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Electron Theory
Electron
Proton
Nucleus
Everything in the world is made of matter.
Matter is anything that has mass (weight) and occupies space.
All matter is made up of molecules that have a certain number of atoms.
Atom is broken down even further into a nucleus, neutrons , protons and electrons.
Molecule is a group of atoms.
Compound is a group of molecules.
Elements a single atom that still maintaining the properties of the original material
called.
Matter has three states:
Solid, Liquid, and Vapor.
MOLECULE
A single molecule of water (H2O) which is made up of two
hydrogen atoms and one oxygen atom.
Not all materials are made up of molecules. Copper, for
example, is made up of a single copper atom.
THE ATOM
A single atom consists of three basic components:
a proton, a neutron, and an electron.
Within the atom there is a Nucleus. The Nucleus contains the
protons and neutrons. Orbiting around the nucleus are the
electrons.
ATOM CONSTRUCTION
An atom is similar to a miniature solar system. As the sun is in the
center of the solar system, so is the nucleus is in the center of the
atom.
Protons and neutrons are contained within the nucleus. Electrons
orbit around the nucleus, which would be similar to planets
orbiting around the sun.
NUCLEUS
The Nucleus is located in the center of the atom (shown in red).
The Nucleus contains the protons and neutrons.
Orbiting around the nucleus are the electrons.
PROTONS
Protons are located within the nucleus of the atom (shown in blue) .
Protons are positively (+) charged.
NEUTRONS
Neutrons add atomic weight to an atom (shown in green).Neutrons
have no electrical charge.
ELECTRONS
Electrons orbit around the nucleus of the atom (shown in
yellow).Electrons are negatively (-) charged.
Normally electrons are prevented from being pulled into the atom
by the forward momentum of their rotation.
Electrons are also prevented from flying away because of the
magnetic attraction of the protons inside the nucleus, the same
type of force that keeps the planets orbiting around the sun.
Unlike Charges Attract
Like Charges Repel
ELECTRICAL CHARGES
Remember:
Unlike charges attract
Like charges, repel
Atoms always try to remain electrically balanced.
BALANCED ATOMS
Atoms normally have an equal number of electrons and
protons.
The negative charge of the electrons will cancel the positive
charge of the protons, thus balancing the charge of the atom.
This cancellation of charges creates a natural attraction or
bonding
ION PARTICLES
When an atom loses or gains an electron, an imbalance occurs.
The atom becomes either a positively or negatively charged particle
called an ION.
IONs will take or release an electron to become balanced again, this
process is responsible for electron flow ( electricity ).
ION CHARGE
A positive (+) ION has one less electron than it has protons.
A negative (-) ION has one more electron than it has protons.
The positive ION attracts a negative ION to become balanced.
ELECTRON ORBITS
Electrons rotate around the atom at different orbits called
Rings, Orbits, or Shells.
BOUND ELECTRONS orbit the nucleus on the inner rings.
Bound
electrons have a strong magnetic attraction to the nucleus.
FREE ELECTRONS orbit on the outermost ring which is known
as the VALANCE RING.
FREE ELECTRONS
Only the FREE ELECTRONS in the outermost shell (Valance Ring) are free
to move from atom to atom. This movement is called ELECTRON FLOW.
Because of their distance from the nucleus, free electrons have a weak
magnetic attraction.
Since this attraction is not strong , the electrons move easily from atom
to atom.
INSULATORS
An INSULATOR is any material that inhibits (stops) the flow of
electrons (electricity).
An insulator is any material with 5 to 8 free electrons in the outer
ring.
A toms with 5 to 8 electrons in the outer ring are held (bound) tightly
to the atom, and make no room for more electrons.
Insulator material includes glass, rubber, and plastic.
CONDUCTORS
A CONDUCTOR is any material that easily allows electrons (electricity)
to flow.
A CONDUCTOR has 1 to 3 free electrons in the outer ring.
Because atoms with 1 to 3 electrons in the outer ring are held loosely to
the atom, they can easily move to another atom or make room for
more electrons.
Conductor material includes copper and gold.
SEMICONDUCTORS
Any material with exactly 4 free electrons in the outer orbit is called
SEMICONDUCTORS.
A semiconductor is neither a conductor or insulator.
semiconductor material includes carbon, silicon, and germanium.
These materials are be used in the manufacturer of diodes,
transistors, and integrated circuit chips.
Two Current Flow theories exist.
The first is:
ELECTRON THEORY
The Electron Theory states that current flows from NEGATIVE to
POSITIVE. Electrons move from atom to atom as they move through
the conductor towards positive.
The second Current Flow theory is:
CONVENTIONAL THEORY
Conventional theory, also known as HOLE THEORY, states that current
flows from POSITIVE to NEGATIVE. Protons or the lack of electrons
(the holes) moves towards the negative. (Current flow direction in
Hole Theory is the opposite of that in Electron Theory) .
VOLTAGE
Voltage is the electrical force that moves electrons through a conductor.
Voltage is electrical pressure also known as EMF (Electro Motive Force)
that pushes electrons.
The greater the difference in electrical potential push (difference
between positive and negative), the greater the voltage force
Voltmeter
The instrument used to measure voltage, difference potential or
electromotive force is called voltmeter.
A voltmeter is wired in parallel with the circuit to measure voltage.
Safety instructions for measuring voltage:
1. choose a suitable voltmeter, each voltmeter is designed with a limit
of voltage measurement.
2. Be sure that the connecting of positive terminal (+) and negative
terminal (-) of voltmeter are correct.
The Voltmeter measures electrical pressure difference between two
points being measured.
Voltage can exist between two points without electron flow.
Voltage is measured in units called VOLTS.
Voltage measurements can use different value prefixes such as millivolt,
volt, Kilovolt, and Megavolt.
VOLTAGE
LESS THAN
BASE UNIT
BASIC
UNIT
LARGER
THAN
BASE UNIT
Symbol
mV
V
kV
Pronounced
millivolt
Volt
Kilovolt
Multiplier
0.001
1
1,000
CURRENT (AMPERES)
CURRENT is the quantity or flow rate of electrons moving past a point
within one second.
Current flow is also known as amperage, or amps for short.
Higher voltage will produce higher current flow, and lower voltage will
produce lower current flow.
Ammeter is the instrument used to measure current.
Safety instructions for current measurement:
1. choose a suitable ammeter, since each ammeter has different limit
of current measurement.
2. Be sure that the connection to positive terminal (+) and negative
terminal (-) of ammeter are correct.
3. Do not directly connect ammeter terminals to dry cell terminals.
Since it can damage the meter.
Ammeters are placed in series (inline) to count the electrons passing
through it.
Current is measured in units called Amperes or AMP
Amperage measurements can use different value prefixes, such as
micro amp, milliamp and Amp.
AMPERAGE
LESS THAN
BASE UNIT
LESS THAN
BASE UNIT
BASIC
UNIT
Symbol
µA
mA
A
Pronounced
Micro amp
milliamp
Amp
Multiplier
0.000001
0.001
1
AFFECTS OF CURRENT FLOW
Two common effects of current flow are
Electromagnetism – Heat Generation
HEAT:
When current flows, heat will be generated. The higher the current
flow the greater the heat generated. An example would be a light
bulb.
ELECTROMAGNETISM:
When current flows, a small magnetic field is created. The higher the
current flow, the stronger the magnetic field.
An example:
Electromagnetism principles are used in alternators, ignition systems,
and other electronic devices.
RESISTANCE
Resistance is the force that reduces or stops the flow of electrons. It
opposes voltage.
Higher resistance will decrease the flow of electrons and lower
resistance will allow more electrons to flow.
Ohmmeter is the instrument used to measure resistance.
Multi meter is a meter combines the functions of ammeter,
voltmeter and ohmmeter.
Steps for resistance measurement:
Turn the face dial to a position for required measuring, resistance, then
touch both of terminals of multi meter (see figure 1) and adjust the
meter range to 0 Ω. Touch both of terminals of meter to a resistance
and take the reading (see figure 2).
An OHMMETER measures the resistance of an electrical circuit or
component.
No voltage can be applied while the ohmmeter is connected, or
damage to the meter will occur.
RESISTANCE UNITS
Resistance is measured in units called OHMS. Resistance measurements
can use different value prefixes, such as Kilo ohm and Mega ohms.
Resistance
BASIC UNIT
More THAN
BASE UNIT
More THAN
BASE UNIT
Symbol
Ω
K
M
Pronounced
Ohm
Kilo Ohm
Mega Ohm
Multiplier
1
1000
1000000
RESISTANCE FACTORS
Various factors can affect the resistance. These include:
LENGTH :
The longer the conductor, the higher the resistance.
DIAMETER :
The narrower the conductor, the higher the resistance.
TEMPERATURE:
Depending on the material, most will increase resistance as
temperature increases.
PHYSICAL CONDITION (DAMAGE)
Damage to the material. Any damage will increase resistance.
TYPE of MATERIAL
Various materials have a wide range of resistances.
There are two basic types of Electricity classifications:
STATIC ELECTRICITY is electricity that is standing still. Voltage
potential with NO electron flow.
