retains its magnetism long after removal of the
magnetizing field. A temporary magnet is a material that loses its
magnetism upon removal of the magnetizing field.
Classification of Magnetic Materials
There are two classes of magnetic materials: magnetic or nonmagnetic,
based on the highly magnetic properties of iron. There are three subgroups
of magnetic materials, based on their relative permeability.
1. Ferromagnetic Materials
Ferrites are nonmagnetic, but have the ferromagnetic properties of
iron. Ferrites are made of ceramic material and have a relative
permeability that ranges from 50 to 200. Coils for RF (radio
frequency) transformers commonly use ferrites. Iron, steel, nickel,
cobalt, and the commercial alloys of alnico and peralloy are examples
of ferromagnetic materials.
2. Paramagnetic Materials
These materials have a relative permeability of slightly more than
one, and lose their magnetism upon removal of the magnetizing field.
Aluminum, platinum, manganese, and chromium are examples of
paramagnetic materials.
3. Diamagnetic Materials
These materials have a relative permeability of less than one, and
magnetic fields repel them. Bismuth, antimony, copper, zinc,
mercury, gold, and silver are examples of diamagnetic materials.
Knowledge Check
Match the followings terms to their appropriate definitions.
1. Iron, steel, nickel, cobalt, alnico and
peralloy
A. Diamagnetic
material
2. Aluminum, platinum, manganese,
and chromium
B. Ferromagnetic
material
3. Bismuth, antimony, copper, zinc,
mercury, gold, and silver
C. Paramagnetic
material
24
Rev 1
ELO 2.4 Left-Hand Rule for Current Carrying Conductors
Introduction
In 1819, a Danish scientist named Oersted discovered the relationship
between magnetism and electrical current. Oersted found that when an
electric current flowed through a conductor, the conductor produced a
magnetic field around that conductor. The figure below depicts the
magnetic field produced by current flow through a conductor.
Figure: Magnetic Field Produced by Current Carrying Conductor
Left-Hand Rule for Current Carrying Conductors
A convenient way to determine the relationship between the current flow
through a conductor and the direction of the magnetic lines of force around
the conductor is the left-hand rule for current carrying conductors.
Step
Action
1.
Determine the direction of electron flow.
2.
Wrap your left hand around the conductor with the thumb pointing
in the direction of electron flow.
3.
Your fingers are coiling around the conductor in the direction of
the magnetic lines of flux.
The illustration below helps explain the use of the left-hand rule.
Figure: Left-Hand Rule for Current Carrying Conductors
Rev 1
25
Left-Hand Rule for Current Carrying Conductors
Note
Remember that this rule works with electron flow only.
When using conventional current, a right-hand rule is used
to depict the magnetic lines of force.
Left-Hand Rule for Current Carrying Conductors
Step
In order to use this rule, imagine a copper wire in front of you,
with electron flow moving from your left to your right.
Employing the steps for use of the left-hand rule:
1.
Determine the direction of electron flow. The problem stated that
electron flow was from your left to your right.
2.
Wrap your left hand around the conductor with the thumb pointing
in the direction of electron flow. In order to do this, your left
thumb must be pointing from left to right, which means your hand
wraps around the conductor with the palm facing down.
3.
Your fingers are coiling around the conductor in the direction of
the magnetic lines of flux. Your fingers are curling over the top of
the conductor, down the far side and under the conductor back to
you. This is the direction of the magnetic lines of flux induced by
current in this conductor.
Knowledge Check
The left-hand rule for current carrying conductors will
work for both electron flow and conventional flow
problems.
A.
True
B.
False
ELO 2.5 Left-Hand Rule for Coils
Introduction
Bending a straight conductor into a loop has two results:
1. Magnetic field lines become denser inside the loop.
2. All lines inside the loop align in the same direction.
Left-Hand Rule for Coils
When a conductor is shaped into several loops, it is considered to be a coil.
To determine the polarity of a coil, use the left-hand rule for coils.
26
Rev 1
Step
Action
1.
Determine the direction of electron flow.
2.
Wrap your left hand around the coil, with your fingers pointing in
the direction of electron flow. (see illustration below)
3.
Your thumb will be pointing to the north pole of the induced
magnetic field.
The figure below illustrates the left-hand rule for coils.
Figure: Left-hand rule for Coils
Left-Hand Rule for Coils Demonstration
Consider a coil lying on the desk in front of you. If electrons are flowing
through the coil, up the side nearest you and over the top of the coil away
from you, use the left-hand rule for coils to identify the north magnetic pole
induced by the coil.
Since the electrons are flowing upward on the near side of the coil and then
over the top of the coil away from you, your left hand should be placed with
the fingers pointing around the coil in the same direction. The palm will be
away from you, and your fingers will point up and away from you over the
coil. Your left thumb will point to your right. This is the direction of the
induced north magnetic pole.
Rev 1
27
Knowledge Check
A student is properly demonstrating the left-hand rule
for coils to another student. If his fingers wrap around
the coil in the direction of current flow, his thumb will
be pointing...
A.
vertically down from the coil.
B.
toward the south magnetic pole.
C.
vertically up from the coil.
D.
toward the north magnetic pole.
ELO 2.6 Hysteresis Losses and Magnetic Circuits
Introduction
In this section, you will learn about hysteresis and magnetic circuits.
Hysteresis
After magnetizing a ferromagnetic material in one direction, the material
will not relax back to zero magnetism upon removal of the imposed
magnetic field.
Ask class to give the definition of a ferromagnetic
material and some common examples of the type of
material, as a review of a previous module ELO.
Hint
Hysteresis Loop
A hysteresis loop exists because some of the magnetic domains in the
material remain aligned after removal of the magnetizing field. This
property is residual magnetism and is desirable in some applications, such
as an electromagnet. However, in a device such as a coil, residual
magnetism is undesirable because considerable energy is required to realign
the magnetic domains as the current reverses direction many times per
second.
Hysteresis is the name for this phenomenon. Hysteresis means a lagging
behind. The magnetic flux in an iron core lags behind the magnetizing
force because of the energy required to align the magnetic domains in the
material.
Hysteresis losses refer to this expenditure of energy to realign magnetic
domains in a ferromagnetic material. The figure below shows an example
of a hysteresis loop for a particular ferromagnetic material. The larger the
area enclosed by the loop, the greater the hysteresis losses associated with
the material.
28
Rev 1
Figure: Hysteresis Loop
Magnetic Circuits
Many common electrical components take advantage of the properties of
electromagnetism discussed above. Electrical contactors, starters, relays
and solenoids all rely on electromagnets for operation. The figure below
shows a circuit where electrical energy creates magnetic flux that actuates a
moveable contact.
Figure: Simple Magnetic Circuit
If the switch in the figure above is closed, electric current flows through the
circuit. The current magnetizes the core of the coil, creating a powerful
magnet. The magnet attracts the movable armature, and the armature
moves towards the magnet (closed). This movement can close valves, close
sets of electrical contacts, etc. Opening the switch interrupts current flow,
the magnetic field collapses and the spring on the armature returns it to its
original position (open).
Rev 1
29
Knowledge Check
The expenditure of energy to realign magnetic domains
in a ferromagnetic material is called...
A.
polarity reversal.
B.
hysteresis.
C.
hysteresis loss.
D.
magnetic permeability.
ELO 2.7 Faraday's Law of Induced Voltage
Introduction
In 1831, Michael Faraday discovered electromagnetic induction. Faraday
found that if a conductor intersects with lines of magnetic force, or if
magnetic lines of force intersect with a conductor, a voltage, or EMF, is
induced into the conductor.
Induced Voltage
Consider a magnet with its magnetic lines of force from the north pole to
the south pole as shown in the figure below. If a conductor (C), connected
to a galvanometer (G), moves across the magnetic field, it will indicate the
presence of voltage, or EMF on the galvanometer. When the conductor is
stationary, the galvanometer indicates zero EMF.
If we move the conductor outside the magnetic field at position 1, the
galvanometer still indicates zero EMF. If we move the conductor to
position 2, intersecting the lines of magnetic force, the galvanometer will
deflect to point A. If we move the conductor d to position 3, the
galvanometer will return to zero.
By reversing the direction in which the conductor is moved (position 3 to
position 1), the same results will be noticed, but of opposite polarity. If the
conductor is stationary in the magnetic lines of force, at position 2, the
galvanometer will indicate zero. The results derived from this example
show that there must be relative motion between the conductor and the
magnetic lines of force in order to induce an EMF or voltage in the
conductor.
30
Rev 1
Figure: Induced EMF
Electric generators demonstrate the most important application of this
relative motion between a conductor and a magnetic field. For example, in
a DC generator, a cylindrical housing contains electromagnets. Conductors,
in the form of coils, rotate on a core such that the coils continually cut the
magnetic lines of force. The result is a voltage induced in each of the
conductors. These conductors are connected in series, and the induced
voltages are added together to produce the generator’s output voltage.
Faraday's Law
The magnitude of the induced voltage depends on two factors:
1. The number of turns of a coil
2. How fast the conductor cuts across the magnetic lines of force, or flux
The equation below is the mathematical representation for Faraday’s Law of
Induced Voltage.
𝑉𝑖𝑛𝑑 = −𝑁
∆Φ
∆𝑡
Where:
Vind = induced voltage
N = number of turns in a coil
ΔΦ = change in flux
Δt = change in time
Faraday's Law Example
Step
1.
2.
Rev 1
Given: Flux = 4 Wb. The flux increases uniformly to 8 Wb in
a period of 2 seconds. Find induced voltage in a coil that has
12 turns, if the coil is stationary in the magnetic field.
𝑉𝑖𝑛𝑑 = −𝑁
∆𝛷
∆𝑡
𝛥𝛷 = 8 𝑊𝑏 − 4 𝑊𝑏 = 4 𝑊𝑏
31
Step
Given: Flux = 4 Wb. The flux increases uniformly to 8 Wb in
a period of 2 seconds. Find induced voltage in a coil that has
12 turns, if the coil is stationary in the magnetic field.
3.
𝛥𝑡 = 2𝑠
4.
∆𝛷 4 𝑊𝑏 2 𝑊𝑏
=
=
∆𝑡
2𝑠
𝑠
5.
𝑉𝑖𝑛𝑑 = −12(2) = −24 𝑣𝑜𝑙𝑡𝑠
Lenz's Law
Lenz’s Law determines the polarity of the induced voltage described by
Faraday. Lenz discovered that the induced voltage has a polarity that will
oppose the change causing the induced voltage.
When current flows due to the induced voltage, a magnetic field is set up
around that conductor such that the conductor’s magnetic field reacts with
the external magnetic field. This reaction produces an induced voltage,
which opposes the change in the external magnetic field.
The negative sign in the mathematical statement of Faraday’s Law is an
indication that the EMF is in such a direction as to produce a current whose
flux, if added to the original flux, would reduce the magnitude of the EMF.
Knowledge Check
According to Faraday's Law, which of the following
factors influence the magnitude of induced voltage?
(Select all that are correct)
32
A.
Diameter of the conductor
B.
Length of the conductor
C.
How fast the conductor cuts across the magnetic lines
of flux
D.
Number of turns in the coil
Rev 1
TLO 2 Summary
In this section, you learned the basic laws of magnetism, magnetism effects
on electric current, and magnetism effects on voltage. You also learned
how magnetic circuits are used as relays, solenoids and other useful circuit
components.
Now that you have completed this lesson, you should be able to:
1. Describe the relationship between magnetic materials, electron
domains, and the law of magnetism.
2. Define the following magnetic terms: flux, flux density, permeability,
magnetomotive force, and reluctance.
3. Describe the following materials as they relate to permeability, giving
an example for each type of material: ferromagnetic, paramagnetic,
and diamagnetic.
4. Apply the Left-Hand Rule for current carrying conductors to
determine the direction of lines of magnetic flux.
5. Apply the Left-Hand Rule for coils to determine the polarity of a coil.
6. Describe the operation of a simple magnetic circuit including effects
of hysteresis.
7. Given Faraday’s Law of Induced Voltage, describe how varying
parameters affect induced voltage.
TLO 3 Electrical Drawings
Overview
This section introduces the different types of electrical drawings and the
purpose of each type. You will also learn the common symbols used and
how to interpret the drawings.
Operators must frequently use electrical drawings to understand equipment
response. This capability is necessary to operate the power plant.
Objectives
Upon completion of this lesson, you will be able to do the following:
1. Given common standard electrical symbols in the lesson, identify the
component that the symbol represents.
2. Identify the following types of diagrams: schematic diagrams, oneline diagrams, and block diagrams.
3. Define the following electrical circuit terms and components:
resistivity, temperature coefficient of resistivity, resistance
temperature detector, electrical circuit, open circuit, closed circuit,
short circuit, series circuit, and parallel circuit.
4. Describe the principles of the following circuit protection devices:
protective relays, fuses, circuit breakers.
ELO 3.1 Electrical Symbols
Introduction
In order to read and interpret electrical system diagrams and schematics,
personnel must be thoroughly familiar with the many symbols used. With
Rev 1
33
mastery of these symbols, it will be relatively easy to understand most
electrical diagrams and schematics.
Electrical Symbols
The figure below contains common symbols for many circuit components.
Most suppliers will provide a dictionary of symbols with drawings, but
knowledge of common symbols is necessary to interpret drawings.
Figure: Common Electrical Drawing Symbols
34
Rev 1
Knowledge Check
Match the electrical symbols with their components.
A.
Fuse
1.
B.
Battery
2.
C.
Diode
3.
D.
Capacitor
4.
E.
AC power source
5.
F.
Relay
6.
ELO 3.2 Types of Drawings
Introduction
In this section, you will learn to identify the different types of electrical
drawings and the uses for each.
Schematic Diagrams
Schematic diagrams are the standard way to show information about
electrical and electronics circuits. On schematic diagrams, graphic symbols
represent the component parts, the previous section presented some of these
symbols. Because graphic symbols are small, it is possible to have
diagrams in a compact form. Lines represent wires connecting components.
The resultant schematic shows the relationship of those components with
one another.
As an example, look at a schematic diagram of a two-transistor radio circuit
in the figure below. This diagram, from left to right, shows the components
in the order the circuit uses them to convert radio waves into sound energy.
By using this schematic, it is possible to trace the operation of the circuit
from outside antenna to headset. Because of this important feature of
schematic diagrams, they are widely used in construction, maintenance, and
servicing of all types of electronic circuits.
