Fundamentals of
Electricity
Review
• Electricity is the flow of electrons
• Electrons create charge which can be harnessed
to do work – lighting, heating, sound etc.
• Electricity is both a basic part of nature and one
of the most widely used forms of energy.
• The electricity that we use is a secondary energy
source because it is produced by converting
primary energy sources such as coal, natural
gas, nuclear energy, solar energy, and wind
energy into electrical power.
Review
• At home for example, people use electricity to do
many jobs every day—from lighting, heating,
and cooling homes to powering televisions and
computers.
• About 100 years ago, candles, whale oil lamps,
and kerosene lamps provided light, iceboxes kept
food cold, and wood-burning or coal-burning
stoves provided heat.
• Electricity supports quality of life (enhances
longevity of life)
• It improves standard of living and economic
well-being.
Review
Electricity is highly unique compared to other forms of
energy:
 Flexible—convertible to virtually any energy service—
light, motion, heat, electronics, and chemical potential
 Permits previously unattainable precision, control, and
speed
 Provides temperature and energy density far greater
than those attainable from standard fuels
•
https://www.eia.gov/energyexplained/?page=electricity_home
• https://learn.sparkfun.com/tutorials/voltage-current-resistanceand-ohms-law#voltage
Review
There are two types of flow of electricity:
1. DC – acronym for direct current
2. AC – acronym for alternating current
Direct Current (dc)
Direct current (dc) is the unidirectional flow of electric
charge. A battery is a good example of a DC power
supply (Wikipedia)
https://www.ndeed.org/EducationResources/HighSchool/Electricity/directcurrent.htm
Some Terminologies
Voltage (E or V):
• This is defined as the difference in charge
between two points. It is the amount of potential
energy between two points in a circuit.
• Going by this definition, the letter symbol for
voltage is V and the unit is volts (V), named
after Alessandro Volta
• Voltage can also be defined as the pressure that
causes the flow of electric current in a circuit.
• The name given to this second definition of
voltage is Electromotive force and the letter
symbol is E the unit still remains as V.
Some Terminologies
Electric Current (I):
• This is the rate at which charge is flowing. This
is the rate of flow of electrons in a circuit. The
letter symbol is I while the unit of measurement
is amperes (A)
Some Terminologies
Resistance (R):
• This is the tendency of a material to resist the
flow of electricity.
• Resistance is the opposition of a material to the
flow of electric current in a circuit.
• The letter symbol for a resistor is R and the unit
of measurement of resistance is ohms (Ω)
• The electrical symbol looks as follows:
• Different materials exhibit different degree of
opposition to the flow of electricity.
A Common Analogy
When describing voltage, current, and resistance, a
common analogy is a water tank. In this analogy,
charge is represented by the water amount, voltage
is represented by the water pressure, and electric
current is represented by the water flow. So for this
analogy, remember:
 Water = Charge
 Pressure = Voltage/Electromotive force
 Flow = Current
Ohm’s Law
• The potential difference (voltage) across an ideal
conductor is proportional to the current (I) through it.
The constant of proportionality is called the
"resistance", R.
• Ohm's Law is given by: V = I R where V is the potential
difference between two points, R is the resistance of the
conductor and I is the current flowing in the conductor.
𝑽
𝑬
• Also, the equation can be written as 𝑹 = =
𝑰
𝑰
𝑪𝒂𝒖𝒔𝒆
• Conceptually, this means Opposition=
𝑬𝒇𝒇𝒆𝒄𝒕
http://en-us.fluke.com/training/training-library/measurements/electricity/what-is-ohmslaw.html
Resistivity
• Electrical resistivity (also known as resistivity or
specific electrical resistance) is a fundamental property
that quantifies how strong a given material opposes the
flow of electric current.
• It is determined by the following equation:
𝑨
ρ=𝑹
𝒍
ρ = resistivity, unit is (Ω-m)
R = resistance of the material, unit is ohm (Ω)
l = length of the material, unit is meters (m)
A = cross sectional area of the material, unit is (m2)
• Different materials exhibit different degree of
opposition to the flow of electricity.
Resistivity-Metric Units
The inverse of resistivity is conductivity.
Series dc Resistors
•
The total resistance of a series configuration is
the sum of the resistances of all the connected
resistors.