DYNAMIC ELECTRICITY is electricity that is in motion. Voltage
potential WITH electron flow.
Two types of Dynamic electricity exist:
Direct Current (DC) Electron Flow is in only one direction.
Alternating Current (AC) Electron flow alternates and flows in
both directions (back and forth).
STATIC ELECTRICITY : Voltage potential with NO electron flow.
Example:
By rubbing a silk cloth on a glass rod, you physically remove electrons
from the glass rod and place them on the cloth. The cloth now has a
surplus of electrons (negatively charged), and the rod now has a
deficiency of electrons (positively charged).
DYNAMIC ELECTRICITY
is electricity in motion, meaning you have electrons flowing, in other
words voltage potential WITH electron flow.
Two types of dynamic electricity exists:
Direct Current (DC)
Alternating Current (AC)
DIRECT CURRENT (DC)
Electricity with electrons flowing in only one direction is called
Direct Current or DC.
DC electrical systems are used in cars.
ALTERNATING CURRENT (AC)
Electricity with electrons flowing back and forth, negative positive- negative, is called Alternating Current, or AC.
The electrical appliances in your home use AC power.
SOURCES OF ELECTRICITY
Electricity can be created by several means:
Friction creates static electricity.
Heat can act upon a device called a thermo couple to create DC.
Light applied to photoelectric materials will produce DC electricity.
Pressure applied to a piezoelectric material produce DC electricity.
Chemical Action – battery produce DC electricity.
magnetic action – Alternator produce AC electricity.
AN ELECTRICAL CIRCUIT
The circuit shown below has a power source, fuse, switch, two lamps
and wires connecting each into a loop or circle.
ELECTRICAL CIRCUIT REQUIREMENTS
A complete Electrical Circuit is required in order to make electricity
practical. Electrons must flow from and return to the power source.
There are three different circuit types, all require the same basic
components:
1. Power Source is needed to supply the flow of electrons (electricity).
2. Protection Device prevents damage to the circuit.
3. Load Device converts the electricity into work.
4. Control Device allows the user control to turn the circuit on or off
5. Conductors provide an electrical path to and from the power source.
BASIC CIRCUIT CONSTRUCTION
1. Power Source (Battery, Alternator, Generator, etc.)
2. Protection Device (Fuse, Fusible Link, or Circuit Breaker)
3. Load Device (Lamp, Motor, Winding, Resistor, etc.)
4. Control (Switch, Relay, or Transistor)
5. Conductors (A Return Path, Wiring to Ground)
LOADS
Any device such as a lamp or horn that consumes electricity is called a
load.
In an electrical circuit, all loads are regarded as resistance.
Loads with high resistance cause less current to flow while those with
lower resistance allow high current rates to flow.
Ohm’s Law
V = IR
The voltage change [V] (volts) across any
resistive load is equal to the product of the
current [I] (amps) and the resistance [R]
(Ohms).
WHAT IS OHM'S LAW?
A simple relationship exists between voltage, current, and resistance
in electrical circuits.
OHM'S LAW
Ohm's Law says:
The current in a circuit is directly proportional to the applied voltage
and inversely proportional to the amount of resistance.
CURRENT is affected by either voltage or resistance.
VOLTAGE is not affected by either current or resistance.
RESISTANCE is not affected by either voltage or current.
OHM'S LAW FORMULA
E=IR
Voltage = Current x Resistance
E
Voltage applied to the circuit, in volts (V)
I
Current flowing in the circuit, in amperes (A)
R
Resistance in the circuit, in ohms
Example 1 – Instructor Example
120 V
i=?
R = 12
ohms
Current
I = V/R = 120 V/12 Ohms = 10 amps
Example 2 – Student Example
240 V
I=?
I=
R = 24 Ohms
APPLICATIONS OF OHM'S LAW
In the following circuit, assume that resistance R is 2 and voltage V
that is applied to it is 12 V. Then, current I flowing in the circuit can
be determined as follows:
APPLICATIONS OF OHM'S LAW
V=IxR
In the following circuit, assume that resistance R is 4 ohms. The voltage
V that is necessary to permit a current I of 3 A to pass through the
resistance can be determined as follows:
APPLICATIONS OF OHM'S LAW
In the following circuit, assume that a voltage V of 12 V is applied to the
circuit and current I of 4 A flows in it. Then, the resistance value R of the
resistance or load can be determined as follows:
Kirchhoff’s Laws
• Voltage Law: The sum of the voltage rises
around a closed loop in a circuit must equal the
sum of the voltage drops.
• Current Law: The sum of all currents into a
junction (node) must equal the sum of all
currents flowing away from the junction.
Resistors in Series
Applying Kirchhoff’s
voltage law gives us:
V = I R1 + I R2 + I R3
TYPES OF CIRCUITS -
SERIES CIRCUITS
A Series Circuit has only one path to ground Therefore:
1. An open in the circuit will disable the entire circuit.
2. The voltage divides between the loads. Vt = V1 + V2 + V3 + V4
It = I1 = I2 = I3 = I4
3. The current flow is the same .
4. The resistance of each load is different. Rt = R1 + R2 + R3 + R4
Equivalent Resistance
If desired, several resistors can sometimes be
replaced by a single “equivalent” resistor:
For resistors in series: Req = R1 + R2 + R3 + …
R1
R2
R3
Req
SERIES CIRCUIT CALCULATIONS
In this example, the circuit includes 4 series resistors.
Rt = R1 + R2 + R3 + R4
Rt = 5 + 1 + 2 + 2
Rt = 10 Ω
--------->
--------->
5Ω
R1
I = 1.2 Amps
1Ω
R2
2Ω
R3
12 Volts
2Ω
R4
10 Ω
Rt
12 Volts
Original Circuit
Equivalent
Circuit
47
VOLTAGE DROP
A voltage drop is the amount of voltage or electrical pressure that is
used or given up as electrons pass through a resistance (load).
1. All voltage will be used up in the circuit.
2. The sum of the voltage drops will equal source voltage.
3. A voltage drop measurement is done by measuring the voltage
before entering the load and the voltage as it leaves the load.
VOLTAGE DROP TOTAL
When more than one load exists in a circuit:
1. the voltage divides and will be shared among the loads.
2. The sum of the voltage drops equal source voltage.
3. The higher the resistance the higher the voltage drop.
4. Depending on the resistance, each load will have a different
voltage drop.
VOLTAGE DROP CALCULATION
TYPES OF CIRCUITS -
PARALLEL CIRCUITS
A Parallel Circuit has multiple paths or branches to ground. Therefore:
1. In the event of an open in the circuit in one of the branches, current
will continue to flow through the remaining.
2. Voltage is the same in each branch. Vt = V1 = V2 = V3 = V4
1. Current flow through each branch is different. It = I1 + I2 + I3 + I4
𝟏
𝟏
𝟏
𝟏
𝟏
2. Resistance of each branch is different. 𝑹𝒕 = 𝑹𝟏 + 𝑹𝟐 + 𝑹𝟑+ 𝑹𝟒
Resistors in Parallel
Applying Kirchhoff’s voltage law gives us:
voltage law: V = I1R1 = I2R2 = I3R3
current law: Ix = I1 + Iy and Iy = I2 + I3
Equivalent Resistors
1
1
1
1



 ...
Req R1 R2 R3
For Resistors
in Parallel
R1
R2
R3
Req
Example Problem:
• If each of the R’s were (R =240 ohm), what would be the
equivalent resistance for all three resistances .
1
Req
R1
R2
R3

1
R1
Req =

1
R2

1
R3
 ...
PARALLEL CIRCUIT CALCULATIONS
To determine the total resistance when resistors are of equal value in
a parallel circuit, use the following illustration , there are three 15 W
resistors. The total resistance is:
R1
R2
R3
15 Ω
15 Ω
15 Ω
Value of any one Resistor
Rt = Number of Resistors
Rt =
𝟏𝟓
𝟑
Rt =3 Ω
In the following illustration, there are three resistors, each of different value. Solve for
the total resistance as follows:
1 = 1
1
1
+
+
R1 R2 R 3
Rt
Insert Values for the Resistors
1 = 1 + 1 + 1
5
10 20
Rt
Find the Lowest Common Denominator
4 + 2 + 1
1
=
20 20 20
Rt
Add the Numerators
1
7
=
Rt
20
Invert Both Sides of the Equation
Rt = 20
7
1
Rt
= 2.86 Ω
R1
5Ω
R2
10 Ω
R3
20 Ω
56
The second formula is used when there are only two resistors.
𝑹𝟏 × 𝑹𝟐
𝐑𝐭 =
𝑹𝟏 + 𝑹𝟐
𝑹𝒕 =
𝟓×𝟏𝟎
𝟓+𝟏𝟎
𝑹𝒕 =
𝟓𝟎
𝟏𝟓
𝑹𝒕 = 𝟑.𝟑𝟑 Ω
R1
R2
5Ω
10 Ω
When unequal value resistors are placed in a parallel circuit,
opposition to current flow is not the same in every circuit branch.