Rev 1
35
Figure: Schematic Diagram
One-line Diagrams
The one-line, or single-line, diagram shows the components of a circuit
using single lines and the appropriate graphic symbols. One-line diagrams
show two or more conductors connected between components in the actual
circuit. The one-line diagram shows all pertinent information about the
sequence of the circuit, but does not give as much detail as a schematic
diagram. Normally, the one-line diagram shows highly complex systems
without showing the actual physical connections between components and
individual conductors.
The figure below shows a typical one-line diagram.
Figure: One-line Diagram
36
Rev 1
Block Diagrams
A block diagram shows the relationship between component groups, or
stages in a circuit. In block form, it shows the path through a circuit from
input to output, as shown in the figure below.
The blocks are squares or rectangles connected by single lines with
arrowheads at the terminal end, showing the direction of the signal path
from input to output. Normally, the necessary information to describe the
stages of components is contained in the blocks.
Figure: Block Diagram
Wiring Diagrams
A wiring diagram is a very simple way to show wiring connections in an
easy-to-follow manner. These types of diagrams are often included with
home appliances and automobile electrical systems. Wiring diagrams show
the component parts in pictorial form, with the components identified by
name. Most wiring diagrams also show the relative location of component
parts and color coding of conductors or leads.
The figure below shows a typical wiring diagram.
Figure: Wiring Diagram
Rev 1
37
Knowledge Check
Match the following terms to the appropriate definitions.
1. Shows wiring connections to trace the
operation of the circuit from beginning to
ending in an easy-to-follow manner,
standard way to show information about
electrical circuits.
A. One-line
diagram
2. Shows highly complex systems without
showing the actual physical connections
between components and individual
conductors.
B. Wiring
diagram
3. Shows the relationship between
component groups, or stages in a circuit.
C. Schematic
diagram
4. Shows wiring connections in an easy-tofollow manner.
D. Block
diagram
ELO 3.3 Circuit Terminology
Introduction
In this section, you will learn common terminology used to discuss
electrical circuits.
Resistivity
Resistivity is the measure of the resistance a material imposes on current
flow. The resistance of a given length of conductor depends upon the
specific resistance of the conductor material, the length of the conductor,
and the cross-sectional area of the conductor, as shown in the equation
below.
𝐿
𝐴
Where:
𝑅=𝜌
R = resistance of conductor, Ω
ρ = specific resistance or resistivity, cm-Ω/ft
L = length of conductor, ft
A = cross-sectional area of conductor, cm2
Specific resistance, denoted by the Greek letter ρ (rho), denotes a material's
inherent resistance, and allows comparisons of different materials'
38
Rev 1
resistances without regard to size, shape, length, or area. A higher rho value
indicates higher resistance.
Temperature Coefficient of Resistivity
Temperature coefficient of resistivity, Greek letter α (alpha), is the amount
of change of the resistance of a material for a given change in temperature.
A positive value of α indicates that R increases with temperature; a negative
value of α indicates R decreases; and zero α indicates that R is constant.
For a given material, α may vary with temperature; therefore, charts are
often used to describe how resistance of a material varies with temperature.
The equation below shows the relationship between resistance and
temperature in a material.
𝑅𝑡 = 𝑅𝑜 + 𝑅𝑜 (𝛼𝛥𝑇)
Where:
Rt = resistance of a material at a higher temperature
Ro = resistance at 20°C
α = temperature coefficient
ΔT = temperature rise above 20°C
Resistance Temperature Detector (RTD)
Temperature detecting devices such as resistance temperature detectors
(RTD) use this phenomenon of changing resistance with changes in
temperature to correlate temperature with a measured resistance change.
A RTD is a temperature probe made from a material that exhibits a linear
coefficient of resistance. As temperature changes, the resistance of the
RTD will vary in a predictable fashion. With a constant amount of current
flowing in the detector circuitry, a change in resistance will cause a change
in the voltage drop across the RTD (Ohm’s Law, E = I x R). When
calibrated to react to this voltage drop, a temperature meter indicates a
substance’s temperature.
Electrical Circuits
Each electrical circuit has at least four basic parts:




A source of electromotive force
Conductors
Load or loads
Some means of control
In the closed circuit below, the source of EMF is the battery and the
conductors are wires that connect the various component parts. The resistor
is the load and a switch is the circuit control device.
Closed Circuit
A closed circuit, shown below, is an uninterrupted, or unbroken, path for
current from the source (EMF), through the load, and back to the source.
Rev 1
39
Figure: Closed Electrical Circuit
Open Circuit
An open circuit, or incomplete circuit, exists if a break in the circuit occurs;
preventing a complete path for current flow. The figure below shows
examples of open circuits interrupting current flow.
Figure: Open Circuits
Short Circuit
A short circuit is a circuit that offers very little resistance to current flow
and can cause dangerously high current flow through the circuit.
An inadvertent connection between two points in a circuit usually causes a
short circuit, which offers little or no resistance to current flow compared to
the designed circuit. Shorting resistor R in the figure below will probably
cause the fuse to blow.
40
Rev 1
Figure: Short Circuit
Series Circuit
A series circuit is a circuit where there is only one path for current flow. In
the series circuit shown in the figure below, the current will be the same at
any point in the circuit. This means that the current flow through R1 is the
same as the current flow through R2 and R3.
Figure: Series Circuit
Parallel Circuits
Parallel circuits are circuits that have two or more components connected
across the same voltage source, as shown in the figure below. Resistors R1,
R2, and R3 are in parallel with each other and the source. Each parallel path
is a branch with its own individual current. When the current leaves the
source V, part I1 of IT will flow through R1; part I2 will flow through R2; and
part I3 will flow through R3. Current through each branch can be different;
however, voltage across each branch of the circuit will be equal.
Rev 1
41
V = V1 = V2 = V3
Figure: Parallel Circuit
Knowledge Check
Match the terms with their appropriate definitions.
1. A circuit with a break that prevents a
complete path so that no current flows
A. Series
Circuit
2. A circuit that offers very little resistance to
current flow and can cause dangerously high
current flow through the circuit
B. Parallel
Circuit
3. A circuit that has two or more components
connected across the same voltage source
C. Open
Circuit
4. A circuit where there is only one path for
current flow
D. Short
Circuit
42
Rev 1
ELO 3.4 Circuit Protection Devices
Introduction
In this section, you will learn about devices used to protect electrical
circuits from undesirable electrical conditions. These devises protect
equipment and people from currents and voltages outside their normal
operating ranges.
Relays
A protective relay is automatic device that senses an abnormal condition
and closes contacts. When these contacts close, they complete the circuit
breaker trip coil circuit and trip the breaker open to protect the rest of the
circuit from the from the abnormal condition. Some typical protective relay
parameters monitored are over current, over voltage, under frequency and
under voltage. The figure below shows two example relays.
Figure: Relays
Fuses
A fuse is a simple circuit protection device. It derives its name from the
Latin word "fusus," meaning, "to melt." Fuses have been in use almost
from the beginning of the use of electricity. The earliest type of fuse was
simply a bare wire between two connections. The wire was smaller than the
conductor it was protecting and, therefore, would melt before damage to the
conductor occurred.
Some "copper fuse link" types are still in use, but most fuses no longer use
copper as the fuse element (the part of the fuse that melts). After changing
from copper to other metals, tubes or enclosures were developed to hold the
melting metal. The enclosed fuse made possible the addition of filler
material, which helps to contain the arc that occurs when the element melts.
Rev 1
43
For many low power uses, the filler material is not required. A simple glass
tube is used. The use of a glass tube gives the added advantage of being
able to see when a fuse is open. Fuses of this type are common in
automobile or small electronic circuits.
The figure below shows several fuses and the symbols used to denote fuses
on schematics.
Figure: Typical Fuses and Schematic Symbols
Circuit Breakers
While a fuse protects a circuit, it destroys itself in the process of opening
the circuit. After correcting the problem that caused the increased current
or heat, personnel must replace the destroyed fuse with a new fuse in the
circuit. A circuit protection device that can be used more than once solves
the problem of replacement fuses. Resetting the device restores its
protection capability without parts replacement. This device is called a
circuit breaker because it breaks (opens) the circuit, when pre-determined
conditions are sensed, or can be used to manually open a circuit.
The figure below shows a typical circuit breaker and the appropriate
schematic symbols.
44
Rev 1
Figure: Typical Circuit Breaker and Schematic Symbols
Operating
Experience
There have been many incidents throughout the industry
where improper operation or lack of full understanding
of the proper circuit breaker operation have contributed
to plant events.
Review SER A 98-0035 and discuss operator/technician
responsibility and human performance barriers that
should have prevented this event.
Knowledge Check
A device which senses abnormal conditions and closes
contacts is called a:
Rev 1
A.
breaker
B.
safety sensor
C.
relay
D.
Thermal fuse
45
TLO 3 Summary
In this section, you learned common electrical symbols used in drawings,
the different types of electrical drawings, terminology for different circuit
types, and how temperature affects electrical resistance. The section also
introduced circuit protective devises used to protect equipment and
personnel from abnormal conditions.
Now that you have completed this lesson, you should be able to:
1. Given common standard electrical symbols in the lesson, identify the
component that the symbol represents.
2. Identify the following types of diagrams: schematic diagrams, oneline diagrams, and block diagrams.
3. Define the following electrical circuit terms and components:
resistivity, temperature coefficient of resistivity, resistance
temperature detector, electrical circuit, open circuit, closed circuit,
short circuit, series circuit, and parallel circuit.
4. Describe the principles of the following circuit protection devices:
protective relays, fuses, circuit breakers.
TLO 4 Batteries
Overview
In this section, you will learn how batteries and voltaic cells function, how
they are charged and discharged, and hazards they pose.
Batteries provide back-up power to vital loads. Operators must understand
batteries to monitor and ensure their proper operation.
Objectives
Upon completion of this lesson, you will be able to do the following:
1. State the purpose of a battery and define the common terms as they
relate to batteries and voltaic cells.
2. Describe the operation of a simple voltaic cell.
3. State the chemical equation that occurs when a lead-acid battery is
being charged or discharged.
4. Describe the relationship between total battery voltage, cell voltage,
and current for a series-connected and parallel-connected battery.
5. State the advantage of each of the common types of batteries.
6. Describe common battery hazards and precautions associated with
battery use.
ELO 4.1 Battery Terminology
Introduction
Modern technology uses batteries for a wide variety of services. The
purpose of a battery is to store chemical energy and to convert this chemical
energy into electrical energy when the need arises. To study battery
operation and characteristics, it is necessary to understand a few terms used
with batteries.
46
Rev 1
Battery Terminology
The table below includes some key battery terms.
Term
Definition
Voltaic Cell
The term voltaic cell is a combination of materials used
to convert chemical energy into electrical energy. A
voltaic or chemical cell consists of two electrodes made
of different types of metals or metallic compounds
placed in an electrolyte solution.
Battery
A battery is a group of two or more voltaic cells, usually
connected in series in order to obtain a desired voltage.
Each individual cell usually produces about 1.5 VDC.
Electrode
An electrode is a metallic compound, or metal, which
has an abundance of electrons (negative electrode) or an
abundance of positive charges (positive electrode).
Electrolyte
An electrolyte is a solution that is capable of conducting
an electric current. The electrolyte of a cell may be a
liquid or a paste. If the electrolyte is a paste, the cell is a
dry cell; if the electrolyte is a solution, it is a wet cell.
Specific Gravity
Specific gravity is the ratio comparing the weight of any liquid to the
weight of an equal volume of water. The specific gravity of pure water is
1.000. Lead-acid batteries use an electrolyte, which contains sulfuric acid.
Pure sulfuric acid has a specific gravity of 1.835, since it weighs 1.835
times as much as pure water per unit volume.
Since the electrolyte of a lead-acid battery consists of a mixture of water
and sulfuric acid, the specific gravity of the electrolyte will fall between
1.000 and 1.835. Normally, the solution of water and sulfuric acid
electrolyte for this type of battery has specific gravity is less than 1.350.
A hydrometer measures specific gravity of a liquid. A simple hydrometer
consists of a glass float inside a glass tube, as shown in the figure below.
The glass hydrometer float has a weight at one end to maintain it vertical,
and seals at both ends. A scale calibrated in specific gravity runs
lengthwise along the body of the float. The float is free to move vertically
inside the glass tube, and the fluid with the unknown specific gravity
partially fills the glass tube. Depressing the suction bulb, inserting the
hydrometer base into the electrolyte, and releasing the suction bulb draws
electrolyte solution into the hydrometer. As the fluid enters the tube, the
hydrometer float will reach a certain equilibrium level in the fluid.
Rev 1
47
The extent to which the hydrometer float protrudes above the level of the
fluid depends on the specific gravity of the fluid. The reading on the float
scale at the surface of the fluid is the specific gravity of the fluid.
Figure: Simple Hydrometer
Battery Terminology
The table below includes additional battery terms and their definitions.
Term
Definition
Ampere-Hour
One ampere-hour is a current of one ampere flowing for
one hour. If you multiply the current in amperes by the
time of flow in hours, the result is the total number of
ampere-hours. Ampere-hours normally indicate the
amount of energy a storage battery can deliver.
Primary Cell
Primary cells are cells that cannot be recharged after their
voltage output has dropped to a value that is not usable.
Dry cells used in flashlights and transistor radios (e.g.,
AA cells, C cells) are examples of primary cells.
Secondary
Cells
Secondary cells are cells that will accept recharging to
nearly their original condition. The most common
example of a secondary, or rechargeable cell, is the leadacid automobile battery.
48
Rev 1
Term
Definition
Capacity
The capacity of a storage battery determines how long
the storage battery will operate at a certain discharge
rate, usually stated in ampere-hours. For example,
discharging a 120 ampere-hour battery at 10 amps per
hour will be completely discharge the battery after 12
hours.
Shelf Life
The shelf life of a battery is the time that a battery may
be stored and retain at least 90 percent of its original
capacity.
Charge
The charge of a battery may refer to one of two things:


Discharge
Relative state of capacity of the battery
Actual act of applying current flow in the reverse
direction to return the battery to a fully charged
state
Discharge is the act of drawing current from a battery.
Knowledge Check
Match the following terms with their appropriate definition.
1. cells that cannot be returned to a good
condition, or recharged after their voltage
output has dropped to a value that is not
usable
A.
Capacity
2. a solution which is capable of conducting
an electric current
B.