RT = 𝑹𝟏 + 𝑹𝟐 + 𝑹𝟑
Series dc Circuits
•
A circuit is any combination of elements that will
result in a continuous flow of current through the
configuration.
•
The direction of conventional current in a series dc
circuit is such that it leaves the positive terminal of the
supply and returns to the negative terminal.
•
The current is the same at every point in a series
circuit.
Parallel Resistors
•
Two or more resistors are in parallel if they have two
points (a, b) in common as shown below:
•
For resistors in parallel as shown above, the total,
effective or resultant resistance is determined from the
following equations:
•
𝟏
𝟏
𝟏
𝟏
= + +
𝑹𝑻
𝑹𝟏
𝑹𝟐
𝑹𝟑
•
RT = resultant (total) resistance.
Parallel Resistors
•
•
𝟏
RT = 𝟏
𝟏
𝟏
𝟏
𝟐
𝟑
+ +
𝑹 𝑹 𝑹
The total resistance of parallel resistors is always less
than the value of the smallest resistor.
Special Case – Two Parallel Resistors
•
𝑹𝟏𝑹𝟐
RT =
𝑹𝟏+𝑹𝟐
•
The total resistance of two parallel resistors is simply
the product of their values divided by their sum.
Parallel dc Circuits
•
A parallel circuit is established by connecting a supply
across a set of parallel resistors as shown below:
•
For a parallel circuit, the voltage is always the same
across parallel elements.
•
From the diagram above,
V1 = 𝑽𝟐 = 𝑬
Power - dc Circuits
•
•
•
•
•
Power is an indication of how much work can be
accomplished in a specific amount of time.
It is the rate of doing work.
𝒘𝒐𝒓𝒌
𝒘
P𝒐𝒘𝒆𝒓 =
, 𝑷=
𝒕𝒊𝒎𝒆
𝒕
The unit of power is watt (W).
𝟏 𝒋𝒐𝒖𝒍𝒆
1 watt (W) =
𝒔𝒆𝒄𝒐𝒏𝒅
• Another unit of power is horsepower (hp)
• 1 horsepower ≌ 𝟕𝟒𝟔 𝒘𝒂𝒕𝒕𝒔
Power - dc Circuits
•
Power delivered to or absorbed by an electrical device
or system can be found in terms of the current and
voltage.
•
Power Equations:
•
P = 𝑬𝑰
• P = 𝑽𝑰 = 𝑽
𝑽
𝑹
𝑽𝟐
=
𝑹
• P = 𝑽𝑰 = 𝑰𝑹 𝑰 = 𝑰𝟐𝑹
Energy - dc Circuits
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•
•
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Energy is the ability to do work.
It is the amount of power used over a period of time.
Therefore the energy lost or gained by any system is determined by the
product of power times time.
W = 𝑷𝒕
The letter symbol representing energy is W. The unit of energy is the
wattsecond (Ws) or joules (J)
Large unit is watthour (Wh) or kilowatthour (kWh).
Energy (watthour) = power (watt) X time (hour) = 𝑾𝒉
V
I R
114 ½½½ OHM ’S LAW, POWER, AND ENERGY
The energy (W) lost or gained by any system is therefore determined by
W = Pt
•
•
(wattseconds, Ws, or joules)
Since power is measured in watts (or joules per second) and time in
seconds, the unit of energy is the wattsecond or joule (note Fig. 4.16). The
wattsecond, however, is too small a quantity for most practical purposes,
so the watthour (Wh) and the kilowatthour (kWh) are defined, as follows:
Energy (Wh) = power (W) * time (h)
(4.17)
power (W) * time (h)
1000
(4.18)
FIG. 4.16
James Prescott Joule.
Energy (kWh) =
Science and Society/Superstock
•
•
(4.16)
British (Salford, Manchester)
(1818–89)
Physicist
Honorary Doctorates from the Universities
of Dublin and Oxford
Contributed to the important fundamental law of
conservation of energy by establishing that various
forms of energy, whether electrical, mechanical, or
heat, are in the same family and can be exchanged
from one form to another. In 1841 introduced Joule’ s
law, which stated that the heat developed by electric
current in a wire is proportional to the product of the
current squared and the resistance of the wire (I 2 R).