Current is greater through the path of least resistance.
In the following circuit R1 is 40 W and R2 is 20 W. Small values of
resistance means less opposition to current flow. More current will
flow through R2 than R1.
12 Volts
+
_
R1
40 Ω
I1 =
0.3 Amps
R2
20 Ω
I2 =
0.6 Amps
Using Ohm’s Law, the total current for each circuit can be calculated.
→→
→→
→→
→→
→→
→→
Or
→→
→→
→→
→→
→→
SERIES PARALLEL CIRCUIT
A series-parallel circuit has some components in series and others in
parallel. The power source and control or protection devices are usually
in series; the loads are usually in parallel.
R1 10 Ω
R3 10 Ω
R2 10 Ω
First, use the formula to determine total resistance of parallel circuit to
find the total resistance of R1 and R2. When the resistors in a parallel
circuit are equal , the following formula is used:
𝐑𝐭′ =
𝐑𝐭′ =
𝑽𝒂𝒍𝒖𝒆 𝒐𝒇 𝒂𝒏𝒚 𝒐𝒏𝒆 𝑹𝒆𝒔𝒊𝒔𝒕𝒆𝒓
𝒏𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒓𝒆𝒔𝒊𝒔𝒕𝒆𝒓𝒔
𝟏𝟎
𝟐
𝐑𝐭′ = 𝟓 Ω
Second, redraw the circuit showing the equivalent values. The
result is a simple series circuit which uses already learned equations and
methods of problem solving.
R3 10Ω
+
_
𝐑𝐭 = 𝟓 + 𝟏𝟎 = 𝟏𝟓 Ω
R3 5Ω
In the following illustration R1 and R2 are in series with each other. R3 is
in parallel with the series circuit of R1 and R2.
R1 10Ω
+
R3 20Ω
_
R2 10Ω
First, use the formula to determine total resistance of a series circuit
to find the total resistance of R1 and R2. The following formula is
used:
Rt' = R1 + R2
Rt' = 10 Ω + 10 Ω
Rt' = 20 Ω
Second, redraw the circuit showing the equivalent values. The result is
a simple parallel circuit which uses already learned equations and
methods of problem solving
+
_
R = 20 Ω
+
_
Rt = 10 Ω
R3 = 20 Ω
Power
Work
Whenever a force of any kind causes motion, work is
accomplished. In the illustration below work is done when a
mechanical force is used to lift a weight. If a force were exerted
without causing motion, then no work is done.
Basic Relationship – Power Law
P = IV
Power dissipated [P] (watts) is equal to
product of the current [I] (amps) and
voltage [V] (volts)
Electric Power
In an electrical circuit, voltage applied to a conductor will cause
electrons to flow.
Voltage is the force and electron flow is the motion.
The rate at which work is done is called power and is represented by
the symbol “P” Power is measured in watts, represented by the
symbol “W” In a direct current circuit.
One watt is the rate work is done in a circuit when 1 amp flows with
1 volt applied.
Power Formulas
In a DC circuit, power is the product of voltage times current.
Later in this course, you will learn a slightly different version of this
relationship for an alternating current (AC) circuit.
𝐏=𝐄x𝐈
or
𝐏 = 𝐄𝐈
Two other power equations can be derived from this formula by
substituting other components of Ohm’s Law.
𝐏 = 𝐈𝟐 x 𝐑
And
E2
𝐏=
𝐑
Example
120 V
i=?
R = 12 ohms
P = V I = 120 V * 10 Amps = 1200 Watts
Example 2
240 V
P=
I=?
R = 24 Ohms
Example 3
• Without doing any calculations, which light bulb
has the lowest resistance?
o 75 W bulb at 120 V
o 150 W bulb at 120 V
In the following illustration, power can be calculated using any of the
power formulas.
P = EI
P = 12 Volts x 2 Amps
P = 24 Watts
or
P = I2R
P = (2 Amps)2 x 6 Ω
P = 24 Watts
or
E2
P=
R
( 12 Volts )2
P=
6Ω
144
P=
6
P = 24 Watts
I = 2 Amps
+
_
12 Volts
R=6Ω
Additional Calculations
For example, a common household lamp may be rated for 120 volts and
100 watts. Using Ohm’s Law, the rated value of resistance of the lamp
can be calculated.
E2
E2
( 120 Volts )2
P=
→ R=
→ R=
→ R= 𝟏𝟒𝟒 Ω
R
P
100 watts
Using the basic Ohm’s Law formula, the amount of current flow
for the 120 volt, 100 watt lamp can be calculated.
E
120 Volts
I=
→ I=
→ I= 𝟎.𝟖𝟑𝟑 𝐀𝐦𝐩𝐬
R
𝟏𝟒𝟒 Ω
By comparison, a lamp rated for 120 volts and 75 watts has a resistance
of 192 W and a current of 0.625 amps would flow if the lamp had the
rated voltage applied to it.
E2
E2
( 120 Volts )2
R=
→ R=
→ R=
→ R= 𝟏𝟗𝟐Ω
P
P
75 watts
E
( 120 Volts )2
I=
→ I=
→ I= 𝟎.𝟔𝟐𝟓 𝐀𝐦𝐩𝐬
R
𝟏𝟗𝟐Ω
Magnetism
The principles of magnetism are an integral part of electricity. In fact,
magnetism can be used to produce electric current and vice versa.
Types of Magnets
Permanent magnets come in many shapes.
Magnets have two characteristics:
1. They attract iron and.
2. If free to move a magnet will assume a north-south orientation.
Magnetic Lines of Flux
Every magnet has two poles, one north pole and one south pole.
Magnetic Lines of Flux follow these rules :
1. Magnetic lines are Invisible .
2. flux leave the north pole and enter the south pole.
3. The magnetic lines of flux always form closed loops.
4. lines of flux never cross each other.
Interaction between Two Magnets
When two magnets are brought together, the magnetic flux field
around the magnets causes some form of interaction.
Two unlike poles brought together cause the magnets to attract.
Two like poles brought together cause the magnets to repel.
Electromagnetism
Left-Hand Rule for Conductors
Every electric current generates a magnetic field.
A relationship exists between the direction of current flow and the
direction of the magnetic field.
The left-hand rule for conductors demonstrates this relationship.
If a current-carrying conductor is grasped with the left hand with the
thumb pointing in the direction of electron flow, the fingers will point
in the direction of the magnetic lines of flux.
Current-Carrying Coil
A coil of wire carrying a current, acts like a magnet. Individual loops of
wire act as small magnets.
The strength of the field can be increased by
1. Adding more turns to the coil
2. Increasing the amount of current
Left-Hand Rule for Coils
A left-hand rule exists for coils to determine the direction of the
magnetic field.
The fingers of the left hand are wrapped around the coil in the
direction of electron flow. The thumb points to the north pole of the
coil.
Electromagnets
An electromagnet is composed of a coil of wire wound around a core
made of soft iron or some other material that easily conducts
magnetic lines of force.
When current is passed through the coil, the core becomes
magnetized.
The ability to control the strength and direction of the magnetic force
makes electromagnets useful.
A large variety of electrical devices such as motors, circuit breakers,
contactors, relays and motor starters use electromagnetic principles.
The supply of current for electrical devices may come from
1. Direct current (DC) , source electrons flow continuously in
one direction from the source of power through a conductor to a
load and back to the source of power.
2. Alternating current (AC) , source electrons flow first in one
direction then in another. AC generator reverses its terminal
polarities many times a second.
AC Sine Wave
A sine wave is The graphic representation of current or voltage of AC.
There are two axes of the graphic representation :
1. The vertical axis represents the direction and magnitude of current or
voltage.
2. The horizontal axis represents time.
+ Direction
0
Time
- Direction
When the waveform is above the time axis, current is
flowing in one direction. This is referred to as the positive
direction.
When the waveform is below the time axis, current is
flowing in the opposite direction. This is referred to as
the negative direction.
A sine wave moves through a complete rotation of 360
degrees, which is referred to as one cycle.
Alternating current goes through many of these cycles
each second.
Single-Phase and Three-Phase AC Power
Alternating current is divided into 2 types
1. single-phase - small electrical demands (home)
2. Three-Three-Phase – large electrical demands (commercial )
Illustration bellow show three overlapping AC cycles, offset by 120
electrical degrees.
Phase 1 Phase 2 Phase 3
+
0
-
AC Generators
A basic generator consists of a magnetic field, an armature, slip rings,
brushes and a resistive load.
The magnetic field is created by an electromagnet.
An armature is any number of conductive wires wound in loops which
rotates through the magnetic field.
Pole Piece
Magnetic Field
Armature
R1
Brush
Slip Ring
Basic Generator Operation
Initial position of zero degrees
An armature rotates through the magnetic field. At an initial position of
zero degrees, the armature conductors are moving parallel to the
magnetic field and not cutting through any magnetic lines of flux. No
voltage is induced.
R1
Operation from Zero to 90 Degrees
.
As the armature rotates from zero to 90 degrees, the conductors cut
through more and more lines of flux, building up to a maximum induced
voltage in the positive direction.