Primary cell
3. a current of one ampere flowing for one
hour
C.
Ampere-hour
4. the length of time that a storage battery
will operate at a certain discharge rate;
usually given in ampere-hours
D.
Electrolyte
Rev 1
49
ELO 4.2 Simple Voltaic Cell
Introduction
The purpose of a battery is to store chemical energy and to convert this
chemical energy into electrical energy when the need arises. A chemical
cell (or voltaic cell) consists of two electrodes of different types of metals or
metallic compounds and an electrolyte solution, which is capable of
conducting an electric current.
Simple Voltaic Cell
A good example of a voltaic cell is one that contains zinc and copper
electrodes. The zinc electrode contains an abundance of negatively charged
atoms, and the copper electrode contains an abundance of positively
charged atoms. Upon insertion of both of these electrodes in an electrolyte,
chemical action begins. The zinc electrode will accumulate a much larger
negative charge because some of it will dissolve into the electrolyte.
The atoms that leave the zinc electrode have a positive charge; the
negatively charged ions of the electrolyte attract these atoms. The
positively charged atoms repel the positive charged ions of the electrolyte
toward the copper electrode as shown in the figure below.
Figure: Chemical Production of Electricity
This action causes removal of electrons from the copper electrode, leaving it
with an excess of positive charge. Upon connection of a load across the
electrodes, the forces of attraction and repulsion will cause the free
electrons in the negative zinc electrode to move through the connecting wire
and load, and toward the positive copper electrode as shown in the figure
below.
The potential difference that results allows the cell to function as a source of
applied voltage.
50
Rev 1
Figure: Electron Flow through a Battery
Knowledge Check
Components of a simple voltaic cell include
_____________. Select all that are correct.
A.
electrolyte solution
B.
terminals
C.
hydrochloric acid
D.
two electrodes
ELO 4.3 Chemistry of a Lead-Acid Battery
Introduction
In this section, you will learn the chemical action that produces electricity in
a lead-acid battery.
Discharge and Charging of a Lead-Acid Battery
In a lead-acid battery, an electrolytic solution of diluted sulfuric acid
(H2SO4) acts electro-chemically on two types of lead. The positive plate
consists of lead peroxide (PbO2), and the negative plate is sponge lead (Pb),
as shown in the figure below.
Figure: Chemical Action during Discharge
Rev 1
51
Discharge
When a lead-acid battery discharges, the electrolyte separates into H2 and
SO4. The H2 will combine with some of the oxygen formed on the positive
plate to produce water (H2O), and thereby reduces the amount of acid in the
electrolyte. The sulfate (SO4) combines with the lead (Pb) of both plates,
forming lead sulfate (PbSO4), as shown below.
𝑃𝑏𝑂2 + 𝑃𝑏 + 2𝐻2 𝑆𝑂4 → 2𝑃𝑏𝑆𝑂4 + 2𝐻2 𝑂
Charging
When charging a lead-acid battery, the action described in the discharge
reverses because the electron flow reverses. This reversed electron flow
drives the lead sulfate (PbSO4) off the plates and back into the electrolyte
(H2SO4). The return of acid to the electrolyte will reduce the sulfate on the
plates and increase the specific gravity of the electrolyte. This will continue
to happen until the process drives all of the lead sulfate from the plates and
back into the electrolyte, as shown in the figure below.
Figure: Chemical Action during Charging
Chemically, the reaction is:
2𝑃𝑏𝑆𝑂4 + 2𝐻2 𝑂 → 𝑃𝑏𝑂2 + 𝑃𝑏 + 2𝐻2 𝑆𝑂4
Gasses during Charging
During charging, and as a lead-acid battery charge nears completion,
operators frequently raise the charging current to drive the remaining lead
sulfate off the plates. This liberates hydrogen (H2) gas at the negative plate,
and oxygen (O2) gas at the positive plate. The excessive current also
ionizes the water (H2O) in the electrolyte.
Since hydrogen is highly explosive, and oxygen is highly flammable, it is
necessary to provide adequate ventilation to the battery whenever charging
is in progress. In addition, do not allow any smoking, electric sparks, or
open flames near a charging battery.
Electrolyte Specific Gravity and State of Charge
The specific gravity of the electrolyte decreases as the battery discharges
and increases to its normal, original value as it is charged. The decrease in
52
Rev 1
specific gravity on discharge is proportional to the ampere-hours
discharged. Since specific gravity of a lead-acid battery decreases
proportionally during discharge, the value of specific gravity at any given
time is an approximate indication of the battery’s state of charge. To
determine the state of charge, compare the specific gravity of the electrolyte
with the full charge specific gravity value from the manufacturer’s data.
Knowledge Check
The electrolyte in a lead-acid battery is
___________________.
A.
made of sulfuric acid and mineral oil
B.
chosen for its properties as a non-conductor
C.
a solution of sulfuric acid and pure water
D.
not involved in the chemical reactions, but just works
as an insulating medium between the electrodes
ELO 4.4 Series and Parallel Connected Batteries
Introduction
In this section, you will learn the characteristics of series connected and
parallel connected batteries.
Series Cells
When connecting several cells in series as shown in the figure below, the
total voltage output of the battery is equal to the sum of the individual cell
voltages. In the example of the batteries shown in the figure below, the
four-1.5 V cells provide a total of 6 volts. When connecting cells in series,
the positive terminal of one cell connects to the negative terminal of the
next cell. The current flow through batteries connected in series is the same
as for one cell.
The advantage of connecting cells in this manner is that multiple seriesconnected battery cells exhibit a higher voltage output than a single cell.
Rev 1
53
Figure: Battery Cells in Series
Parallel Cells
When connecting cells in parallel, the total current capacity of the battery is
equal to the sum of the individual cell amperages. When connecting cells in
parallel, all the positive terminals connect together, and all the negative
terminals connect together, as shown in the figure below.
The total voltage output of a battery connected in parallel is the same as that
of a single cell. Cells connected in parallel have the same effect as
increasing the size of the electrodes and electrolyte in a single cell.
The advantage of connecting cells in parallel is that it will increase the
current-carrying capability of the battery.
Figure: Battery Cells in Parallel
54
Rev 1
Internal Resistance
Internal resistance in a chemical cell is due mainly to the resistance of the
electrolyte between electrodes. Current flowing through a battery will
produce a voltage drop across the battery due to this internal resistance,
lowering the battery’s terminal voltage. This resistance to current flow
through the battery itself can limit the amount of current the battery is able
to produce when it is discharging.
Knowledge Check
A series connected battery provides a higher voltage
than connecting the same cells in parallel.
A.
True
B.
False
ELO 4.5 Types of Battery Materials
Introduction
The type of electrolyte the battery uses determines its basic category; there
are wet and dry cells. The electrolyte of a cell may be a liquid or a paste. If
the electrolyte is a paste, the cell is a dry cell. If the electrolyte is a liquid
solution, the cell is a wet cell.
Carbon-Zinc Cell
The carbon-zinc cell is one of the oldest and most widely used types of dry
cells. The carbon in the battery is a rod in the center of the cell, which acts
as the positive terminal. Zinc comprises the case, and acts as the negative
electrode. The electrolyte for this type of cell is a chemical paste-like
mixture that fills the space between the carbon electrode and the zinc case.
Sealing the cell prevents any of the liquid in the paste from evaporating.
The advantage of a carbon-zinc battery is that it is durable and very
inexpensive to produce. The cell voltage for this type of cell is about 1.5
volts.
Alkaline Cell
The alkaline cell has an alkaline electrolyte of potassium hydroxide. Zinc
comprises the negative electrode, and manganese dioxide comprises the
positive electrode. The typical alkaline cell also generates 1.5 volts. The
alkaline cell has the advantage of an extended life over that of a carbon-zinc
cell of the same size; however, it is usually more expensive to produce.
Nickel-Cadmium Cell
The nickel-cadmium cell is a secondary cell, and the electrolyte is
potassium hydroxide. The negative electrode is nickel hydroxide, and the
positive electrode is cadmium hydroxide. The nominal voltage of a nickelcadmium cell is 1.25 volts. The nickel-cadmium battery has the advantage
of being a dry cell that is a true storage battery with a reversible chemical
reaction (i.e., it can be recharged). The nickel-cadmium battery is a rugged,
Rev 1
55
dependable battery. It gives dependable service under extreme conditions
of temperature, shock, and vibration. Due to its dependability, it is ideally
suited for use in portable communications equipment.
Knowledge Check
Match the battery type with the appropriate description.
1. Electrolyte is a paste
A. Wet cell
2. Rechargeable dry cell
B. Dry cell
3. Longer life than carbon zinc cell
C. Nickelcadmium cell
4. Electrolyte is a liquid solution
D. Alkaline cell
ELO 4.6 Battery Hazards
Introduction
In this section, you will learn the dangers posed by batteries and methods to
minimize these hazards.
Shorted Cell
It is possible to have a short circuit in a cell. Possible causes include the
following: faulty separators, lead particles or other metals forming a circuit
between the positive and negative plates, buckling of the plates, or
excessive sediments in the bottom of the cell. The primary cause of some
of these occurrences is overcharging and over-discharging of the battery,
which causes sediment to build up in bottom of the cell due to flaking of
active material and buckling of cell plates.
Avoid overcharging and over-discharging at all costs. Shorted cells cause a
great reduction in battery capacity. Each shorted cell reduces battery
capacity by a fraction equal to one divided by the total number of cells.
Hydrogen and Oxygen Gas Generation
A lead-acid battery cannot absorb all the energy from the charging source
when the battery is nearing the completion of the charge. This excess
energy dissociates water by way of electrolysis into hydrogen and oxygen.
The positive plate produces oxygen, and the negative plate produces
hydrogen. This process is gassing.
56
Rev 1
Gassing is first noticed when cell voltage reaches 2.30-2.35 volts per cell
and increases as the charge progresses. At full charge, the amount of
hydrogen produced is about one cubic foot per cell for each 63 amperehours input. If gassing occurs and the gases collect, they produce an
explosive mixture of hydrogen and oxygen. It is necessary to provide
adequate ventilation near the charging battery and keep the area free of any
open flames or spark-producing equipment.
When the battery voltage is greater than 2.30 volts per cell, gassing will
occur and cannot be prevented entirely. To reduce the amount of gassing,
limit charging voltage level to 2.30 volts per cell. For example, limit
charging voltage level to 13.8 volts for a 12-volt battery with 6 cells (2.30
volts/cell x 6 cells = 13.8 volts).
Heat Generation
For best battery service, maintain the operating temperature of a battery in
the band of 16-27°C (60-80°F). Whenever the battery is charged, the
current flowing through the battery will cause heat generation by the
electrolysis of water.
The current flowing through the battery (I) will also cause heat to be
generated (P) during charge and discharge as it passes through the internal
resistance (Ri), as illustrated using the formula for power below.
𝑃 = 𝐼 2 𝑅𝑖
Higher temperatures will give some additional capacity, but they will
eventually reduce the life of the battery. Very high temperatures, 52°C
(125°F) and higher, can actually do damage to the battery and cause early
failure.
Low temperatures will lower battery capacity but also prolong battery life
under floating (i.e., slightly charging) operation or storage. Extremely low
temperatures can freeze the electrolyte, but only if the battery is low in
specific gravity.
Knowledge Check
Battery temperatures exceeding 105°F can cause
damage and early failure of the battery
Rev 1
A.
True
B.
False
57
TLO 4 Summary
In this section, you learned the types of batteries, the chemical reactions in
which batteries produce electricity, and the hazards of battery operation.
Now that you have completed this lesson, you should be able to:
1. State the purpose of a battery and define the common terms as they
relate to batteries and voltaic cells.
2. Describe the operation of a simple voltaic cell.
3. State the chemical equation that occurs when a lead-acid battery is
being charged or discharged.
4. Describe the relationship between total battery voltage, cell voltage,
and current for a series-connected and parallel-connected battery.
5. State the advantage of each of the common types of batteries.
6. Describe common battery hazards and precautions associated with
battery use.
TLO 5 DC Circuit Analysis
Overview
In this section, you will learn to analyze DC circuits and determine currents,
voltages, and resistances in the circuits.
Operators must be able to analyze basic circuits in order to understand how
electrical circuits and machines operate and how they may fail.
Objectives
Upon completion of this lesson, you will be able to do the following:
1. Calculate total resistance for a series or parallel circuit.
2. Explain the terms voltage divider and current divider.
3. Given a DC electrical circuit, identify the polarity of the voltage drops
in the circuit.
4. State Kirchhoff’s voltage law and current law.
5. Solve problems for voltage and current using Kirchhoff’s laws.
ELO 5.1 Total Resistance
Introduction
In this section, we will review how to calculate the total resistance in series
and parallel circuits, and work problems calculating resistance.
Each type of DC circuit includes certain characteristics that determine the
way its voltage and current behave. To begin analysis of the voltages and
currents at each part of a circuit, an understanding of these characteristics is
necessary.
Series Circuits
A series circuit is an electrical circuit in which there is only one flow path
for current, and it passes through all circuit components sequentially. There
may be many different types of circuit components, but one current path
goes to each component sequentially.
58
Rev 1
The figure below shows an example of a simple series circuit with three
resistors.
Figure: Series Circuit
Parallel Circuit
A parallel circuit has multiple branches through which current can flow,
with the circuit voltage applied across each of the circuit branches. Current
will flow through each branch based on the voltage applied and the
resistance of that branch, with no effect from the other branches.
The figure below shows a simple parallel circuit with three resistors.
Figure: Parallel Circuit
Compound Circuit
A compound circuit has portions that are in series and portions that are in
parallel. To analyze a compound circuit, calculate equivalent resistances
and replace the more complex parts of the circuit with simpler equivalents,
and then solve for the individual sections. The figure below shows a simple
compound circuit.
Rev 1
59
Figure: Compound Circuit
Resistance in Series Circuits
The table below gives direction for finding the total (or equivalent)
resistance in a series circuit.
Step
Action
1.
Determine the type of circuit (series, parallel, or compound).
2.
If it is a series circuit, continue. If not, go to the appropriate
section for guidance.
3.
Add the individual resistance values.
4.
The sum of the individual resistances is the total or equivalent
resistance.
The total resistance in a series circuit is equal to the sum of all the parts of
that circuit, as shown below.
𝑅𝑇 = 𝑅1 + 𝑅2 + 𝑅3 … 𝑒𝑡𝑐.