He further determined that the heat emitted was
equivalent to the power absorbed, and therefore heat
is a form of energy.
Note that the energy in kilowatthours is simply the energy in watthours divided by 1000. To develop some sense for the kilowatthour
energy level, consider that 1 kWh is the energy dissipated by a 100 W
bulb in 10 h.
The kilowatthour meter is an instrument for measuring the energy
supplied to the residential or commercial user of electricity. It is normally connected directly to the lines at a point just prior to entering the
power distribution panel of the building. A typical set of dials is shown
in Fig. 4.17, along with a photograph of an analog kilowatthour meter.
As indicated, each power of ten below a dial is in kilowatthours. The
more rapidly the aluminum disc rotates, the greater is the energy demand.
The dials are connected through a set of gears to the rotation of this disc.
A solid-state digital meter with an extended range of capabilities also
appears in Fig. 4.17.
𝒑𝒐𝒘𝒆𝒓 𝑾 𝑿 𝒕𝒊𝒎𝒆 (𝒉)
• Energy (kilowatthour) =
= 𝒌𝑾𝒉
𝟏𝟎𝟎𝟎
•
The kilowatthour meter is an instrument for measuring the energy supplied
to the residential or commercial user of electricity.
(a)
(b)
FIG. 4.17
Units of measurement – Scientific Notation
Units of measurement – Scientific Notation
Examples:
•
•
•
•
•
•
•
•
•
1,000 ohms = 1 X 103 ohms = 1 kilo-ohms =1kΩ
0.001 ampere = 1 X 10-3 ampere = 1 milliampere =1 mA
1,000,000 hertz = 1 X 106 hertz = 1 megahertz =1 MHz
0.000001 farad = 1 X 10-6 farad = 1 microfarad = 1µF
0.0001 second = 0.1 X 10-3 second = 0.1 millisecond = 0.1ms
10,000 meters = 10 X 103 meters = 10 kilometers = 10 km
50, 000 grams = 50 X 103 grams = 50 kilogram = 50 kg
0.008 volt = 8 X 10-3 volt = 8 millivolt = 8 mV
20,000,000 watts = 20 X 106 watts = 20 megawatts = 20 MW
Circuit Components
•
There are mostly three passive components you will
find in any electrical circuit/equipment:
 Resistor (R)
 Capacitor (C)
 Inductor (L)
• While resistors dissipate energy in heat form,
capacitors and inductors store energy.
𝟏
• Capacitors store energy in electric field ( 𝑪𝑽𝟐)
•
𝟐
𝟏
Inductors store energy in magnetic field ( 𝑳𝑰𝟐)
𝟐
Capacitors
•
•
•
•
A capacitor, is a passive two-terminal electrical
component that stores potential energy in an electric
field when voltage is applied across it.
The measure of a capacitor to store charge is known as
capacitance.
The letter symbol for a capacitance is C and the unit of
measurement of capacitance is farad (F)
The electrical symbols representing different types of
capacitor are as shown below
https://en.wikipedia.org/wiki/Capacitor
Capacitors
•
A capacitor is made of two parallel plates of metallic
material such as aluminum.
The two plates are separated by insulating material
known as dielectric.
•
•
The relationship connecting the applied voltage, the
charge on the plate and the capacitance level is given as
follows.
•
𝑸
𝑨
C= = ϵ
𝑽
𝒅
•
•
•
•
•
•
Capacitors
C = capacitance (farads, F)
Q = electric charge (coulombs, C)
V = E = applied voltage (volts, V)
A = cross sectional area of plates (square meters, m2)
d = distance between parallel plates (meters, m)
ϵ = permittivity of dielectric medium (F/m)
Inductors
•
An inductor, also called a coil, choke or reactor is a
passive two-terminal electrical component that stores
energy in a magnetic field when electric current flows
through it.
• An inductor typically consists of an insulated wire
wound into a coil around a core.
• Inductors (coils) constitute a substantial component of
most electrical machines today
 Generators
 Motors
 Transformers
 Circuit breakers
 etc.
Inductors
•
•
The inductance of an inductor determines the strength
of the magnetic field around the coil due to an applied
current.