90
Degrees
R1
Operation from 90 to 180 Degrees
The armature continues to rotate from 90 to 180 degrees, cutting fewer
lines of flux. The induced voltage decreases from a maximum positive
value to zero.
S
R1
180
Degrees
Operation from 180 to 270 Degrees
As the armature continues to rotate from 180 degrees to 270 degrees,
the conductors cut more lines of flux, but in the opposite direction,
and voltage is induced in the negative direction, building up to a
maximum at 270 degrees.
270
Degrees
R1
Operation from 270 to 360 Degrees
As the armature continues to rotate from 270 to 360 degrees, induced
voltage decreases from a maximum negative value to zero.
This completes one cycle.
360
Degrees
S
One Revolution
R1
Four-Pole AC Generator
An increase in the number of poles, would cause an increase in the
number of cycles completed in a revolution.
A two-pole generator would complete one cycle per revolution .
A four-pole generator would complete two cycles per revolution.
An AC generator produces one cycle per revolution for each pair of
poles.
One Revolution
R1
Frequency
Frequency is the number of cycles per second of voltage induced in
the armature.
If the armature rotates at a speed of 60 revolutions per second, the
generated voltage will be 60 cycles per second.
The unit for frequency is hertz(Hz)
1 Hz is equal to 1 cycle per second.
The standard power line frequency in the Kuwait is 50 Hz.
The following illustration shows 15 cycles in 1/4 second which is
equivalent to 60 Hz.
Voltage and Current
Peak Value
Voltage and current in an AC circuit rise and fall over time in a
pattern referred to as a sine wave.
The peak value of a sine wave occurs twice each cycle, once at the
positive maximum value and once at the negative maximum value.
Peak Value
+
0
Time
Peak Value
Peak-to-Peak Value
The value of the voltage or current between the peak positive and
peak negative values is called the peak-to-peak value.
+
0
Time
-
Peak-to-Peak
Value
Instantaneous Value
The instantaneous value is the value at any one point in the sine
wave.
+
Instantaneous Value
Time
-
Calculating Instantaneous Voltage
The voltage waveform produced as the armature rotates through 360
degrees rotation is called a sine wave because the instantaneous
voltage (e) is related to the sine trigonometric function.
The sine of an angle is represented symbolically as sin θ, where the
Greek letter theta (θ) represents the angle. The sine curve is a graph of
the following equation for values of θ from 0 to 360 degrees:
Instantaneous voltage is equal to the peak voltage times the sine of the
angle of the generator armature.
e = Epeak x sin θ
The following example
illustrates instantaneous values at 90,150, and 240 degrees.
The peak voltage is equal to 100 volts.
By substituting the sine at the instantaneous angle value, the
instantaneous voltage can be calculated.
+
90° = +100 Volts
150° = +50 Volts
0
240° = -86.6 Volts
-
Any instantaneous value can be calculated. For example theta θ =240°
e = Epeak x sin θ
e = 100 x -0.866
e = -86.6 volts
Effective Value of an AC Sine Wave
Translating the varying values into an equivalent constant value,
referred to at the effective value of voltage or current.
This is also known as the RMS value ( root-mean-square ).
RMS value is equal to the peak value times 0.707.
+
Peak Value
169.7 Volts
0
-
RMS= Epeak x 0.707
Epeak = RMS x 1.41
Inductance
The circuits studied to this point have been resistive.
Resistance and voltage are not the only circuit properties that effect
current flow, however inductance is the property of an electric
circuit that opposes change in electric current.
Resistance opposes current flow
Inductance opposes change in current flow.
Inductance is designated by the letter ( L ) .
The unit of measurement for inductance is the henry (h).
Current Flow and magnetic Field Strength
• Current flow produces a magnetic field in a conductor.
• The amount of current determines the strength of the magnetic
field.
• As current flow increases, field strength increases, and as
current flow decreases, field strength decreases.
0 Degrees
No Current
30 Degrees
Increasing
Current
90 Degrees
Maximum
Current
• Any change in current causes a corresponding change in the magnetic
field surrounding the conductor.
• A change in the magnetic field surrounding the conductor induces a
voltage in the conductor, this self-induced voltage opposes the
change in current.
• This self-induced voltage known as counter EMF .
• This opposition causes a delay in the time it takes current to attain its
new steady value.
• If current increases, inductance tries to hold it down.
• If current decreases, inductance tries to hold it up.
• Inductance is somewhat like mechanical inertia
* get object moving
* stop a mechanical object from moving.
Example:
A vehicle takes few moments to accelerate to a desired speed, or
decelerate to a stop.
Inductors
All conductors have inductance.
inductors are coils of wire wound for a specific inductance, or wound
around a metal core to concentrate the inductance.
The inductance of a coil is determined by :
1. number of turns in the coil
2. coil diameter
3. Length
4. core material.
An inductor is usually indicated symbolically on drawing as
Simple Inductive Circuit
In a resistive circuit, current change is considered instantaneous.
If an inductor is used, the current does not change as quickly.
The electrical wire used in the circuit has some resistance and
inductance.
Inductors also have resistance.
However, to simplify examples in this book,
the resistance and inductance of the wiring and the resistance of
inductors are not considered.
In the following circuit, initially the switch is in position 2, and there
is no current flowing through the ammeter (A).
When the switch is moved to position 1, current will rise rapidly
at first, then more slowly as the maximum value is approached.
1
A
2
+
_
R1
L1
Inductive Time Constant
In an inductive circuit , time constant is the ratio of inductance (in
henrys) to resistance (in ohms).
During the first time constant current rises to 63.2% of its maximum
value.
During the second time constant, current rises to 63.2% of
the remaining 36.8%, or a total of 86.4%.
It takes about five time constants for current to reach its maximum
value.
100.0%
98.1%
94.9%
86.4%
63.2%
First Time
Constant
Second Time
Constant
Third Time
Constant
Fourth Time
Constant
Fifth Time
Constant
Similarly, when the switch in the previous circuit is returned to
position 2, the magnetic field around the inductor will begin to
collapse, returning stored energy to the circuit, and it will take about
five time constants for current to reach zero.
100.0%
First Time Second Time Third Time
Constant
Constant
Constant
36.8%
13.6%
5.1%
1.9%
0%
Fourth Time
Constant
Fifth Time
Constant
Calculating the Time Constant of an Inductive
Circuit
. The time constant is designated by the symbol “t” To determine
the time constant of an inductive circuit use one of the following
formulas:
L (henrys)
τ (in seconds) =
R (ohms)
τ (in milliseconds) =
τ (in microseconds) =
L (millihenrys)
R (ohms)
L (microhenrys)
R (ohms)
In the following illustration, L1 is equal to 15 millihenrys and R1 is
equal to 5 W.
When the switch is closed, it will take 3 milliseconds for current to
rise from zero to 63.2% of its maximum value and approximately 15
milliseconds for full current to be reached.
+
R1 5 Ω
_
L1 15 mh
τ=
15 mh
5Ω
τ = 3 milliseconds
Formula for Series Inductors
The same rules for calculating total resistance can be applied to
calculating total inductance.
In the following circuit, an AC generator is used to supply electrical
power to four inductors. Total inductance of series inductors is
calculated using the following formula:
Lt = L1 + L2 + L3 ... + L n
AC Generator
Lt = L 1 + L 2 + L 3 + L4
Lt = 2 mh + 2 mh + 1 mh + 1 mh
Lt = 6 mh
2 mh
2 mh
L1
L2
1 mh
L3
1 mh
L4
Formula for Parallel Inductors
In the following circuit, an AC generator is used to supply electrical
power to three inductors.
Total inductance of parallel inductors is calculated using the following
formula:
1 + 1 +
1
1 ..1
Lt =
L2
L1
L3
L1
L2
5 mh
1 =
Lt
1 + 1 +
5
10
1 = 7
Lt
20
Lt = 20
7
Lt =
2.86 mh
+
Ln
10 mh
1
20
L3
20 mh
Capacitance
Capacitance and Capacitors
Capacitance is a measure of a circuit’s ability to store an electrical
charge.
A device manufactured to have a specific amount of capacitance is
called a capacitor.
A capacitor is made up of a pair of conductive plates separated by a
thin layer of insulating material.
Another name for the insulating material is dielectric material.
When a voltage is applied to the plates, electrons are forced onto
one plate. That plate has an excess of electrons while the other
plate has a deficiency of electrons.
The plate with an excess of electrons is negatively charged. The
plate with a deficiency of electrons is positively charged.
Negative Plate
Dielectric Material
Positive Plate
Direct current cannot flow through the dielectric material because it
is an insulator; however, the electric field created when the capacitor
is charged is felt through the dielectric.
Capacitors are rated for the amount of charge they can hold.
The capacitance of a capacitor depends on:
1. Area of the plates
2. Distance between the plates
3. Type of dielectric material used.
The unit of measurement for capacitance is farads (F).
Farad is a large unit and capacitors are often rated in microfarads
(mF) or picofarads (pF).
Capacitor Circuit Symbols
Capacitance is usually indicated symbolically on an electrical
drawing by a combination of a straight line with a curved line, or
two straight lines.