Where:
RT = total resistance
R1, R2, and R3 = resistance in series
60
Rev 1
Figure: Resistance in a Series Circuit
Resistance in a Series Circuit Example
A series circuit has a 60Ω, a 100Ω, and a 150Ω resistor in series (see figure
above). What is the total resistance of the circuit?
Solution:
𝑅𝑇 = 𝑅1 + 𝑅2 + 𝑅3 = 60 + 100 + 150 = 310 𝛺
Voltage in a Series Circuit
The total voltage across a series circuit is equal to the sum of the voltages
across each resistor in the circuit (see figure below).
𝑉𝑇 = 𝑉1 + 𝑉2 + 𝑉3...etc.
Where:
VT = total voltage
V1 = voltage across R1
V2 = voltage across R2
V3 = voltage across R3
Figure: Voltage Drops in a Series Circuit
Rev 1
61
Voltage Drops in Series Circuits
You may now apply Ohm’s law to the entire series circuit or to individual
component parts of the circuit. When used on an individual component
part, the voltage across that part is equal to the current (I) times the
resistance (R) of that part. For the circuit shown in the figure below, the
voltage can be determined as shown.
V1 = IR1
V2 = IR2
V3 = IR3
VT = V1 + V2 + V3
VT = 10 volts + 24 volts + 36 volts
VT = 70 volts
Figure: Voltage Total in a Series Circuit
To find the total voltage across a series circuit, multiply the current by the
total resistance as shown below.
𝑉𝑇 = 𝐼𝑅𝑇
Where:
VT = total voltage
I = current
RT = total resistance
The voltages of V1, V2, and V3 are termed voltage drops or IR drops. Their
effect is to reduce the available voltage that is available across the other
circuit components. The sum of the voltage drops in any series circuit is
always equal to the applied voltage.
62
Rev 1
Resistance in Parallel Circuits
The table below provides instructions for calculating resistance in parallel
circuits.
Step
Action
1.
Determine the type of circuit (series, parallel, or compound).
2.
If it is a parallel circuit, continue. If not, go to the appropriate
section for guidance.
3.
Determine the current in each branch. (𝐼 = 𝑅)
4.
Determine the Total Resistance. (𝑅𝑇 = )
5.
The Total (Equivalent) Resistance for resistors in parallel
calculated above is always less than the smallest of the individual
resistances.
𝑉
𝑉
𝐼𝑇
Parallel Currents
The sum of the currents flowing through each branch of a parallel circuit is
equal to the total current flow in the circuit. Using Ohm’s Law, the branch
current for a three-branch circuit shown in the figure below equals the
applied voltage divided by the resistance as shown in the equations below.
𝑉
𝑉
Branch 1: 𝐼1 = 𝑅1 = 𝑅
1
𝑉
1
𝑉
Branch 2: 𝐼2 = 𝑅2 = 𝑅
2
2
𝑉3
𝑉
3
3
Branch 3: 𝐼3 = 𝑅 = 𝑅
Figure: Current in a Parallel Circuit
In this example:
𝐼1 =
𝑉
120
=
= 8A
𝑅1
15
Rev 1
63
𝐼2 =
𝑉
120
=
= 6𝐴
𝑅2
20
𝑰𝟑 =
𝑽
𝟏𝟐𝟎
=
= 𝟏𝟐𝑨
𝑹𝟑
𝟏𝟎
Parallel Currents Example
A circuit includes two resistors, each drawing 3A, and a third resistor,
drawing 2A, connected in parallel across a 115-volt source shown in the
figure above. What is total current (IT)?
Solution:
𝐼𝑇 = 𝐼1 + 𝐼2 + 𝐼3
𝐼𝑇 = 3𝐴 + 3𝐴 + 2𝐴
𝐼𝑇 = 8𝐴
Resistance in Parallel
To determine total resistance in a parallel circuit, apply Ohm’s Law. Divide
the voltage across the parallel resistance by the total line current as shown.
𝑅𝑇 =
𝑉
𝐼𝑇
Figure: Resistance in a Parallel Circuit
Solution
You can also find the total resistance in a parallel circuit by using the
equation below:
1
1
1
1
1
=
+
+ +. . . .
𝑅𝑇 𝑅1 𝑅2 𝑅3
𝑅𝑁
64
Rev 1
Resistance in Parallel Example
Find the total resistance of a 4Ω, an 8Ω, and a 16Ω resistor
in parallel.
Step
1.
1
1
1
1
=
+
+
𝑅𝑇 𝑅1 𝑅2 𝑅3
2.
1
1 1 1
= + +
𝑅𝑇 4 8 16
3.
1
4
2
1
7
=
+
+
=
𝑅𝑇 16 16 16 16
4.
𝑅𝑇 =
16
= 2.29 𝑜ℎ𝑚𝑠
7
Whenever resistors are in parallel, the total resistance is
always smaller than any single branch.
Note
Equal Resistors in Parallel
Total resistance of equal resistors in a parallel circuit is equal to the
resistance of one resistor divided by the number of resistors.
𝑅
𝑁
Where:
𝑅𝑇 =
RT = total resistance
R = resistance of one resistor
N = number of resistors
Equal Resistors in Parallel Example
Step
1.
Five lamps, each with a resistance of 40Ω, are connected in
parallel. Find the total resistance.
𝑅𝑇 =
𝑅1 𝑅2 𝑅3 𝑅4 𝑅5 40𝛺
=
=
=
=
=
𝑁
𝑁
𝑁
𝑁
𝑁
𝑁
2.
𝑁 = 5
3.
𝑅𝑇 = 𝑅/𝑁 = 40/5 = 8 𝑜ℎ𝑚𝑠
Rev 1
65
When any two resistors are unequal in a parallel circuit, it is easier to
calculate RT by multiplying the two resistances and then dividing the
product by the sum, as shown in the figure below. This approach is valid
when there are only two resistors in parallel.
𝑅𝑇 =
𝑅1 𝑅2
𝑅1 + 𝑅2
Figure: Parallel Circuit
Step
What value of resistance must be added, in parallel, with an
8Ω resistor to provide a total resistance of 6Ω (See above
figure)?
1.
𝑅𝑇 =
2.
3.
6 =
𝑅1 𝑅2
𝑅1 + 𝑅2
8𝑅𝑋
8 + 𝑅𝑋
6(8 + 𝑅𝑋 ) = 8𝑅𝑋
48 + 6 𝑅𝑋 = 8 𝑅𝑋
4.
5.
48 = 2 𝑅𝑋
6.
𝑅𝑋 = 24 𝑜ℎ𝑚𝑠
Resistance in Compound Circuits
The table below provides instructions for analyzing compound circuits.
Step
Action
1.
Determine the type of circuit (series, parallel, or compound).
2.
If it is a compound circuit, continue. If not, go to the appropriate
section for guidance.
66
Rev 1
Step
Action
3.
Identify parallel circuits within the compound circuit. Solve
them for RT, until you have an equivalent series circuit.
4.
Solve the equivalent series circuit for I and for voltage drops
across each resistance or equivalent resistance.
5.
Solve each parallel portion for I through each resistor.
6.
Check the solution.
Series Circuit Demonstration
A series circuit has a 50Ω, a 75Ω, and a 100Ω resistor in series as shown in
the figure below. Find the voltage necessary to produce a current of 0.5
amps.
Figure: Series Circuit Example
Step
Action
Result
1.
Find circuit current.
As we already know, current is the
same throughout a series circuit,
which equals 0.5 amps.
2.
Find RT.
𝑅𝑇 = 𝑅1 + 𝑅2 + 𝑅3
𝑅𝑇 = 50 𝛺 + 75 𝛺 + 100 𝛺
𝑅𝑇 = 225 𝛺
3.
Find VT. Use Ohm’s law.
𝑉𝑇 = 𝐼𝑅𝑇
𝑉𝑇 = (0.5 𝑎𝑚𝑝𝑠)(225 𝛺)
𝑉𝑇 = 112.5 𝑣𝑜𝑙𝑡𝑠
Rev 1
67
Parallel Circuit Demonstration
Two branches, R1 and R2, are across a 120 V power source, as shown in the
figure below. The total current flow is 30 A. Branch R1 takes 22 amps.
What is the current flow in branch R2, the resistance provided by R1 and R2,
and the equivalent resistance for the circuit?
Figure: Parallel Circuit Example
Step
1.
2.
3.
4.
Solution
𝐼𝑇 =
𝐼2 =
𝐼2 =
𝐼2 =
𝐼1 + 𝐼2
𝐼𝑇 − 𝐼1
30 𝑎𝑚𝑝𝑠 – 22 𝑎𝑚𝑝𝑠
8 𝑎𝑚𝑝𝑠
𝑅1 =
𝑉
𝐼1
𝑅1 =
120
= 5.5 𝑂ℎ𝑚𝑠
22
𝑉
𝐼2
120
𝑅2 =
= 15 𝑂ℎ𝑚𝑠
8
𝑅2 =
𝑉
𝐼𝑇
120
𝑅𝑇 =
= 4 𝑂ℎ𝑚𝑠
30
𝑅𝑇 =
Compound Circuit Demonstration
Given the following:
68
Rev 1


The voltage source is 12 V.
A = 6 ohms
B = 24 ohms
C = 12 ohms
Find the current flow through each resistor and the equivalent resistance for
resistors B and C, shown in the figure below.
Figure: Compound Circuit
Step
1.
Action
Result
First, find the equivalent
Resistance for resistors B
and C.
(𝑅𝐵 )(𝑅𝐶 )
(𝑅𝐵 + 𝑅𝐶 )
(24)(12)
=
(24 + 12)
𝑅𝑒𝑞 =
𝑅𝑒𝑞
𝑅𝑒𝑞 = 8 𝑜ℎ𝑚𝑠
2.
Next, use Req to find total
current (IT) which is also
the current through resistor
A.
3.
Use IT and RA to find the
voltage drop across RA,
and then subtract that from
V to find the voltage drop
across RB and RC.
4.
Finally, Use VB (VC) and
RB and RC to determine the
current through resistances
B and C.
Rev 1
𝐼𝑇 =
𝑉
𝑅𝑇
𝑉
𝑅𝐴 + 𝑅𝑒𝑞
12
𝐼𝑇 =
(6 + 8)
12
𝐼𝑇 =
= 0.86 𝑎𝑚𝑝𝑠
14
𝐼𝑇 =
𝑉𝐴 = (𝐼𝑇 )(𝑅𝐴 )
𝑉𝐴 = (0.86𝑎𝑚𝑝𝑠)(6𝑜ℎ𝑚𝑠)
= 5.16𝑉
𝑉𝐵 = 𝑉𝐶 = 𝑉𝑇 − 5.16
𝑉𝐵 = 𝑉𝐶 = 12 − 5.16 = 6.84𝑉
𝐼𝐵 =
𝑉𝐵
𝑅𝐵
𝐼𝐵 =
6.84𝑉
= 0.29𝑎𝑚𝑝𝑠
24𝑜ℎ𝑚𝑠
69
Step
Action
Result
𝐼𝐶 =
𝐼𝐶 =
𝑉𝐶
𝑅𝐶
6.84𝑉
= 0.57𝑎𝑚𝑝𝑠
12𝑜ℎ𝑚𝑠
Knowledge Check
A 120 V battery connects in series with three resistors:
40Ω, 60Ω, and 100Ω, as shown in the figure below.
Find the voltage across each resistor.
70
A.
V1 = 24 volts, V2 = 36 volts, V3 = 60 volts
B.
V1 = 40 volts, V2 = 60 volts, V3 = 100 volts
C.
V1 = 30 volts, V2 = 30 volts, V3 = 60 volts
D.
V1 = 20 volts, V2 = 40 volts, V3 = 60 volts
Rev 1
Knowledge Check
A parallel circuit consists of R1 = 15Ω, R2 = 20Ω and
R3 =10Ω, with an applied voltage of 120 V, shown in
the figure below. What current will flow through each
branch, and what is the equivalent resistance (RT) for
the circuit?
A.
I1 = 8 amps, I2 = 6 amps, I3 = 12 amps, RT = 4.6 ohms
B.
I1 = 6 amps, I2 =8 amps, I3 = 10 amps, RT = 5.0 ohms
C.
I1 =6 amps, I2 =8 amps, I3 = 12 amps, RT = 5.0 ohms
D.
I1 = 8 amps, I2 = 6 amps, I3 = 10 amps, RT = 4.6 ohms
Knowledge Check
Given the following circuit shown in the figure below:




Rev 1
The voltage source is 24 VDC.
Resistors A, D, and E are each 4 ohms.
Resistor B and C are each 8 ohms.
Find the current through each resistor.
A.
IA = - 2.86 amps, IB = - 1.28 amps, IC = - 1.58 amps, ID
= IE = - 0.64 amps
B.
IA = 2.86 amps, IB = 1.43 amps, IC = 1.43 amps, ID = IE
= 0.71 amps
C.
IA = 2.86 amps, IB = 1.28 amps, IC = 1.58 amps, ID = IE
= 0.64 amps
D.
IA = - 2.86 amps, IB = - 1.43 amps, IC = - 1.43 amps, ID
= IE = - 0.71 amps
71
ELO 5.2 Voltage and Current Dividers
Introduction
In this section, you will learn how voltage and current dividers work.
Voltage Divider
When it is necessary to obtain different values of voltage from a single
energy source, a circuit includes a voltage divider, or voltage network. The
figure below shows a simple voltage divider. In this circuit, 24 volts acts on
three resistors in series. The total resistance limits the current through the
circuit to one ampere. Calculate individual voltages as follows.
Figure: Voltage Divider
Individual Voltages
Total current:
Solutions
𝐼 =
𝑉
24
24
=
=
= 1 𝑎𝑚𝑝
(4 + 8 + 12)
𝑅
24
Voltage drop across AB:
𝑉 = 𝐼𝑅
𝑉 = (1)(4)
𝑉 = 4 𝑣𝑜𝑙𝑡𝑠
Voltage drop across BC:
𝑉 = 𝐼𝑅
𝑉 = (1)(8)
𝑉 = 8 𝑣𝑜𝑙𝑡𝑠
Voltage drop across CD:
𝑉 = 𝐼𝑅
𝑉 = (1)(12)
𝑉 = 12 𝑣𝑜𝑙𝑡𝑠
Voltage drop across AC:
𝑉 = 𝐼𝑅
𝑉 = (1)(8 + 4)
𝑉 = 12 𝑣𝑜𝑙𝑡𝑠
72
Rev 1
Current Divider
Sometimes it is necessary to find the individual branch currents in a parallel
circuit, knowing only resistance and total current. When only two branches
are involved, the current in one branch will be some fraction of IT. Use the
resistance in each circuit to divide the total current into fractional currents in
each branch. This process is current division.