The electrical symbols representing different types of
inductors are as shown below
https://en.wikipedia.org/wiki/Inductor
Inductors
•
•
•
•
•
•
•
The inductance depends on the cross sectional area of the coil,
the length of the coil and the permeability of the core material
as shown in the equation below:
µ𝑵𝟐𝑨
L=
𝒍
N = number of turns (t)
A = cross sectional area (square meter, m2)
l = length of coil (meters, m)
L = inductance (henries, H)
µ = permeability (webers/meter/ampere, Wb/Am)
https://en.wikipedia.org/wiki
/Inductor
Alternating Current (ac)
• Alternating current (AC) is an electric current which
periodically reverses direction, in contrast to direct
current (DC) which flows only in one direction.
• AC alternates between two prescribed levels in a set time
sequence.
• Alternating current is the form in which electric power is
delivered to businesses and residences.
• There are many types of ac waveforms such as sine wave,
square wave, triangular wave etc.
• The pattern of particular interest is the sinusoid (sine or
cosine wave).
https://en.wikipedia.org/wiki/Alternating_current
Alternating Current (ac)
• What makes the sinusoidal alternating current or voltage
stands out is that electricity is generated, transmitted and
distributed by utilities in this form throughout the world.
https://learn.sparkfun.com/tutorials/alternating-currentac-vs-direct-current-dc
SINUSOIDAL ac VOLTAGE CHARACTERISTICS AND
DEFINITIONS
• Waveform-The path traced by a quantity, plotted as a function of some variables
such as time, position, degrees, radians, temperature, and so on.
•
•
•
•
•
•
•
•
Instantaneous value
Amplitude
Peak value
Peak-to-peak value
Periodic waveform
Period (T)
Cycle
Frequency
Instantaneous value - The magnitude of a waveform at any instant in time;
denoted by lower case letters (e1, e2)
Amplitude – The maximum value of a waveform as measured from its average, or
mean value. It is denoted by upper case letters such as Em for voltage sources or
Vm for the voltage drop across a load.
SINUSOIDAL ac VOLTAGE/CUURENT
CHARACTERISTICS AND DEFINITIONS
• Peak value – The maximum instantaneous value of a function as
measured from the zero volt level. For sinusoidal waveforms, the
amplitude and the peak values are the same.
• Peak-to-peak value – This is the full voltage between the positive and
negative peaks of the waveform. It is denoted by Ep-p or Vp-p.
• Periodic waveform – The waveform that continually repeats itself after the
same time interval.
• Period (T) – The time for one complete cycle in a periodic waveform.
• Cycle – The portion of a waveform contained in one period of time.
• Frequency (f) – The number of cycles that occur in one second. Cycles per
second.
f = 1/T
f = frequency (Hz)
T = Period (s)
GENERAL FORMAT FOR REPRESENTING
SINUSOIDAL VOLTAGE OR CURRENT
Voltage
• 𝒆 = 𝑬𝒎𝒔𝒊𝒏 ω𝒕 ± θ
• ω =𝟐π𝐟𝐭
where
e = instantaneous voltage (volts, V)
Em = Peak or maximum voltage (volts, V)
ω = angular velocity (radian per second, rad/s)
t = time (seconds, s)
f = frequency (hertz, Hz)
f = 60 Hz, electric power frequency in the U.S.A
θ = phase angle in degree or radian
When the phase angle, θ, is equal to zero,
• 𝒆 = 𝑬𝒎𝒔𝒊𝒏 ω𝒕 = 𝑬𝒎𝒔𝒊𝒏 𝟐π𝒇𝒕
GENERAL FORMAT FOR REPRESENTING
SINUSOIDAL VOLTAGE OR CURRENT
Current
• 𝒊 = 𝑰𝒎𝒔𝒊𝒏 ω𝒕 ± θ
• ω =𝟐π𝐟𝐭
where
i = instantaneous current (amperes, A)
Im = Peak or maximum current (amperes, A)
ω = angular velocity (radian per second, rad/s)
t = time (seconds, s)
f = frequency (hertz, Hz)
f = 60 Hz, electric power frequency in the U.S.A
θ = phase angle in degree or radian
When the phase angle, θ, is equal to zero,
• 𝒊 = 𝑰𝒎𝒔𝒊𝒏 ω𝒕 = 𝑰𝒎𝒔𝒊𝒏 𝟐π𝒇𝒕
Effective (Root-Mean-Square) Value
Effective or root-mean-square (rms) values help determine the amplitude of a
sinusoidal ac current or voltage required that deliver the same power as a
particular dc current or voltage.