Simple Capacitive Circuit
In a resistive circuit, voltage change is instantaneous.
In a circuit with a resistor and capacitor in series, the voltage across the
capacitor does not change as quickly.
In the following circuit, initially the switch is in position 2 and no
voltage is measured by the voltmeter (V).
When the switch is moved to position 1, voltage across the capacitor
will rise rapidly at first, then more slowly as the maximum value is
1
approached.
2
+
_
3
R1
Capacitive Time Constant
time constant of a capacitive circuit is the product of capacitance, in
farads, times resistance, in ohms.
The time constant gives the time in seconds required for voltage
across the capacitor to reach 63.2% of its maximum value.
During the first time constant, voltage will rise to 63.2% of its
maximum value. During the second time constant, voltage will rise to
63.2% of the remaining 36.8%, or a total of 86.4%. It takes about five
time constants for voltage across the capacitor to reach its maximum.
100.0%
98.1%
94.9%
86.4%
63.2%
First Time
Constant
Second Time
Constant
Third Time
Constant
Fourth Time
Constant
Fifth Time
Constant
When the switch in the previous circuit is returned to position 2, the
capacitor will retain its charge because there is no path for current
flow. When the switch is moved to position 3, the capacitor will
begin to discharge, and it will take about five time constants for the
voltage across the capacitor and the current through the resistor to
reach zero.
100.0%
First Time
Constant
36.8%
13.6%
5.1%
1.9%
0%
Second Time
Constant
Third Time
Constant
Fourth Time
Constant
Fifth Time
Constant
Calculating the Time Constant of a Capacitive
Circuit
To determine the time constant of a capacitive circuit, use one of the
following formulas:
τ (in seconds) = R (megohms) x C (microfarads)
τ (in microseconds) = R (megahms) x C (picofarads)
τ (in microseconds) = R (ohms) x C (microfarads)
In the following illustration, C1 is equal to 2 mF, and R1 is equal to 10 Ω.
When the switch is closed, it will take 20 microseconds for voltage
across the capacitor to rise from zero to 63.2% of its maximum value. It
will take about five time constants, 100 microseconds, for this voltage
to rise to its maximum value.
+
_
R1 10 Ω
C1 2µF
V
τ = RC
τ = 2µF x 10 Ω
τ = 20 microseconds
Formula for Series Capacitors
Connecting capacitors in series decreases total capacitance.
The formula for series capacitors is similar to the formula for parallel
resistors.
In the following circuit, an AC generator supplies electrical power to
three capacitors. Total capacitance is calculated using the following
formula:
5µF
10µF
20µF
C1
C2
C3
Formula for Parallel Capacitors
Adding capacitors in parallel increases circuit capacitance.
In the following circuit, an AC generator is used to supply electrical
power to three capacitors. Total capacitance is calculated usingthe
following formula:
...
Ct = C1 + C2 + C3+ Cn
C1
C2
C3
10 µF
10 µF
20 µF
Ct = 5 µF + 10 µF + 20 µF
Ct = 35 µF
circuit with only inductance, capacitance, or both, but no
resistance, opposition to current flow is called Reactance,
designated by the symbol “X”.
Total opposition to current flow in an AC circuit that contains both
reactance and resistance is called Impedance, designated
by the symbol “Z”.
resistance, reactance and impedance are expressed in ohms
AC circuit only has inductance and resistance
Z= 𝑹𝟐 + 𝑿𝑳𝟐
AC circuit only has capacitance and resistance
Z= 𝑹𝟐 + 𝑿𝑪𝟐
Inductive Reactance
Inductance only affects current flow when the current is changing.
Inductance produces a self-induced voltage (counter emf) that opposes
changes in current.
This opposition to current flow is called inductive reactance and is
designated by the symbol “XL.
Inductive reactance is proportional to both the inductance and the
frequency applied. The formula for inductive reactance is:
XL = 2πfL
XL = 2 x 3.14 x frequency x inductance
For a 60 hertz circuit containing a 10 mh inductor, the inductive
reactance is:
XL = 2πfL
XL = 2 x 3.14 x 60 x 0.010
XL = 3.768 Ω
The formula for inductive reactance is:
XL = 2πfL
Where:
XL = inductive reactance measured in ohms
2π = a constant (2 x 3.1416 = 6.28)
f = the AC frequency of the electrical supply in hertz
L = the inductance value of the coil in henries.
XL = 2 x 3.14 x frequency x inductance
For a 60 hertz circuit containing a 10 mh inductor, the inductive
reactance is:
XL = 2πfL
XL = 2 x 3.14 x 60 x 0.010
XL = 3.768 Ω
For this example, the resistance is zero so the impedance is equal
to the reactance. If the voltage is known, Ohm’s Law can be used
to calculate the current. If, for example, the voltage is 10 volts, the
current is calculated as follows;
𝐄
𝐈=
𝐙
𝟏𝟎
𝐈=
𝟑. 𝟕𝟔𝟖
𝐈 = 𝟐. 𝟔𝟓 𝐀𝐦𝐩𝐬
In the following illustration, resistance and inductive reactance are
equal. Current lags voltage by 45 degrees.
45 Degrees
+
XL = 10 Ω
Voltage
Current
0
R = 10 Ω
_
Z= 𝑹𝟐 + 𝑿𝑳𝟐
Z= 𝟏𝟎𝟐 + 𝟏𝟎𝟐
Z= 𝟐𝟎𝟎
Z=𝟏𝟒. 𝟏𝟒𝟐𝟏Ω
Capacitive Reactance
Capacitance also opposes AC current flow. Capacitive reactance is
designated by the symbol XC.
The larger the capacitor, the smaller the capacitive reactance.
Current flow in a capacitive AC circuit is also dependent on frequency.
The following formula is used to calculate capacitive reactance:
1
Xc =
2πfc
Where:
XL = Capacitive reactance measured in ohms
2π = a constant (2 x 3.1416 = 6.28)
f = the AC frequency of the electrical supply in hertz
C = the capacitance value of the capacitor in microfarads.
The capacitive reactance for a 60 hertz circuit with a 10
microfarad capacitor is calculated as follows:
𝟏
𝑿𝒄 =
𝟐 × 𝟑. 𝟏𝟒 × 𝟔𝟎 × 𝟎. 𝟎𝟎𝟎𝟎𝟏𝟎
𝑿𝒄 = 265.39 Ω
For this example, the resistance is zero so the impedance is
equal to the capacitance. If the voltage is known, Ohm’s Law can
be used to calculate the current. If, for example, the voltage is
10 volts, the current is calculated as follows;
𝐄
𝐈=
𝐙
𝟏𝟎
𝐈=
𝟐𝟔𝟓. 𝟑𝟗
𝐈 = 𝟎. 𝟎𝟑𝟕𝟔 𝐀𝐦𝐩𝐬
In the following illustration, resistance and capacitive reactance are
equal. Current lags voltage by 45 degrees.
45 Degrees
XC = 10 Ω
+
Voltage
Current
0
R = 10 Ω
_
Z= 𝑹𝟐 + 𝑿𝑪𝟐
Z= 𝟏𝟎𝟐 + 𝟏𝟎𝟐
Z= 𝟐𝟎𝟎
Z=𝟏𝟒. 𝟏𝟒𝟐𝟏Ω
Series R-L-C Circuit
Circuits often contain resistance, inductance, and capacitance.
In an inductive AC circuit, current lags voltage by 90 degrees.
In a capacitive AC circuit, current leads voltage by 90 degrees.
In vector form, inductive and capacitive reactance are 180 degrees
apart.
net reactance is determined by taking the difference between the two
quantities.
• Resistive if XL and XC are equal
• Inductive if XL is greater than XC
• Capacitive if XC is greater than XL
XL
R
XC
Calculating Total Impedance in a Series R-L-C circuit
The following formula is used to calculate total impedance of a circuit
containing resistance, capacitance, and inductance:
Z= 𝑹𝟐 + (𝑿𝑳 − 𝑿𝑪)𝟐
Where:
Z = total impedance in ohms
R = resistance of the circuit in ohms
XC = Capacitive reactance of circuit in ohms
XL= Inductive reactance of circuit in ohms
In the case inductive reactance is greater than capacitive reactance,
subtracting XC from XL results in a positive number , indicating :
1. circuit reactance is inductive
2. current lags voltage.
In the case capacitive reactance is greater than inductive reactance,
subtracting XC from XL results in a negative number , indicating:
1. circuit reactance is capacitive.
2. current leads voltage.
In either case, the value squared will result in a positive number.
Calculating Reactance and Impedance
in a Series R-L-C circuit
In the following 120 volt, 60 hertz circuit, resistance is 1000 W,
inductance is 5 mh, and capacitance is 2 mF , calculate impedance
for this circuit.