𝐼1 =
(𝑅2 )(𝐼𝑇 )
𝑅1 + 𝑅2
𝐼2 =
(𝑅1 )(𝐼𝑇 )
𝑅1 + 𝑅2
Note that the equation for each branch current has the opposite R in the
numerator. This is because the current in each branch is inversely
proportional to the branch resistance.
The figure below shows an example current divider.
Figure: Current Divider
Rev 1
73
Current Divider Example
Step
1.
2.
3.
Find branch current for I1 and I2 for the circuit shown
above.
𝐼1 =
(𝑅2 )(𝐼𝑇 ) (8)(24) (8)(24)
=
=
= 13.7 𝑎𝑚𝑝𝑠
(6 + 8)
𝑅1 + 𝑅2
14
𝐼2 =
(𝑅1 )(𝐼𝑇 ) (6)(24) (6)(24)
=
=
= 10.3 𝑎𝑚𝑝𝑠
(6 + 8)
𝑅1 + 𝑅2
14
Since we know I1 and IT, we could have also simply subtracted I1
from IT to find I2.
Knowledge Check
Given the following properties for the figure below:
The voltage source is 24 VDC.
RA = 12 ohms.
RB = 12 ohms.
RC = 6 ohms.
What is the voltage drop across RC?
74
A.
8.0 volts
B.
9.6 volts
C.
24 volts
D.
4.8 volts
Rev 1
Knowledge Check
Given the following for the figure shown below:




IT = 10 amps.
RA = 10 ohms.
RB = 20 ohms.
RC = 50 ohms.
Determine the current through resistor C.
A.
1.18 amps
B.
2.0 amps
C.
2.95 amps
D.
5.9 amps
ELO 5.3 Polarity of Voltage Drops
Introduction
In this section, you will learn to determine the polarity of voltages in DC
circuits.
Polarity of Voltage Drops
Step
Action
1.
Determine the direction of electron flow through the circuit.
2.
Where the electron flow enters each circuit component is the
negative end of that component. Label that end as negative.
3.
Label the opposite end of each component as positive.
4.
Check the solution.
Polarity in DC Circuits
All voltages and currents have polarity as well as magnitude. In a series DC
circuit, there is only one current, and its polarity is from the negative battery
terminal through the rest of the circuit to the positive battery terminal.
Voltage drops across loads also have polarities. The easiest way to find
these polarities is to use the direction of the electron current as a basis.
Rev 1
75
Then, where the electron current enters the load, the voltage is negative.
This holds true regardless of the number or type of loads in the circuit. The
drop across the load is opposite to that of the source, as shown in the figure
below. The voltage drops oppose the source voltage and reduce it for the
other loads. This is because each load uses energy, leaving less energy for
other loads.
Figure: DC Circuit Voltage Polarity
Knowledge Check
The negative poles in the circuit shown are found
at_________________.
76
A.
The left end of resistor A and the left end of resistor C.
B.
The right end of resistor A and the left end of resistor C.
C.
The bottom end of resistor B and the right end of resistor
A.
D.
The left end of resistor A and the right end of resistor C.
Rev 1
ELO 5.4 Kirchhoff's Laws
Introduction
In this module, we will review Kirchhoff's laws for determining voltage and
current in a circuit.
In all of the circuits examined so far, Ohm’s Law described the relationship
between current, voltage, and resistance. These circuits have been
relatively simple in nature. Many circuits are so complex that solving them
with Ohm’s Law is impossible. These circuits have many power sources
and branches, which would make the use of Ohm’s Law impractical or
impossible.
Through experimentation, in 1857 the German physicist Gustav Kirchhoff
developed methods to solve complex circuits. Kirchhoff developed two
conclusions, known today as Kirchhoff’s Laws.
Kirchhoff’s two laws reveal a unique relationship between current, voltage,
and resistance in electrical circuits that is vital to performing and
understanding electrical circuit analysis.
Kirchhoff's First Law (Voltage)
Kirchhoff’s first law describes voltage in closed loop (circuit). It states that
the sum of the voltage drops around a closed loop (circuit) is equal to the
sum of the voltage sources of that loop (circuit). Another way of stating
this law is that the algebraic sum of the voltage sources and voltage drops in
a closed loop (circuit) must always be equal to zero.
Kirchhoff's Second Law (Current)
Kirchhoff’s second law describes current in a closed loop (circuit). It states
that the current arriving at any junction point in a circuit is equal to the
current leaving that junction. In other words, the current going into a
junction equals the current going out of a junction (the sum of the goes-ins
equals the sum of the goes-outs).
Kirchhoff’s two laws may seem obvious based on what we already know
about circuit theory. Even though they may seem very simple, they are
powerful tools in solving complex and difficult circuits.
Conservation of Energy and Charge
We can relate Kirchhoff’s laws to conservation of energy and charge if we
look at a circuit with one load and source. Since the load consumes all of
the power provided from the source, there is conservation of energy and
charge. Since we can relate voltage and current to energy and charge, then
Kirchhoff’s laws are simply restating the laws governing energy and charge
conservation.
Rev 1
77
Knowledge Check
Kirchhoff's Voltage Law states that the sum of currents
entering a junction must equal the sum of currents
exiting that junction.
A.
True
B.
False
ELO 5.5 Applying Kirchhoff's Laws
Introduction
In this section, you will learn to use Kirchhoff's laws in DC circuit analysis.
Applying Kirchhoff's Laws
The table below gives instructions for using Kirchhoff’s voltage law.
Step
Action
1.
Determine the sum of all voltage sources in the circuit.
2.
Simplify the circuit, if necessary, by determining equivalent
resistances for any parallel sections.
3.
Determine the current in the simplified series circuit.
4.
Determine the voltage drop across each resistance or equivalent
resistance in the simplified series circuit.
5.
Ensure the sum of the voltage sources equals the sum of the
voltage drops.
6.
Determine the current in parallel branches, if necessary.
The table below gives instructions for using Kirchhoff’s current law.
Step
Action
1.
Label the current in each flow path in the circuit (I1, I2, etc.), and
include direction. Currents can be negative if the chosen
direction goes against current flow. Choosing directions will not
impede problem solution.
2.
For each junction, incoming current equals outgoing current.
78
Rev 1
Step
Action
3.
Write an equation for the current at each junction. (Current in
equals current out)
4.
Solve the equations until determining all currents.
5.
Check the solution.
Kirchhoff's Voltage Law Demonstration
Kirchhoff’s first law is sometimes termed his voltage law. The voltage law
gives the relationship between the voltage drops around any closed loop in a
circuit, and the voltage sources in that loop. The total of these two
quantities is always equal. In equation form:
𝐸𝑠𝑜𝑢𝑟𝑐𝑒 = 𝐸1 + 𝐸2 + 𝐸3 + 𝑒𝑡𝑐. = 𝐼1 𝑅1 + 𝐼2 𝑅2 + 𝐼3 𝑅3 + 𝑒𝑡𝑐.
𝛴𝐸𝑠𝑜𝑢𝑟𝑐𝑒 = 𝛴𝐼𝑅
Where the Greek symbol Σ (the Greek letter sigma) means we apply the
sum of Kirchhoff’s voltage law only to closed loops. A closed loop must
meet two conditions:
1. It must have one or more voltage sources.
2. It must have a complete path for current flow from any point, around
the loop, and back to that point.
Simple Voltage Source
Recall that in a simple series circuit, the sum of the voltage drops around
the circuit is equal to the applied voltage. Actually, this is Kirchhoff’s
voltage law applied to the simplest case, that is, where there is only one
loop and one voltage source, as shown in the figure below.
Figure: Using Kirchhoff's Voltage Law
For a simple series circuit, Kirchhoff’s voltage law corresponds to Ohm’s
Law. To find the current in the circuit above by using Kirchhoff’s voltage
law, use the equation below.
Rev 1
79
𝛴𝐸𝑠𝑜𝑢𝑟𝑐𝑒 = 𝛴𝐼𝑅
Solution:
80 = 20(𝐼) + 10(𝐼)
0 = 30(𝐼)
80
𝐼 =
= 2.66 𝑎𝑚𝑝𝑒𝑟𝑒𝑠
30
Kirchhoff's Voltage Law Demonstration
In the problem above, we knew the direction of current flow before solving
the problem. When there is more than one voltage source, we may or may
now know the direction of current flow. In such a case, we must assume a
direction of current flow in the beginning of the problem. All the sources
that would aid the current in the assumed direction of current flow are then
positive, and all that would oppose current flow are negative. If the
assumed direction is correct, the answer will be positive. The answer would
be negative if the direction assumed was wrong. In any case, we will
compute the correct magnitude. For example, what is the current flow in
the figure below? Assume that the current is flowing in the direction
shown.
Figure: Kirchhoff's Voltage Law
Solution
Using Kirchhoff’s Voltage Law:
𝛴𝐸𝑠𝑜𝑢𝑟𝑐𝑒 = 𝛴𝐼𝑅
50 − 70 = 30𝐼 + 10𝐼
−20 = 40𝐼
𝐼 = −0.5
The result is negative, indicating that the assumed flow direction is
incorrect. The current is actually 0.5 ampere in the opposite direction to
that assumed.
Kirchhoff's Current Law Demonstration
Kirchhoff’s second law states: "At any junction point in a circuit, the
current arriving is equal to the current leaving." Thus, if 15 amperes of
80
Rev 1
current arrives at a junction that has two paths leading away from it, 15
amperes will divide between the two branches, but a total of 15 amperes
must leave the junction. We are already familiar with Kirchhoff’s current
law from parallel circuits, that is, the sum of the branch currents is equal to
the total current entering the branches, as well as the total current leaving
the branches. The figure below illustrates Kirchhoff’s Current Law
graphically.
Figure: Kirchhoff's Current Law
In equation form, we can express Kirchhoff’s current law as follows:
𝐼𝐼𝑁 – 𝐼𝑂𝑈𝑇 = 0
or
𝐼𝐼𝑁 = 𝐼𝑂𝑈𝑇
Normally Kirchhoff’s current law is not used by itself, but with the voltage
law, in solving a problem.
Kirchhoff's Laws Demonstration
Find I2 in the circuit shown in the figure below using Kirchhoff’s voltage
and current laws.
Figure: Using Kirchhoff's Laws
Rev 1
81
Step
1.
Action
First, apply Kirchhoff’s
voltage law to both loops.
Result
Loop ABCDEF:
𝐼𝑅 =
𝐸𝑠𝑜𝑢𝑟𝑐𝑒
2𝛺 𝐼𝑡𝑜𝑡𝑎𝑙 + 6𝛺 𝐼1 = 6𝑉
Loop ABGHEF:
𝐼𝑅 =
𝐸𝑠𝑜𝑢𝑟𝑐𝑒
2𝛺 𝐼𝑡𝑜𝑡𝑎𝑙 + 3𝛺 𝐼2 = 6𝑉
2.
Since Kirchhoff’s current
law states 𝐼𝑡𝑜𝑡𝑎𝑙 = 𝐼1 +
𝐼2 , substitute (I1 + I2) in
the place of Itotal in both
loop equations and
simplify.
Loop ABCDEF
2𝛺(𝐼1 + 𝐼2 ) + 6𝛺𝐼1 = 6𝑉
2𝛺𝐼1 + 2𝐼2 + 6𝛺𝐼1 = 6𝑉
8𝛺𝐼1 + 2𝛺𝐼2 = 6𝑉
Loop ABGHEF
2𝛺(𝐼1 + 𝐼2 ) + 3𝛺𝐼2 = 6𝑉
2𝛺𝐼1 + 2𝛺𝐼2 + 3𝛺𝐼2 = 6𝑉
2𝛺𝐼1 + 5𝛺𝐼2 = 6𝑉
3.
We now have two
equations and two
unknowns and must
eliminate I1 to find I2.
One way is to multiply
Loop ABGHEF equation
by four, and subtract Loop
ABCDEF equation from
the result.
Multiply loop ABGHEF by 4:
4(2𝛺𝐼1 + 5𝛺𝐼2 = 6𝑉)
8𝛺𝐼1 + 20𝛺𝐼2 = 24𝑉
4.
82
Now we have an equation
with only I2, which is the
current we are looking for.
Subtract Loop ABCDEF from Loop
ABGHEF.
18 𝐼2 = 18
Rev 1
Knowledge Check
Given the following properties of the circuit shown in
the figure below:
A = 20 V
B = 12 V
C = 15 ohms
D = 12 ohms
Find the current in this loop.
Rev 1
A.
10.7 amps
B.
1.2 amps
C.
2.7 amps
D.
0.3 amps
83
Knowledge Check
Given the following properties of the circuit shown in
the figure below:
A = 24 V
B = 12 V
C = 6 ohms
D = 12 ohms
E = 6 ohms
Find the current through each resistor.
A.
IC = - 3.6 amps, ID = - 1.2 amps, IE = - 2.4 amps
B.
IC = -1.2 amps, ID = -0.4 amps, IE = -0.8 amps
C.
IC = 1.2 amps, ID = 0.4 amps, IE = 0.8 amps
D.
IC = 3.6 amps, ID = 1.2 amps, IE = 2.4 amps
TLO 5 Summary
In this section, you learned the tools for DC circuit analysis.
Now that you have completed this lesson, you should be able to:
1. Calculate total resistance for a series or parallel circuit.
2. Explain the terms voltage divider and current divider.
3. Given a DC electrical circuit, identify the polarity of the voltage drops
in the circuit.
4. State Kirchhoff’s voltage law and current law.
5. Solve problems for voltage and current using Kirchhoff’s laws.
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TLO 6 DC Motors
Overview
In this section, you will learn how DC motors operate.
Many special applications in a nuclear facility use DC motors; operators
must know how they work to monitor and control them.
Objectives
Upon completion of this lesson, you will be able to do the following:
1. Describe the action of a current carrying conductor in a magnetic
field.
2. Using the right-hand rule for motors, determine the direction of the
magnetic field, direction of current flow, or force on a conductor.
3. State the function of torque in a direct current motor and how it is
developed.
4. Describe how counter-electromotive force (CEMF) is developed, and
the affect it has on a DC motor.
5. Describe how the speed of a DC motor is adjusted, the relationship
between field current and induced voltage, and the relationship
between armature current and torque produced in a DC motor.
6. Describe why starting resistors are necessary for large DC motors.
7. List the four nameplate ratings for a DC motor.
ELO 6.1 Current Carrying Conductors
Introduction
In this section, we will review the forces applied to a current carrying
conductor positioned in a magnetic field.
Two conditions are necessary to produce a force on a conductor:
1. The conductor must be carrying current.
2. The conductor must be within a magnetic field.
When these two conditions exist, the conductor will experience a force,
which will attempt to move the conductor in a direction perpendicular to the
magnetic field. This is the basic theory by which all DC motors operate.
Current Carrying Conductor in a Magnetic Field
Every current-carrying conductor has a magnetic field around it. The lefthand rule for current-carrying conductors shows the direction of this
magnetic field. When the left thumb points in the direction of current flow,
the fingers will point in the direction of the magnetic field produced, as
shown in the figure below.
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85
Figure: Left-Hand Rule for Current Carrying Conductors
If a current-carrying conductor is in a magnetic field, the combined fields
will be similar to those shown in the figure below. The direction of current
flow through the conductor is indicated with an X or a • “dot,” similar to
how an arrow would look in a drawing, either going away from you as an
X, or coming toward you as a •. The X indicates the current flow is away
from the reader, or into the page. The • indicates the current flow is towards
the reader, or out of the page.
Figure: Current Carrying Conductor in a Magnetic Field
Below the conductor on the left, the field caused by the conductor is in the
same direction as the main field, and therefore, aids the main field. The net
result is that above the left conductor, the main field is weaker, or flux
density decreases; below the conductor, the main field strengthens, or flux
density increases. A force develops on the conductor that moves the
conductor in the direction of the weakened field (upward).
Above the conductor on the right, the field caused by the conductor is in the
same direction as the main field, and therefore, aids the main field. Below
the conductor on the right, the field caused by the conductor is in the
opposite direction of the main field, and therefore, opposes the main field.
The net result is that above the right conductor, the main field strengthens,
or flux density is increased, and below the conductor, the main field is
weaker, or flux density decreases. A force develops on the conductor that
moves the conductor in the direction of the weakened field (downward).
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Knowledge Check
The left-hand rule for current carrying conductors
states that _____________________.
A.
when the thumb points in the direction of electron
flow, it is also pointing in the direction of the induced
North magnetic pole
B.
when the thumb points in the direction of electron
flow, the fingers will wrap around the conductor in the
direction of the magnetic lines of force (South to
North)
C.
when the thumb points in the direction of conventional
current flow, the fingers will wrap around the
conductor in the direction of the magnetic lines of force
(North to South)
D.
when the thumb points in the direction of electron
flow, the fingers will wrap around the conductor in the
direction of the magnetic lines of force (North to
South)
ELO 6.2 Right-Hand Rule for Motors
Introduction
In this section, we will cover the right-hand rule for motors and the forces
applied to a current carrying conductor positioned in a magnetic field.
A DC motor uses a conductor formed in a loop such that two parts of the
conductor are in the magnetic field at the same time. The effects of the
magnetic fields created by current flow through both parts of the conductor
distort the main magnetic field and produce a force on each part of the
conductor. When the conductor is on a rotor, the force exerted on both
parts of the conductor will cause the rotor to rotate clockwise, as shown in
the figure below.
Figure: DC Motor Action
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87
You can think of these magnetic lines of force as rubber bands that are
always trying to straighten themselves. The lines of force above the
conductor exert a downward force due to the magnetic lines of force trying
to straighten themselves.
Right-Hand Rule for Motors
The explanation of how a force develops on a conductor uses a fundamental
principle of physics: a current carrying conductor in a magnetic field tends
to move at right angles to that field. Another way to show the relationship
between the current carrying conductor, magnetic field, and motion is the
right-hand rule for motors, shown in the figure below.
Figure: Right-Hand Rule for Motors
The right-hand rule for motors shows the direction in which a currentcarrying conductor moves in a magnetic field. When the forefinger points
in the direction of the magnetic field lines, and the middle finger is pointed
in the direction of current flow, the thumb will point in the direction of
force (motion).
The table below gives instructions for using the right-hand rule for motors.
Step
Action
1.
Use the right-hand rule for motors with electron flow in a
conductor.
2.
Hold your right hand with the thumb, index finger, and middle
finger all at right angles to each other.
3.
Point the forefinger in the direction of the magnetic field (North to
South), and the middle finger in the direction of electron flow.
88
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Step
Action
4.
The thumb will be pointing in the direction of motion.
5.
This gives the direction of motion due to the force on the current
carrying conductor.
Knowledge Check
The right-hand rule for motors states
that_____________________________________.
A.
when the middle finger is pointed in the direction of
the magnetic field lines, and the forefinger is pointed in
the direction of current flow, the thumb will point in
the direction of force (motion)
B.
when the middle finger is pointed in the direction of
the magnetic field lines, and the thumb is pointed in the
direction of current flow, the forefinger will point in
the direction of force (motion)
C.
when the forefinger is pointed in the direction of the
magnetic field lines, and the thumb is pointed in the
direction of current flow, the middle finger will point
in the direction of force (motion)
D.
when the forefinger is pointed in the direction of the
magnetic field lines, and the middle finger is pointed in
the direction of current flow, the thumb will point in
the direction of force (motion)
ELO 6.3 Torque in DC Motors
Introduction
In this section, you will learn how a DC motor develops torque.
Torque
Torque is that force which tends to produce and maintain rotation. The
function of torque in a DC motor is to provide a mechanical output or drive
a piece of equipment attached (coupled) to the motor, such as a pump,
valve, etc.
When a voltage acts on a motor, current will flow through the field winding,
establishing a magnetic field. Current will also flow through the armature
winding, from the negative brush to the positive brush as shown in the
figure below.
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89
Figure: Armature Current in a Basic DC Motor
Since the armature is a current-carrying conductor in a magnetic field, the
conductor has a force exerted on it, tending to move it at right angles to that
field. Using the left-hand rule for current-carrying conductors, you will see
that the magnetic field on one side strengthens at the bottom, while it
weakens on the other side.
Using the right-hand rule for motors, we can see that there is a force exerted
on the armature, which tends to turn the armature in the counter-clockwise
direction. The sum of the forces, Newtons, multiplied by the radius of the
armature, in meters, is equal to the torque developed by the motor in
Newton-meters (N-m).
Referring to the figure above, reversing the armature current while
maintaining the magnetic field in the same direction will result in torque
developing in the opposite direction. Likewise, reversing the field polarity
and maintaining the armature current the same will result in torque
developing in the opposite direction.
The force developed on a conductor that is part of a DC motor armature is
due to the combined action of the magnetic fields (main and armature). The
force developed is directly proportional to the strength of the main field flux
and the strength of the field around the armature conductor. As we know,
the field strength around each armature conductor depends on the amount of
current flowing through the armature conductor. Therefore, the torque
developed by the motor can be determined using the following equation:
𝑇 = 𝐾𝛷𝐼𝑎
Where:
T = torque, N-m
K = a constant depending on physical size of motor
Φ = field flux, number of lines of force per pole
Ia = armature current, A
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Knowledge Check
Select all of the statements about DC motors that are
correct.
A.
The physical dimensions of the motor do not influence
torque.
B.
The magnitude of armature current does not influence
torque.
C.
Torque is the product of the force exerted on the rotor
and the radius of the rotor.
D.
The field strength, in part, determines force.
ELO 6.4 Counter-Electromotive Force (CEMF) in DC Motors
Introduction
In this section, you will learn how counter-electromotive force (CEMF) is
developed and how it affects DC motors.
Counter-Electromotive Force
Every motor develops a generator action (inducing a voltage). When a
conductor cuts lines of force, the result is an induced EMF in that
conductor.
Current to start the armature turning will flow in the direction determined
by the applied DC power source. After rotation starts, the conductor cuts
lines of force. By applying the left-hand rule for generators, the induced
EMF in the armature will produce a current in the opposite direction. The
induced EMF that results from motor operation is counter-electromotive
force, or CEMF, as illustrated in the figure below.
Figure: Counter-Electromotive Force
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91
Since the action of the armature cutting lines of force generates the CEMF,
the value of CEMF will depend on field strength and armature speed, as
shown below.
𝐸𝐶𝐸𝑀𝐹 = 𝐾𝛷𝑁
Where:
ECEMF = counter EMF
K = constant
Φ = field flux strength
N = speed of the armature
The CEMF opposes the applied voltage and functions to lower armature
current. The effective voltage acting in the armature of a motor is the
applied voltage, minus the CEMF. To calculate armature current, use
Ohm’s law, as shown in the equation below.
𝐼𝑎 =
𝐸𝑡 − 𝐸𝐶𝐸𝑀𝐹
𝑅𝑎
Where:
Ia = armature current
Et = terminal voltage
ECEMF = counter EMF
Ra = armature resistance
Knowledge Check
Select all of the statements that are true about CEMF.
A.
Counter-electromotive force always opposes the
applied force.
B.
Hysteresis causes counter-electromotive force.
C.
Rotation of the current carrying conductor in the
magnetic field causes counter-electromotive force.
D.
Counter-electromotive force exists when the rotor is
stationary.
ELO 6.5 DC Motor Control
Introduction
In this section, you will learn how to adjust the speed of a DC motor.
DC Motor Speed Control
External devices, usually field resistors vary the field of a DC motor. If a
constant voltage is applied to the field (E), as the resistance of the field (RF)
is lowered, the amount of current flow through the field (IF) increases, as
shown by Ohm’s law.
𝐼𝐹 =
92
𝐸
𝑅𝐹
Rev 1
An increase in field current will cause field flux (ΦF) to increase.
Conversely, if the resistance of the field is increased, field current and field
flux will decrease.
If the field flux of a DC motor decreases, the motor speed will increase.
The reduction of field strength reduces the CEMF of the motor, since the
armature conductors, as shown in the equation below are cutting fewer lines
of flux.
↓ 𝐸𝐶𝐸𝑀𝐹 =
→ ↓ →
𝐾 Φ𝐹 𝑁
A reduction of counter EMF allows an increase in armature current as
shown below.
𝐼𝑎 =
𝐸𝑡 − 𝐸𝐶𝐸𝑀𝐹
𝑅𝑎
This increase in armature current causes a larger torque to be developed; the
increase in armature current more than offsets the decrease in field flux as
shown below.
→ ↓ →
↑𝑇=
𝐾 Φ𝐹 𝐼𝑎
This increased torque causes the motor to increase in speed.
↑T∝N↑
This increase in speed will then proportionately increase the CEMF. The
speed and CEMF will continue to increase until the armature current and
torque decline to values just large enough to supply the load at a new
constant speed.
Knowledge Check
Increasing field resistance will increase DC motor
speed.
A.
True
B.
False
ELO 6.6 Starting DC Motors
Introduction
In this section, you will learn the starting sequence for DC motors.
Starting Current
At the instant a DC motor is started the rotor (armature) is stationary and
there is no generated counter EMF. The only component available to limit
starting current is the resistance of the armature, which is really just a length
of copper wire. In most DC motors, this resistance is very low
(approximately one ohm or less).
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93
𝐼𝑎 =
𝐸𝑡 − 𝐸𝐶𝐸𝑀𝐹
𝑅𝑎
In order to reduce this very high starting current, there must be an external
resistance in series with the armature during the starting period. To show
why this is essential, let us consider a 10-hp motor with an armature
resistance of 0.4 ohms. If a 260 VDC source supplies the motor, the
resulting current would be as shown below.
𝐸𝑡 − 𝐸𝐶𝐸𝑀𝐹
𝐼𝑎 =
𝑅𝑎
(260 − 0)
= 650 𝑎𝑚𝑝𝑠
0.4
This large current is approximately twelve times greater than actual fullload current for this motor. This high current would likely cause severe
damage to the brushes, commutator, or windings. Most motor designs
incorporate starting resistors to limit starting current to 125 to 200 percent
of full load current.
𝐼𝑎 =
Starting Resistance
The equation below shows how to calculate the amount of starting
resistance necessary to limit starting current to a more desirable value:
𝑅𝑆 =
𝐸𝑡
− 𝑅𝑎
𝐼𝑆
Where:
RS = starting resistance
Et = terminal voltage
IS = desired armature starting current
Ra = armature resistance
Example: If the full load current of the motor mentioned previously is 50
amps, and we want to limit starting current to 125% of this value, find the
additional required resistance in series with the armature.
Solution:
𝐸𝑡
− 𝑅𝑎
𝐼𝑆
(260𝑉 𝐷𝐶)
𝑅𝑆 =
− 0.4 𝑜ℎ𝑚𝑠
(50 𝑎𝑚𝑝𝑠)(125%)
260
𝑅𝑆 =
− 0.4 = 3.76 𝑜ℎ𝑚𝑠
62.5
Most DC motors use starting resistors in the motor control circuit to limit
the starting current. These starting resistors insert a maximum amount of
resistance when the motor is first started, since no CEMF exists in the
armature. As the speed of the motor increases, CEMF will begin to
increase, limiting armature current. The starting resistors are then “cut out”,
in successive steps, until the motor reaches full running speed and the
starting resistors are no longer necessary. When running at full speed,
CEMF limits armature current and circuitry bypasses the starting resistors.
𝑅𝑆 =
94
Rev 1
Knowledge Check
Starting resistors are needed in DC motors to... (Select
all that are correct)
A.
overcome the starting resistance.
B.
limit the voltage during a motor start.
C.
compensate for the high values of CEMF at startup.
D.
limit the current during a motor start.
ELO 6.7 DC Motor Ratings
Introduction
In this section, we will review the nameplate ratings that a manufacturer
provides for DC motor operation.
Nameplate ratings of DC motor typically refer to conditions of voltage,
current, speed, and power for which the manufacturer designed the motor;
these conditions normally match motor operating conditions.
Continuous Power
The principal rating for a DC motor is known as the continuous rating; this
is the rating described on the nameplate of a motor. The continuous power
rating is a thermal rating. At this power, the motor will operate for long
periods without a large rise in temperature and within temperature limits of
the conductor insulating material, bearings and other components, which are
temperature dependent.