R = 1000 Ω
L=5
C=2
𝑋𝐿 = 2 𝜋𝑓𝐿
𝑋𝐿 = 6.28 × 60 × 0.005
𝑋𝐿 = 1.884 Ω
1
𝑋𝑐 =
2𝜋𝑓𝐶
1
𝑋𝑐 =
6.28 × 60 × 0.000002
𝑋𝑐 = 1327 Ω
𝑍 = 𝑅2 + 𝑋𝐿 − 𝑋𝐶 2
𝑍 = 10002 + 1.884 − 1327
𝑍 = 1000000 + −1325.116
𝑍 = 1000000 + 1755932.41
𝑍 = 2755932.41
𝑍 = 1660.1 Ω
2
2
Given that the applied voltage is 120 volts, current can be calculated as
follows:
𝐄
𝐈=
𝐙
𝟏𝟐𝟎
𝐈=
𝟏𝟔𝟔𝟎. 𝟏
𝐈 = 𝟎. 𝟎𝟕𝟐𝟑 𝐀𝐦𝐩𝐬
Calculating Impedance in a Parallel R-L-c circuit
In the following 120 volt, 60 hertz circuit, capacitive reactance is 25 Ω,
inductive reactance is 50 Ω, and resistance is 1000 Ω. A simple
application of Ohm’s Law will find the branch currents.
120 V
R =1000 Ω
XL = 50 Ω
XC = 25 Ω
𝐄
𝐈𝐑 =
𝐑
𝟏𝟐𝟎
𝐈𝐑 =
𝟏𝟎𝟎𝟎
𝐈𝐑 = . 𝟏𝟐𝟎 𝐀𝐦𝐩𝐬
𝐄
𝐈𝐋 =
𝐗𝐋
𝟏𝟐𝟎
𝐈𝐋 =
𝟓𝟎
𝐈𝐋 = 𝟐. 𝟒 𝐀𝐦𝐩𝐬
𝐄
𝐈𝐂 =
𝐗𝐂
𝟏𝟐𝟎
𝐈𝐂 =
𝟐𝟓
𝐈𝐂 = 𝟒. 𝟖 𝐀𝐦𝐩𝐬
Total current can be calculated :
IT =
IR2 + IC − IL
2
IT =
0.122 + 4.8 − 2.4
IT =
0.0144 + 5.76
IT =
5.7744
2
IT = 2.403 Amps
Impedance can then be calculated as follows:
𝑬
𝐙𝐓 =
𝐈𝑻
𝟏𝟐𝟎
𝐙𝐓 =
𝟐. 𝟒𝟎𝟑
𝐙𝐓 = 𝟒𝟗. 𝟒𝟗 Ω
Voltage Drop – Definition
Voltage drop is defined as the amount of voltage loss that occurs through
all or part of a circuit due to impedance.
Excessive voltage drop in a circuit can cause lights to flicker or burn dimly,
heaters to heat poorly, and motors to run hotter than normal and burn
out.
This condition causes the load to work harder with less voltage pushing
the current.
The National Electrical Code recommends limiting the voltage drop from
the breaker box to the farthest outlet for power, heating, or lighting to 3
percent of the circuit voltage.
This is done by selecting the right size of wire
If the circuit voltage is 120 volts, then 3 percent of 120 volts is 3.6 volts.
This means that voltage lost from the wires in the circuit should not
exceed 3.6 volts and the outlet should still have 120 or 116.4 volts to
supply.
Causes
Resistance in the conductor causes voltage drop.
There are four fundamental causes of voltage drop:
1. Material - Copper is a better conductor than aluminum and will have
less voltage drop than aluminum for a given length and wire size.
2. Wire Size - Larger wire sizes (diameter) will have less voltage drop
than smaller wire sizes (diameters) of the same length.
3. Wire Length - Shorter wires will have less voltage drop than longer
wires for the same wire size (diameter).
4. Current Being Carried - Voltage drop increases on a wire with an
increase in the current flowing through the wire.
Voltage Drop Formulas
Mathematical formulas are used to calculate the voltage drop for
given wires sizes, lengths, and types under load.
These formulas may be used to determine any one of the four factors
affecting voltage drop if the other three factors are known.
Keep in mind there are separate formulas for single and three
phase.
Formulas For Copper Single Phase Circuits:
𝐦𝐚𝐭𝐞𝐫𝐢𝐚𝐥 𝐜𝐨𝐧𝐬𝐭𝐚𝐧𝐭 × 𝐀 × 𝐋
𝐂𝐌 =
𝐕𝐨𝐥𝐭𝐚𝐠𝐞 𝐃𝐫𝐨𝐩
Where:
CM = Area of conductor in circular mills
A = Single Phase line current in Amperes
L = Length (one-way) of circuit in feet
V = Voltage Drop (Volts)
Example 1
Find the size of copper ( constant 25 ) wire to carry a load of 40 amperes
at 240 volts a distance of 500 feet with 2% voltage drop. Use the
formula:
𝐦𝐚𝐭𝐞𝐫𝐢𝐚𝐥 𝐜𝐨𝐧𝐬𝐭𝐚𝐧𝐭 × 𝐀 × 𝐋
𝐂𝐌 =
𝐕𝐨𝐥𝐭𝐚𝐠𝐞 𝐃𝐫𝐨𝐩
𝟐𝟓 × 𝟒𝟎 𝐚𝐦𝐩𝐬 × 𝟓𝟎𝟎 𝐟𝐞𝐞𝐭
𝐂𝐌 =
𝟒. 𝟖 𝐯𝐨𝐥𝐭𝐬
𝐂𝐌 = 𝟏𝟎𝟒𝟏𝟔𝟕 𝐜𝐢𝐫𝐜𝐮𝐥𝐚𝐫 𝐦𝐢𝐥𝐬
Example 2
How far can No. 6 copper wire be used to carry a load of 30 amperes at
240 volts and keep within 1% voltage drop?
𝐂𝐌 × 𝐕𝐨𝐥𝐭𝐚𝐠𝐞 𝐃𝐫𝐨𝐩
𝐋=
𝐦𝐚𝐭𝐞𝐫𝐢𝐚𝐥 𝐜𝐨𝐧𝐬𝐭𝐚𝐧𝐭 × 𝐀
𝟐𝟔𝟐𝟓𝟎 𝐜𝐢𝐫𝐜𝐮𝐥𝐚𝐫 𝐦𝐢𝐥𝐬 × 𝟐. 𝟒 𝐯𝐨𝐥𝐭𝐬
𝐋=
𝟐𝟓 × 𝟑𝟎 𝐚𝐦𝐩𝐬
𝐋 = 𝟖𝟒 𝐟𝐞𝐞𝐭
True Power and Apparent Power Formulas
The formula for apparent power is:
P = EI
The formula for true power is:
P = EI cos θ
Calculating Apparent Power in a simple R-L-C
In the following 120 volt circuit, current is equal to 84.9 mA.
Inductive reactance is 100 Ω and capacitive reactance is 1100 Ω. The
phase angle is -45 degrees. By referring to a trigonometric table, the
cosine of -45 degrees is found to be 0.7071.
R = 1000 Ω XL = 100 Ω XC = 1100 Ω
120 V
The apparent power consumed by the circuit is:
P = EI
P = 120 x 0.0849
P = 10.2 VA
The true power consumed by the circuit is:
P = EI cos θ
P = 120 x 0.0849 x 0.7071
P = 7.2 Watts
Another formula for true power is:
P = I2R
P = 0.08492 x 1000
P = 7.2 Watts
Power Factor
Power factor is the ratio of true power to apparent power in an AC
circuit. Power factor is expressed in the following formula:
𝐓𝐫𝐮𝐞 𝐏𝐨𝐰𝐞𝐫
𝐏𝐨𝐰𝐞𝐫 𝐅𝐚𝐜𝐭𝐨𝐫 =
𝐀𝐩𝐩𝐚𝐫𝐞𝐧𝐭 𝐏𝐨𝐰𝐞𝐫
EI cos θ
𝐏𝐅 =
EI
𝐏𝐅 = cos θ
In a purely resistive circuit, where current and voltage are in phase,
there is no angle of displacement between current and voltage. The
cosine of a zero degree angle is one. The power factor is one. This
means that all energy delivered by the source is consumed by the
circuit and dissipated in the form of heat.
+
Voltage
Current
0
_
In a purely reactive circuit, voltage and current are 90 degrees apart.
The cosine of a 90 degree angle is zero. The power factor is zero. This
means the circuit returns all energy it receives from the source to the
source.
90 Degrees
+
Voltage
Current
0
_
In a circuit where reactance and resistance are equal, voltage and
current are displaced by 45 degrees. The cosine of a 45 degree
angle is 0.7071. The power factor is 0.7071. This means the circuit
uses approximately 70% of the energy supplied by the source and
returns approximately 30%.
45 Degrees
+
XL = 10 Ω
Voltage
Current
0
R = 10 Ω
_
Transformers are electromagnetic devices that transfer electrical
energy from one circuit to another by mutual induction. A singlephase transformer has two coils, a primary and a secondary. Mutual
induction is the transfer of electrical energy from the primary to the
secondary through magnetic fields .
Primary Coil
Secondary Coil
Transformers are used to step a voltage up to a higher level, or down to
a lower level.
The following discussion of step-up and step-down transformers
applies to transformers with an iron core.