Speed
The nameplate provides the speed rating of a DC motor. This speed is the
upper limit for motor operation without sustaining mechanical damage. As
with DC generators, the mechanical limitations of rotor construction
determine the upper speed limit.
Knowledge Check
The common ratings for DC motors include
_________________________. (Select all that are
correct)
Rev 1
A.
speed
B.
ambient temperature
C.
starting current
D.
continuous power
95
TLO 6 Summary
In this section you learned how DC motors work, including how torque and
CEMF are developed, and how the different types of DC motors are used.
Now that you have completed this lesson, you should be able to:
1. Describe the action of a current carrying conductor in a magnetic
field.
2. Using the right-hand rule for motors, determine the direction of the
magnetic field, direction of current flow, or force on a conductor.
3. State the function of torque in a direct current motor and how it is
developed.
4. Describe how counter-electromotive force (CEMF) is developed, and
the affect it has on a DC motor.
5. Describe how the speed of a DC motor is adjusted, the relationship
between field current and induced voltage, and the relationship
between armature current and torque produced in a DC motor.
6. Describe why starting resistors are necessary for large DC motors.
7. List the four nameplate ratings for a DC motor.
TLO 7 Producing DC Voltage
Overview
In this section, we will explain production of DC voltage.
Operators must understand the principles behind electrical machines to
monitor their performance.
Objectives
Upon completion of this lesson, you will be able to do the following:
1. Describe the common methods for producing a DC voltage and give
an example of each.
2. State the purpose of a rectifier and describe the outputs of rectifier
circuits.
3. Describe the effects of commutation in a DC generator.
4. State the purpose of each of the components of a DC machine.
5. List the three conditions necessary to induce a voltage.
6. Using the left-hand rule of generators, determine the direction of the
magnetic field, the motion of the conductor, or the direction of current
induced into a conductor.
7. Define terminal voltage as it applies to DC generators and describe
how terminal voltage of a DC generator is adjusted.
8. Identify the four categories and their bases for DC generator
nameplate ratings.
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ELO 7.1 Methods of Producing DC Voltage
Introduction
When most people think of DC electricity, they usually think of batteries.
In addition to batteries, however, there are other means of producing DC
voltage. Modern technology employs some of these methods. This chapter
describes various methods for producing a DC voltage and some of the
more common industrial applications.
Electrochemistry
When combined with specific metals, certain chemicals cause a chemical
reaction that will transfer electrons to produce electrical energy. This
process works on the electrochemistry principle. One example of this
principle is the voltaic chemical cell. A chemical reaction produces and
maintains opposite charges on two dissimilar metals that serve as the
positive and negative terminals. The metals are in contact with an
electrolyte solution. Connecting together more than one of these cells
produces a battery.
Chemical Cell
The chemical cell is composed of two electrodes made of different types of
metal or metallic compounds immersed in an electrolyte solution. The
chemical actions that result vary, depending on the type of material used in
cell construction. Some knowledge of the basic action of a simple cell will
be helpful in understanding the operation of a chemical cell in general.
In the cell, electrolyte ionizes to produce positive and negative ions as
shown in the figure below. Simultaneously, chemical action causes the
atoms within one of the electrodes to ionize.
Figure: Basic Chemical Cell
This action results in electron deposition on the electrode, and positive ions
from the electrode pass into the electrolyte solution (Part B). This causes a
negative charge on the electrode and leaves a positive charge in the area
near the electrode (Part C).
The positive ions, produced by ionization of the electrolyte, are repelled to
the other electrode. At this electrode, these ions will combine with the
electrons. Because this action causes removal of electrons from the
electrode, it becomes positively charged.
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97
Batteries
A battery consists of two or more chemical cells connected in series. The
combination of materials inside a battery converts chemical energy into
electrical energy.
Static Electricity
Atoms with the proper number of electrons in orbit around them are in a
neutral state, or have a zero charge. A body of matter consisting of these
atoms will neither attract nor repel other matter in its vicinity.
Removal of electrons from the atoms in this body of matter, as happens due
to friction when rubbing a glass rod with a silk cloth, results in the body
becoming electrically positive as shown in the figure below.
If this body of matter (e.g., glass rod) comes near, but not in contact with,
another body having a normal charge, an electric force acts between them
because of their unequal charges. The existence of this force is static
electricity or electrostatic force.
Figure: Static Electricity
An example of static electricity producing a voltage occurs when someone
walks across a carpet and receives a shock when touching a metal
doorknob. The soles of the person’s shoes build up a charge by rubbing on
the carpet, and this charge transfers to their body. Their body becomes
positively charged and upon touching the zero-charged doorknob, electrons
transfer to the person’s body until both the body and the doorknob are at
equal charges.
Magnetic Induction
A generator is a machine that converts mechanical energy into electrical
energy by using the principle of magnetic induction. Magnetic induction
produces a voltage by rotating coils of wire through a stationary magnetic
field, as shown in the figure below, or by rotating a magnetic field through
stationary coils of wire.
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Figure: Magnetic Induction
DC Generator
A simple DC generator consists of an armature coil with a single turn of
wire. (When discussing motors and generators the term armature generally
refers to the portion of the device where the voltage is induced.) The
armature coil cuts across the magnetic field to produce a voltage output. As
long as a complete path is present, current will flow through the circuit in
the direction shown by the arrows in the figure below. As the armature
rotates the first commutator segment contacts the first brush, while the
second commutator segment is in contact with the second brush.
Rotating the armature one-half turn in the clockwise direction causes
reversal of the contacts between the commutator segments. Now, the first
segment contacts the second brush and the second segment contacts the first
brush.
Figure: Basic DC Generator
Due to this commutator action, the side of the armature coil that is in
contact with either of the brushes is always cutting the magnetic field in the
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99
same direction. Both brushes and have a constant polarity, and pulsating
DC results. Magnetic induction is one of the most widely employed
methods of producing electrical power and will be discussed in more detail
in later chapters of this lesson.
Piezoelectric Effect
By applying pressure to certain crystals (such as quartz or Rochelle salts) or
ceramics (like barium titanate), it is possible to force electrons out of orbit
in the direction of the force.
Electrons leave one side of the material and accumulate on the other side,
building up positive and negative charges on opposite sides, as shown in the
figure below. Upon release of the pressure, the electrons return to their
orbits. (Some materials will react to bending pressure, while others will
respond to twisting pressure.)
This generation of voltage is the piezoelectric effect. If external wires
provide connectivity while pressure and voltage are present, electrons will
flow and produce current. By holding the pressure constant, the current will
flow until equalization of the potential difference.
Upon removal of the force, the material decompresses and an electric force
is created in the opposite direction. The power capacity of these materials
is extremely small. However, these materials are very useful because of
their extreme sensitivity to changes of mechanical force.
Figure: Pressure Applied to Crystal Produces Electric Charge
An example of the piezoelectric effect is the crystal phonograph cartridge
that contains a Rochelle salt crystal. A phonograph needle attaches to the
crystal. As the needle moves in the grooves of a record, it swings from side
to side, applying compression and decompression to the crystal. This
mechanical motion applied to the crystal generates a voltage signal that
reproduces sound.
Thermoelectricity
Some materials readily give up their electrons and others readily accept
electrons. For example, when joining two dissimilar metals like copper and
zinc together, a transfer of electrons can take place. Electrons will leave the
copper atoms and enter the zinc atoms. The zinc gains surplus electrons
from the copper, and becomes negatively charged. The copper loses
100
Rev 1
electrons and takes on a positive charge. This creates a voltage potential
across the junction of the two metals.
The heat energy of normal room temperature is enough to make these
metals release and gain electrons, causing a measurable voltage potential.
Applying more heat energy to the junction causes release of more electrons,
and the voltage potential increases. Upon removal of the heat, the junction
cools, the charges dissipate, and the voltage potential decreases. This
process is thermoelectricity. A thermocouple is an example of a device that
relies on thermoelectricity to produce a voltage.
Thermocouple
A thermocouple is a device used to convert heat energy into a voltage
output. The thermocouple consists of two different types of metal joined at
a junction as shown in the figure below.
As the junction is heated, the electrons in one of the metals gain enough
energy to become free electrons. These free electrons then migrate across
the junction and into the other metal. This displacement of electrons
produces a voltage across the terminals of the thermocouple.
The thermoelectric voltage produced by a thermocouple is dependent upon
the heat energy applied to the junction of the two dissimilar metals.
Thermocouples are widely used to measure temperature and as heat-sensing
devices in automatic temperature controlled equipment. The voltage
produced causes a current to flow through a meter; calibration of the meter
correlates current with temperature. One advantage of thermocouples in
power plants is that they can withstand higher temperatures than ordinary
mercury or alcohol thermometers.
Thermocouple power capacities are much smaller than some other sources,
but are somewhat greater than those of piezoelectric crystals. The
combinations used in the makeup of a thermocouple include iron and
constantan; copper and constantan; antimony and bismuth; and chromel and
alumel.
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101
Figure: Production of DC Voltage Using a Thermocouple
Photoelectric Effect
Light is a form of energy; many scientists consider light to consist of small
particles of energy called photons. When the photons in a light beam strike
the surface of a material, they release their energy and transfer it to the
atomic electrons of the material. This energy transfer may dislodge
electrons from their orbits around the surface of the substance. Upon losing
electrons, the photosensitive (light sensitive) material becomes positively
charged and an electric force is created, as shown in the figure below.
Figure: Producing Electricity from Light Using a Photovoltaic Cell
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Knowledge Check
Match the following terms with the correct descriptions.
1. Electrochemistry
A. Applying pressure to certain crystals
(such as quartz or Rochelle salts) or
certain ceramics (like barium
titanate) forces electrons out of orbit
in the direction of the force.
2. Piezoelectric
effect
B. Photons in a light beam strike the
surface of a material and release
their energy to the atomic electrons
of the material. This energy transfer
may dislodge electrons from their
orbits around the surface of the
substance.
3. Magnetic
induction
C. A chemical reaction produces and
maintains opposite charges on two
dissimilar metals that serve as the
positive and negative terminals.
4. Photoelectric
effect
D. Producing a voltage by rotating coils
of wire through a stationary
magnetic field, or by rotating a
magnetic field through stationary
coils of wire.
ELO 7.2 Rectifiers
Introduction
Most electrical power generating stations produce alternating current. AC
power transmission results in significantly less power loss as compared to
DC, however, many of today’s devices operate only, or more efficiently,
with DC. For example, transistors, and certain electronic control devices
require DC for operation. In order to operate these devices from ordinary
AC outlet receptacles, they must be equipped with rectifier units to convert
AC to DC. Therefore, the purpose of a rectifier circuit is to convert AC
power to DC.
The most common type of solid-state diode rectifier is made of silicon. The
diode acts as a gate, which allows current to pass in one direction and
blocks current flow in the other direction. The polarity of the applied
Rev 1
103
Duration
 20 minutes
Logistics
 Use PowerPoint slides
234–241 and the IG to
present ELO 7.2.
voltage determines if the diode will conduct. The two polarities are forward
bias and reverse bias.
Forward Bias
A forward biased diode has the positive terminal of a voltage source
connected to its anode, and the negative terminal connected to the cathode
as shown in the figure below. The power source’s positive side will tend to
repel the holes in the p-type material toward the negative side of the p-n
junction. A hole is a vacancy in the electron structure of a material. Holes
behave as positive charges.
As the holes and the electrons reach the p-n junction, some of them break
through it. Holes combine with electrons in the n-type material, and
electrons combine with holes in the p-type material.
Figure: Forward-Biased Diode
When a hole combines with an electron, or an electron combines with a
hole near the p-n junction, an electron from an electron-pair bond in the ptype material breaks its bond and enters the positive side of the source.
Simultaneously, an electron from the negative side of the source enters the
n-type material as shown in part C of the figure above. This produces a
flow of electrons in the circuit.
Reverse Bias
Reverse biasing occurs when the diode’s anode connects to the negative
side of the source, and the cathode connects to the positive side of the
source as shown in the figure below. The negative terminal attracts holes
within the p-type material, and the positive terminal (part B) attracts
electrons in the n-type material. This prevents the combination of electrons
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and holes near the p-n junction, and therefore causes a high resistance to
current flow. This resistance prevents current from flowing through the
circuit.
Figure: Reverse-Biased Diode
Half-Wave Rectifier
When a diode is connected to a source of alternating voltage, it will be
alternately forward-biased, and then reverse-biased, during each cycle of the
AC sine wave. When using a single diode in a rectifier circuit, current will
flow through the circuit only during one-half of the input voltage cycle,
when forward biased as shown in the figure below. For this reason, this
type of rectifier circuit is a half-wave rectifier. The output of a half-wave
rectifier circuit is pulsating DC.
Figure: Half-Wave Rectifier
Full-Wave Rectifier
A full-wave rectifier circuit is a circuit that rectifies the entire cycle of the
AC sine wave. A basic full-wave rectifier uses two diodes. The figure
below shows the action of these diodes during each half cycle.
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105
Figure: Full-Wave Rectifier
Full-Wave Rectifier Bridge
Another type of full-wave rectifier circuit is the full-wave bridge rectifier.
This circuit utilizes four diodes. The figure below shows these diodes’
actions during each half cycle of the applied AC input voltage. The output
of this circuit is a pulsating DC, with rectification of all of the waves of the
input AC. The output looks identical to that obtained from the full-wave
rectifier.
Figure: Full-Wave Rectifier Bridge
Full-Wave Rectifier Output
The figure below shows the output of a full-wave rectifier or full-wave
rectifier bridge.
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Figure: Full-Wave Rectifier Output
Knowledge Check
Select all the statements that are true.
A.
A half-wave rectifier can be built with one diode.
B.
Rectifiers convert DC power into AC power.
C.
A full-wave rectifier can be built with one diode.
D.
A forward biased diode allows current flow with little
resistance.
ELO 7.3 Commutation
Introduction
Commutation is the positioning of the DC generator brushes so that the
commutator segments change brushes at the same time the armature current
changes direction. Simply stated, commutation is the mechanical
conversion from AC to DC at the brushes of a DC machine, as shown in the
figure below.
Figure: Commutation
Commutation
The EMF induced in the rotor is actually an AC voltage. A commutator
converts the AC voltage generated in the rotating loop into a DC voltage.
The commutator also serves as a means of connecting the brushes to the
rotating loop. The purpose of the brushes is to connect the generated
voltage to an external circuit. In order to do this, each brush must make
contact with one of the ends of the loop. Since the loop or armature rotates,
a direct connection is impractical. Instead, the brushes contact the ends of
the loop through the commutator.
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In a simple one-loop generator, the commutator is made up of two semicylindrical pieces of a smooth, conducting material, usually copper,
separated by an insulating material, usually mica, as shown in the figure
below. Each commutator segment is permanently attached to one end of the
rotating loop, and the commutator rotates with the loop. The brushes,
usually made of carbon, rest against the commutator and slide along the
commutator as it rotates. Springs hold the brushes against the commutator,
completing brush contact with each end of the loop.
Figure: Commutator Segment and Brushes
Each brush slides along one half of the commutator and then along the other
half as the commutator rotates. The brushes are positioned on opposite
sides of the commutator; they will pass from one commutator half to the
other at the instant the loop reaches the point of rotation, where the induced
voltage reverses the polarity. Every time the ends of the loop reverse
polarity, the brushes switch from one commutator segment to the next. This
means that one brush is always positive with respect to the other. The
voltage between the brushes fluctuates in amplitude between zero and some
maximum value, but is always of the same polarity, as shown in the figure
below.
Figure: Commutation in a DC Generator
It is important to note that, as the brushes pass from one segment to the
other, there is an instant when the brushes contact both segments at the
same time. The induced voltage at this point is zero. If the induced voltage
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Rev 1
at this point were not zero, the brushes would short the ends of the loop
together, producing extremely high currents. The point at which the
brushes contact both commutator segments, when the induced voltage is
zero, is the neutral plane.
Because commutators in DC generators convert AC to DC, they are
sometimes referred to as mechanical rectifiers.
Knowledge Check
Commutation is...
A.
a means of increasing the voltage output of a DC
generator.
B.
a means of increasing the total power output of a DC
generator.
C.
the positioning of the DC generator brushes so that the
commutator segments change brushes at the same time
the armature current changes direction to convert from
AC to DC at the brushes of a DC machine.
D.
the positioning of the DC generator brushes so that the
commutator segments change brushes at the same time
the armature current changes direction to convert from
DC to AC at the brushes of a DC machine.
ELO 7.4 DC Machine Components
Introduction
Direct current machines are energy transfer devices. These machines can
function as either a motor or a generator. DC motors and generators have
the same basic construction, differing primarily in the energy conversion.
To understand the operation and construction of DC machines, we must
define a few basic terms.
Armature
The purpose of the armature is to provide the energy conversion in a DC
machine (refer to the figure below). In a DC generator, an external
mechanical force, such as a steam turbine, rotates the armature. This
rotation induces a voltage and current flow in the armature. Thus, the
armature converts mechanical energy into electrical energy. In a DC motor,
the armature receives voltage from an outside electrical source and converts
electrical energy into mechanical energy in the form of torque.
Rev 1
109
Figure: Basic DC Machine Components
Rotor
The purpose of the rotor is to provide the rotating element in a DC machine
(refer to the figure above). In a DC generator, an external force rotates the
rotor. In a DC motor, the rotor is the component that turns a piece of
equipment. In both types of DC machines, the rotor is the armature.
Stator
The stator is the part of a motor or generator that is stationary (refer to the
figure above). In DC machines, the purpose of the stator is to provide the
magnetic field. The stator in the figure above has a magnetic field provided
by a permanent magnet.
Field
The purpose of the field in a DC machine is to provide a magnetic field for
producing either a voltage (generator) or a torque (motor) (refer to the
figure above). A permanent magnet or an electromagnet provides the field
in a DC machine. Normally, fields use electromagnets because they have
increased magnetic strength, and the magnetic strength is more easily varied
using external devices. In the figure above, the stator provides the field.
110
Rev 1
Knowledge Check
Match the DC machine component to their appropriate
definition.
1. The component that provide a magnetic field
for producing either a voltage (generator) or
a torque (motor).
A. Field
2. The component that provides the energy
conversion. In a generator, it is the
component in which the voltage is induced.
B. Stator
3. The stationary portion of the DC machine.
C. Rotor
4. The rotating element of the DC machine.
D. Armature
ELO 7.5 Conditions for Inducing Voltage
Introduction
In this section, you will learn the conditions required to induce voltage in a
conductor.
Voltage Production (Generator Action)
Recall that there are three conditions necessary to induce a voltage into a
conductor:
1. A magnetic field
2. A conductor
3. Relative motion between the conductor and the magnetic field
A DC generator provides these three conditions to produce a DC voltage
output.
Theory of Operation
A basic DC generator has four parts:
1.
2.
3.
4.
A magnetic field
A single conductor, or loop
A commutator
Brushes
Field
As mentioned earlier, either a permanent magnet or an electromagnet may
provide the magnetic field. This example will use a permanent magnet to
describe a basic DC generator (see the figure below).
Rev 1
111
Figure: Basic DC Generator Operation
Voltage Induction
A single conductor, shaped in the form of a loop, lies between the north and
south poles of the magnet. As long as the loop is stationary, the magnetic
field has no effect (there is no relative motion). If we rotate the loop, the
loop cuts through the magnetic field, inducing an EMF (voltage) into the
loop.
When there is relative motion between a magnetic field and a conductor in
that magnetic field, and the direction of rotation is such that the conductor
cuts the lines of flux, the conductor gains an induced EMF. The magnitude
of the induced EMF (voltage) depends on the strength of the magnetic field
and the rate at which the conductor cuts the lines of flux. The stronger the
field or the more lines of flux cut for a given period of time, the larger the
induced EMF (voltage).
𝐸𝑔 = 𝐾𝛷𝑁
Where:
Eg = generated voltage
K = fixed constant
Φ = magnetic flux strength
N = speed of rotation in RPM
Counter-Electromotive Force (CEMF)
In a DC machine using a rotating armature, the conductors of the rotor cut
the magnetic lines of force in the magnetic field and induce voltage in the
armature conductors. This induced voltage opposes the applied voltage; it
counteracts some of the applied voltage, which reduces the current flow
through the armature. Since the induced voltage acts counter to the applied
voltage, we call it counter-electromotive force (CEMF).
Knowledge Check
Relative motion between the conductor and the
magnetic field is necessary to induce voltage.
112
A.
True
B.
False
Rev 1
Knowledge Check
Select all the statements that are true.
A.
The counter-electromotive force always opposes the
applied voltage.
B.
The counter-electromotive force always opposes
current flow.
C.
The counter-electromotive force is induced if the rotor
is not turning.
D.
The counter-electromotive force is induced only in
rotating armature machines.
ELO 7.6 Left-Hand Rule for Generators
Introduction
In this section, you will learn to apply the left-hand rule for generators.
Left-Hand Rule for Generators
The table below gives instructions for using the left-hand rule for
generators.
Step
Action
1.
Hold your left hand with the thumb, index finger, and middle
finger at right angles to each other (see illustration below).
2.
Point your thumb in the direction of motion of the conductor.
3.
Point your index finger in the direction of magnetic flux (north to
south).
4.
Your middle finger will point in the direction of current flow
(electron flow).
5.
Note that the other side of the conductor loop is traveling in the
opposite direction, so you have to reverse your thumb. Doing so
will demonstrate that current is induced to flow around the loop.
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113
Note
Note that the left-hand rule gives the direction of electron
flow. In some applications, conventional current is used
instead of electron flow, and conventional current is
opposite of electron flow.
To determine conventional current flow, follow the same
process using the right hand.
Left-Hand Rule Demonstration
The direction of the induced current flow resulting from the EMF induced
in the rotor can be determined using the left-hand rule for generators. This
rule states that if you point the index finger of your left hand in the direction
of the magnetic field (from north to south) and point the thumb in the
direction of motion of the conductor, the middle finger will point in the
direction of current flow. In the generator shown below, the conductor
closest to the north (N) pole is traveling upward across the field; therefore,
the motion is to the left, upper corner. Applying the left-hand rule to both
sides of the loop will show that current flows in a counter-clockwise
direction in the loop.
Figure: Left-hand Rule for Generators
114
Rev 1
Knowledge Check
The left-hand rule for generators is used as follows:
A.
Point the index finger of your left hand in the direction
of the magnetic field (from north to south) and point
the thumb in the direction of motion of the conductor,
the middle finger will point in the direction of electron
flow.
B.
Point the index finger of your left hand in the direction
of the magnetic field (from north to south) and point
the thumb in the direction of motion of the conductor,
the middle finger will point in the direction of
conventional current flow.
C.
Point the thumb of your left hand in the direction of the
magnetic field (from north to south) and point the
index finger in the direction of motion of the
conductor, the middle finger will point in the direction
of electron flow.
D.
Point the thumb of your left hand in the direction of the
magnetic field (from north to south) and point the
index finger in the direction of motion of the
conductor, the middle finger will point in the direction
of conventional current flow.
ELO 7.7 Terminal Voltage
Introduction
In this section, you will learn the meaning of terminal voltage as it applies
to DC machines.
Terminal Voltage
Terminal voltage, as applied to DC generators, is the voltage measured at
the output of the generator.
Applied voltage is the voltage delivered across the load and should be the
same as terminal voltage. However, various circuit characteristics, such as
losses, may reduce the applied voltage from the terminal voltage value.
Field Excitation
Electromagnets commonly provide the magnetic fields in DC generators. A
current must flow through the electromagnet’s conductors to produce a
magnetic field. In order for a DC generator to operate properly, the
magnetic field must always be in the same direction. Therefore, the current
through the field winding must be direct current. This current is the field
excitation current and the field winding receives the current in one of two
ways.
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It can come from a separate DC source external to the generator (e.g., a
separately excited generator).
It can come directly from the output of the generator, in which case the
generator is a self-excited generator.
Self-Excited Generator
In a self-excited generator, the field winding connects directly to the
generator output. There are three orientations for connections between field
and output. The field winding can be in series with the output, in parallel
with the output, or in some combination of the two.
Separately Excited Generator
Separate excitation requires an external source, such as a battery or another
DC generator. This type of generator is generally more expensive than a
self-excited generator, and used only where a self-excited generator is not
satisfactory. For example, instances where the generator must respond
quickly to an external control source or where it is necessary to vary the
generated voltage over a wide range during normal operations call for a
separately excited generator.
Regulating Terminal Voltage
DC generator output voltage depends on three factors:
1. The number of conductor loops in series in the armature
2. Armature speed
3. Magnetic field strength
In order to change the generator output, it is necessary to change one of
these three factors. It is impossible to change the number of conductor
loops in the armature of an operating generator, and it is usually impractical
to change the speed at which the armature rotates. Varying the current
through the field winding easily changes the magnetic field strength. This
is the most widely used method for regulating the output voltage of DC
generator. The figure below shows a simple voltage regulator circuit.
Figure: Varying DC Generator Terminal Voltage
116
Rev 1
Knowledge Check
Which of the following does not affect the magnitude
of voltage generated?
A.
Speed of rotation of the armature
B.
Direction of rotation of the armature
C.
Number of current loops in the armature
D.
Magnetic field strength
ELO 7.8 DC Generator Ratings
Introduction
There are generally four rating categories for DC Generators: voltage,
current, power and speed. These ratings are based on limitations associated
with the design and construction of the particular generator, and are
normally provided by the manufacturer on a label plate attached to the
machine. The engineering documentation associated with the generator will
also include these ratings.
Voltage
The voltage rating of a machine depends on the insulation type and design
of the machine. The voltage rating provides a measure of the insulation’s
capability to prevent electrical grounds and short circuits from developing
inside the machine.
Current
The current rating depends on the size of the conductors used in the
armature and field of the machine and the internal heat dissipation
capability of the generator.
Power
The power rating is based on the mechanical limitations of the device that is
used to turn the generator (referred to as the prime mover) and on the
thermal limits of conductors, bearings, and other components of the
generator.
Speed
The upper limit on speed for a DC machine depends on the speed at which
mechanical damage will occur to the machine. The maximum speed
limitation usually depends on the mechanical construction of the generator’s
rotor. A rotor assembled from separate parts (shaft and pole pieces)
connected or keyed together, will have a lower speed limit than a rotor
machined as a single unit.
The lower speed rating for a DC machine depends on the maximum field
current limit (as speed decreases, it is necessary to apply a higher field to
produce the same voltage output from the generator).
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117
Knowledge Check
Match each DC generator rating with the limiting factor it is based on.
Duration
 30 minutes
Logistics
 Use PowerPoint slides
270–271, Crossword
activity and the IG to
review TLO 7 material.
Use directed and nondirected questions to
students, check for
understanding of ELO
content, and review any
material where student
understanding of ELOs
is inadequate.
1. Insulation type and design
A. Speed
2. Size of conductors in the armature
B. Power
3. Mechanical limits of the prime mover
C. Current
4. Mechanical construction of the rotor
D. Voltage
TLO 7 Summary
In this section, you learned the different means of producing a DC voltage,
and you learned the basic workings of rectifiers and DC generators.
Now that you have completed this lesson, you should be able to:
1. Describe the common methods for producing a DC voltage and give
an example of each.
2. State the purpose of a rectifier and describe the outputs of rectifier
circuits.
3. Describe the effects of commutation in a DC generator.
4. State the purpose of each of the components of a DC machine.
5. List the three conditions necessary to induce a voltage.
6. Using the left-hand rule of generators, determine the direction of the
magnetic field, the motion of the conductor, or the direction of current
induced into a conductor.
7. Define terminal voltage as it applies to DC generators and describe
how terminal voltage of a DC generator is adjusted.
8. Identify the four categories and their bases for DC generator
nameplate ratings.
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Basic Electricity Part 1 Summary
Now that you have completed this module, you should be able to
demonstrate mastery of this topic by passing a written exam with a grade of
80 percent or higher on the following Terminal Learning Objectives
(TLOs):
1. Describe basic electrical theory principles of operation.
2. Describe the magnetic properties of materials and the use of
magnetism in electrical applications.
3. Differentiate between types of electrical symbols, drawings, and
diagrams.
4. Describe the operating characteristics, terminology, and hazards of a
lead-acid battery and voltaic cell.
5. Analyze various DC circuits to find resistances, currents, and voltages
at any given point within the circuit.
6. Describe the principles of operation, control, and characteristics of
DC motors.
7. Explain how a DC generator produces DC voltage.
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119
Duration
 30 minutes
Logistics
 Review PowerPoint slide
272.