Lines of Flux
Confined to
Iron Core
Lines of Flux
that don’t Couple
It is the number of turns which determine if a transformer is a
step up or step down transformer. The following “rules-of-thumb”
apply to transformers:
1. If the primary coil has fewer turns than the secondary coil, the
transformer is a step-up transformer.
2. If the primary coil has more turns than the secondary coil, the
transformer is a step-down transformer.
3. When the number of turns on the primary and secondary coils of a
transformer are equal, input voltage, impedance, and current are
equal to output voltage, impedance, and current.
Step-Up Transformer
The primary coil has fewer turns than the secondary coil.
Voltage and impedance are stepped up.
Secondary has twice as many turns as the primary
Voltage is stepped up from 120 VAC to 240 VAC.
Because impedance is also stepped up, current is stepped down from 10
amps to 5 amps.
1:2
Primary Coil
900 Turns
120 VAC Supply
10 Amps
Secondary Coil
1800 Turns
240 VAC
5 Amps
Step-Down Transformer
The following circuit illustrates a step-down transformer.
The primary coil has more turns than the secondary coil.
The step-down ratio is 2:1
Voltage and impedance are stepped down, current is stepped up
2:1
Primary Coil
1800 Turns
240 VAC Supply
5 Amps
Seconday Coil
900 Turns
120 VAC Out
10 Amp
Formulas for Calculating the
Number of Primary and
Secondary Turns of a Transformer
There are a number of useful formulas for calculating, voltage, current,
and the number of turns between the primary and secondary of a
transformer. These formulas can be used with either step-up or stepdown transformers. The following legend applies to the transformer
formulas:
ES = secondary voltage
EP = primary voltage
IS = secondary current
IP = primary current
NS = turns in the secondary coil
NP = turns in the primary coil
To find voltage:
𝐄𝐩 × 𝐈𝐩
𝐄𝐬 =
𝐈𝐬
𝐄𝐬 × 𝐈𝐬
𝐄𝐩 =
𝐈𝐩
To find current:
𝐄𝐩 × 𝐈𝐩
𝐈𝐬 =
𝐄𝐬
𝐄𝐬 × 𝐈𝐬
𝐈𝐩 =
𝐄𝐩
To find number of turns:
𝐄𝐬 × 𝐍𝐩
𝐍𝐬 =
𝐄𝐩
𝐄𝐩 × 𝐍𝐬
𝐍𝐩 =
𝐄𝐬
Optional equipment that can be included in a circuit is of two kinds:
Control devices
Protective devices
A control device is something that allows us to determine where
and when electricity flows.
Most control devices either open or close the path of the circuit.
Switches, thermostats, and time clocks are examples of common
control devices found in circuits.
A protective device is used to protect either the load or the path
from:
1. excessive heat
2. overcurrent
3. Overvoltage
Most protective devices open the circuit path if excessive current is
flowing in the circuit.
Common examples of protective devices include fuses and circuit
breakers
Control devices are needed to start, stop, or redirect current flow
in an electrical circuit.
Control devices include :
1. Switches
• Single Pole Single Throw (SPST)
• Single Pole Double Throw (SPDT)
• Momentary Contact
• Multiple Pole Multiple Throw (MPMT or Gang Switch)
• Mercury
• Temperature (Bimetal)
• Time Delay
• Flasher
2. Relays
3. solenoids
Most switches require physical movement for operation
Relays and Solenoids
are operated with electromagnetism.
SWITCHES
A switch is the most common circuit control device. Switches usually
have two or more sets of contacts. Opening these contacts is called
"break" or "open" the circuit, Closing the contacts is called "make" or
"completing" the circuit.
Switches are described by the number of Poles and Throws they have.
"Poles" refer to the number of input circuit terminals
"Throws" refer to the number of output circuit terminal.
Switches are referred to as:
• SPST (single-pole, single-throw)
• SPDT (single-pole, double-throw)
• MPMT (multiple-pole, multiple-throw)
SINGLE POLE SINGLE THROW (SPST)
The simplest type of switch.
It either "completes" (turn on) or "break" (turn off) the circuit in a single
circuit. This switch has a single input pole and a single output throw.
SINGLE POLE DOUBLE THROW (SPDT)
A single-pole input, double-throw output switch has one wire going it
and two wires coming out.
MULTIPLE POLE MULTIPLE THROW (MPMT)
Multiple-Pole input, Multiple-Throw output switches, have movable
contacts wired in parallel. These switches move together to supply
different sets of output contacts with current.
The dotted line between the switches indicates they move together;
one will not move without the other moving as well.
MOMENTARY CONTACT
The momentary contact switch has a spring-loaded contact that keeps it
from making the circuit except when pressure is applied to the button.
This is a "normally open" type (shown below). START switch
A variation of this type is the normally closed (not shown) which works
the opposite as described above. STOP switch
The spring holds the contacts closed except when the button is pressed.
In other words the circuit is "ON" until the button is pushed to break
the circuit.
MERCURY
A mercury switch is made of a sealed capsule that is partially filled with
mercury. In one end of the capsule are two electrical contacts. As the
switch is rotated (moved from true vertical) the mercury flows to the
opposite end of the capsule with the contacts, completing the circuit..
Mercury is a hazardous waste and should be handled with care.
BI-METALLIC
A temperature-sensitive switch, also known as a "bi-metallic" switch,
usually contains a bimetal element that bends when heated to make
contact completing a circuit or to break contact opening a circuit.
TIME DELAY SWITCH
The time delay switch contains a bimetal strip, contacts, and a heating
element. The time delay switch is normally closed. As current flows
through the switch, current flows through the heating element causing
it to heat, which causes the bimetal strip to bend and open the contacts.
As current continues to flows through the heating element, the bimetal
strip is kept hot, keeping the switch contacts open.
The amount of time delay before the contacts open is determined by the
1. characteristics of the bimetal strip
2. amount of heat produced by the heating element
RELAYS
A relay is simply a remote-control switch, which uses a small amount of
current to control a large amount of current.
A typical relay has both a:
• Control circuit
• Power circuit.
Relay construction contains :
• iron core
• electromagnetic coil
• An armature (moveable contact set).
There are two types of relays:
• normally open.
• normally closed.
A Normally open (N.O.) relay has contacts that are "open" until the relay
is energized
A normally closed (N.C.) relay has contacts that are "closed" until the
relay is energized.
SOLENOIDS - PULLING TYPE
A solenoid is an electromagnetic switch that converts current flow into
mechanical movement. As current flows through the winding, a
magnetic field is created. The magnetic field will pull the moveable
iron core into the center of the winding. This type of solenoid is called
a "pulling" type solenoid, as the magnetic field pulls the moveable iron
core into the coil.
CIRCUIT PROTECTION
Circuit protection devices are used to protect wires and connectors from
being damaged by excess current flow either caused by an over current
or short-circuit. Excess current causes excess heat, which causes circuit
protection to "open circuit".
CIRCUIT PROTECTION DEVICES
Fuses and circuit breakers are used as circuit protection devices.
Circuit protection devices are available in a variety of types, shapes,
and specific current ratings.
FUSES
A fuse is the most common protection device. A fuse is placed in an
electrical circuit, so that when current flow exceeds the rating of the
fuse it "blows" or "blows out". The element in the fuse melts, opening
the circuit and preventing other components of the circuit from being
damaged by the overcurrent.
The size of the metal fuse element determines its rating.
Remember, excessive current causes excess heat, and it's the heat and
not the current that causes the circuit protector to open. Once a fuse
"blows" it must be replaced with a new one.
FUSE TYPES
Fuses are classified into basic categories:
1. blade type fuses
2. cartridge type fuses
BASIC CONSTRUCTION
The blade type fuse is a compact design with a metal element and
transparent insulating housing which is color-coded for each current
rating. (Standard Auto shown below; however construction of
both the mini and maxi fuses are the same.)
Color Ratings For STANDARD and MINI Fuses
Fuse Amp Rating
Identification Color
3
Violet
5
Tan
7.5
Brown
10
Red
15
Blue
20
Yellow
25
Colorless
Color Ratings For MAXI Fuses
Fuse Amp Rating
Identification Color
20
Yellow
30
Green
40
Amber
50
Red
60
Blue
70
Brown
80
Colorless
CIRCUIT BREAKERS
Circuit breakers are used in place of fuses for the protection of
complicated power circuits such as the power windows, sunroofs and
heater circuits. Three types of circuit breakers exists: The manual reset
type - mechanical, the automatic resetting type - mechanical, and the
automatically reset solid state type - PTC. Circuit breakers are usually
located in relay/fuse boxes; however, some components like power
window motors have circuit breakers built in.
CIRCUIT BREAKER CONSTRUCTION
(MANUAL TYPE)
A circuit breaker basically consists of a bimetal strip connected to two
terminals and to a contact in between. Manual circuit breaker when
tripped (current flow beyond its rating) will open and must be
reset manually. These manual circuit breakers are called "noncycling" circuit breakers.
CIRCUIT BREAKER OPERATION (MANUAL TYPE)
The circuit breaker contains a metal strip made of two different metals
bonded together called a bimetal strip. This strip is in the shape of a
disc and is concaved downward. When heat from the excessive current
is higher than the circuit breaker current rating, the two metals change
shape unevenly. The strip bends or warps upwards and the contacts
open to stop current flow. The circuit breaker can be reset after it is
tripped.
AUTOMATIC RESETTING TYPE – MECHANICAL
Circuit breakers that automatically reset are called "cycling" circuit
breakers. This type of circuit breaker is used to protect high current
circuits, such as power door locks, power windows, air conditioning, etc.
The automatically resetting circuit breaker contains a bimetal strip. The
bimetal strip will overheat and open from the excess current by an
overcurrent condition and is automatically reset when the temperature
of the bimetal strip cools.
AUTO RESET CONSTRUCTION AND OPERATION
A cycling circuit breaker contains a metal strip made of two different
metals bonded together called a bimetal strip. When heat from the
excessive current is higher than the circuit breaker current rating the
two metals change shape unevenly. The strip bends upwards and a
set of contacts open to stop current flow. With no current flowing
the bimetal strip cools and returns to its normal shape, closing the
contacts, and resuming the current flow. Automatically resetting
circuit breakers are said to "cycle "because they cycle open and
closed until the current returns to a normal level.
RESISTORS
All electrical circuits require resistance to operate correctly. Resistors are
sometimes added to an electrical circuit to limit current flow, create
voltage drops, or provide different operating modes. All resistors are
rated in both a fixed ohm value of resistance and a power rating in watts.
(Watt = Volts X Amps)
Basic categories of resistors are :
1. Fixed
2. Variable
Each has different characteristics and usage.
FIXED RESISTORS
Fixed-value resistors are divided into two category types of resistors:
1. Carbon / Metal Oxide
2. Wire-Wound.
Carbon and Metal Oxide Film
Fixed Resistor
Electrical Symbol
CARBON RESISTORS
Carbon resistors are commonly used in electronic systems. Carbon is
mixed with binder; the more carbon, the lower the resistance.
Carbon resistors have a fixed resistance value and are used to limit
current flow. They are rated in watts and most have color-code
bands to show the resistance value. A typical resistor has a watt
rating from 0.125W to 2.0 W.
Note: Metal-Oxide Film is sometimes used instead of carbon. While
carbon is commonly used for ratings up to 0.5 watt , Metal-Oxide
Film provide, better high-temperature satiability and is often used
for 1.0 - 2.0 watt resistors.
Carbon
Metal Oxide Film
RESISTOR RATING COLOR BANDS
The first two bands set the digit or number value of the resistor.
The third band, also known as the multiplier band, is the number of
zeros added to the number value.
The last band is the Tolerance band. Example: +/- 10%
RESISTOR COLOR BAND CHART
The chart below is used to interpret the color bands on the carbon
resistor. Another chart is used to show the value of tolerance band
colors (not shown).
READING COLOR BANDS - RATING VALUE
Using the illustration below:
The first color band is Green with a value of "5".
The second color band is Red with a value of "2".
The third band is Black with a value of "0" zero. (No zeros are added)
So the resistor has a base value of 52 ohms.
READING COLOR BANDS - TOLERANCE VALUE
Resistors vary in tolerance (accuracy). Common tolerance values are
20%, 10%, 5%, 2%, or 1%, simply meaning the maximum percent
allowable difference the resistor value actually is from the designed
value rating.
A 1% resistor is a higher quality resistor than one with a 20% rating.
The tolerance band (last band) is silver with a value of 10%.
So, the resistance value is "52 ohms plus or minus 5.2 ohms"
(46.8 to 57.2 ohms)
VARIABLE RESISTORS
Variable resistors provide an infinite amount of resistance values.
Variable resistors are used by electrical circuits to provide information
on temperature, position, or light source.
Variable Resistors are used in the headlamp switch to dim or brighten
dash panel lighting. Variable Resistors have two connections, one to
the fixed end of a resistor and the other to a sliding contact on the
resistor. Turning the control moves the sliding contact away from or
toward the fixed end, increasing or decreasing the resistance. Variable
Resistors control resistance, thus controlling current flow.
Generic Variable Resistor
Electrical Symbol
Variable Resistors OPERATION
As the wiper moves along the Variable Resistors it exposes more or
less of the resistor. Moving the wiper towards the high places a
small portion of the resistor in series with the light, causing the
light to glow bright. Moving the wiper toward the low, places a
larger portion of the resistor in series with the lamp; this increased
resistance causes less current to flow lowering the intensity of the
light.
Lockout procedures
There are nine steps involved in the lockout procedures.
1. Think, plan and check. Think through the entire procedure and identify all parts of any
systems that need to be shutdown.
2. Communicate. Let other employees working on the equipment know when and why you are
shutting down the system.
3. Locate all power sources. Locate all switches and other electrical sources that need to be
locked out.
4. Neutralize all power at its sources. Lower any suspended parts, block any moveable parts,and
disconnect the electricity.
5. Lockout all power sources. Used a lock designed for only this purpose and a lockout tag that
includes your name, and the time, the date and department.
6. Test operating controls. Test the operating controls to make certain the power has been
removed.
7. Turn the controls back off. Be sure to check each and every control is in the "OFF" position
before beginning any necessary maintenance or repairs.
8. Perform any maintenance or repairs.
9. Remove locks and restore energy.
• Tools should be removed from equipment and machine guards put back in place. Notify other
workers that the machines are working and back on.
• Restart equipment only after all workers are at a safe distance.
What is Voltage ?
Voltage is the electrical force that causes free electrons to move from
one atom to another.
"Volts" is the measure of "electrical pressure" that causes current
flow. Voltage is sometimes referred to as a potential difference
between two points along a conductor.
Voltage is typically supplied by either a generator or battery. The
scientific symbol for voltage is an "E", for "Electromotive force” or "V"
as the voltage symbol.
What is Current ?
Current is a measure of the rate of electron flow through a material.
Electrical current is measured in units of amperes or "amps" for
short. This flow of electrical current develops when electrons are
forced from one atom to another.
One amp is defined as 6.28 x 10 18 electrons per second.
When current flows in a conductor, heat is produced. This happens
because every conductor offers some resistance to current flowing.
The scientific symbol for amperage is an "I", or "A" as the amperage
symbol.
What is Power ?
The ability to do work. Watt is the standard unit in the metric system.
746 watts equals one horsepower in the English system of units.
AC power is represented graphically by a sinusoidal or sine waveform. -called sine wave for short.
There are five characteristics of AC power;
Amplitude, Cycles, Frequency, Peak to Peak, and RMS.
What is the Amplitude ?
Amplitude is the maximum value of current or voltage. It is
represented by either of the two peaks of the since wave.
This voltage level is also referred to as the peak voltage, and can be
either positive or negative.
Positive and negative refer only to the direction of current flow.
What is RMS ?
Is the actual useful voltage that is available and is called RMS. This
stands for Root Mean Square and it is the standard way of measuring
and reporting alternating current and voltage. It is not the peak; it is
the average.
The RMS is found by dividing the peak amplitude by the square root
of 2 (approximately 1.414).
It is typically represented by a dotted line drawn across each peak
near the 70 percent point.
What is a Cycle ?
A cycle is one complete repetition of the sine wave pattern. It is
produced by one complete revolution (360 degrees) of the AC
generator.
Since the sine wave begins at zero, goes positive through the
positive peak, then negative through zero and reaches the negative
peak, and to zero, we say a full cycle has been completed.
What is Frequency ?
Frequency is the number of cycles per second of voltage induced
in the armature.
The unit for frequency is hertz(Hz)
1 Hz is equal to 1 cycle per second.
What is Peak to Peak ?
"peak-to-peak" voltage , this is the voltage measured between the
maximum positive and negative amplitudes on the sine wave.
It is twice the amplitude. This value is the maximum voltage
available, but is not all useable
in practical applications.
What is a kWh or Kilowatt-hour?
Electrical energy is the average amount of power used over a given time
period and is commonly measured in "kilowatt-hours."
Electric meters accurately measure the kilowatt-hour energy use by the
customer.
Let's calculate the energy use for a blow dryer. Say the blow dryer is
rated at 1,500 watts by the manufacturer. This is how much electric
power it uses when it operates. If the blow dryer is operated for a total
of 2 hours each month, the blow dryer consumes 1,500 watts x 2 hours
= 3000 watt-hours , or 3 kilowatt-hours.
How much electricity does it take to kill a person?
At levels of current flow exceeding 1/10 of an amp or 100 milliamps,
the heart stops. This is called fibrillation. A person may survive an
electrocution if his or her heart can be started again. This is why CPR
is such an important skill in the electrical industry.
Why are some electrical cords and wires fatter than
others?
The current carrying capacity of a particular wire is dictated by its
"ampacity" - how many amps it can handle , and it is a function of :
1. Cross section area or diameter of the wire, Larger diameter wires
have larger cross section areas and can safely carry more electrical
current
2. Material type , the maximum ampacity for different types of wires is
defined by electrical codes.