Mathematically, for voltage:
𝑬𝒓𝒎𝒔 =
𝑬𝒎
𝟐
Erms = Effective voltage value (volts, V)
Em = Peak or maximum voltage (volts, V)
For current:
𝑰𝒓𝒎𝒔 =
𝑰𝒎
𝟐
Irms = Effective current value (amperes, A)
Im = Peak or maximum current (amperes, A)
Capacitors and Inductors in ac Electrical Circuits
• Like resistors, the measure of opposition given by capacitors and inductors in
ac electrical circuits are knowns as capacitive reactance and inductive
reactance respectively.
• The letter symbol for capacitive reactance is XC and the unit of measurement is
Ohms (Ω)
• The letter symbol for inductive reactance is XL and the unit of measurement is
Ohms (Ω)
• The generic name for resistance, capacitive reactance and inductive reactance
in ac electrical circuits is called impedance.
• The letter symbol for impedance is Z and the unit of measurement is Ohms (Ω)
𝒁𝑻 = 𝒁𝟏 + 𝒁𝟐 + 𝒁𝟑 = 𝑹 + 𝒋𝑿𝑳 − 𝒋𝑿𝑪 = 𝟔Ω+j10 Ω-j12 Ω
AC Electrical Power System
• AC electrical power are supplied in two forms:
1.
2.
Single phase
Three phase
• For most businesses and industrial settings, it is
delivered in three phase to accommodate higher loads.
• Residences are generally provided single phase to
sufficiently power household items.
Single Phase AC Power
• A single phase AC power system peaks in voltage and current at 900 and 2700, with
a complete cycle at 3600.
• In a single phase system, there is one neutral wire and one power wire (hot leg) with
current flowing between them. The cyclical changes in magnitude and direction
usually change flow in current and voltage about 60 times per second.
•
•
•
𝒆(𝒕) = 𝑬𝒎 𝑺𝒊𝒏 (𝟐π𝒇𝒕)
Em = 170 V
𝑬
𝟏𝟕𝟎 𝑽
Erms = 𝐦 =
= 120 V
•
f = 60 Hz
•
e(t), Em, Erms and 𝒇 are
instantaneous voltage, peak
voltage, effective voltage and
frequency respectively.
𝟐
𝟐
http://aegispower.com/index.php/2015-01-15-19-35-10/179-what-is-the-differencebetween-single-phase-and-three-phase-ac-power-supplies
Three- phase AC Power
• Three-phase electric power is a common method of alternating
current (ac) power generation, transmission, and distribution.
• It is a type of poly-phase system and is the most common method
used by electrical grids worldwide to transfer power.
• It is also used to power large motors and other heavy loads.
• The phase order is 1-2-3. This cycle repeats with the frequency of the
power system. Ideally, each phase’s voltage, current, and power is
offset from the others’ by 120°.
Three- phase AC Power
• In a symmetric three-phase power supply system, three conductors each carry
an alternating current of the same frequency and voltage amplitude relative to
a common reference but with a phase difference of 1200 between each
• The common reference is usually connected to ground through a currentcarrying conductor called the neutral.
• Due to the phase difference, the voltage on any conductor reaches its peak at
one third of a cycle after one of the other conductors and one third of a cycle
before the remaining conductor.
https://learn.sparkfun.com/tutorials/alternating-current-
Three- phase AC Power
• Three-phase generator has three coils placed 1200 apart on the stator as shown
below.
• The three coils have an equal number of turns and they rotate with the same
angular velocity.
• Therefore, the voltage induced across each coil has the same peak value, shape
and frequency.
• As the shaft of the generator is turned by some external means, the induced
voltage eAN, eBN and eCN are generated simultaneously.
• Note the 1200 phase shift between waveforms and the similarities in
appearance of the three sinusoidal functions.
Three- phase AC Power
•
•
•
𝒆𝑨𝑵 = 𝑬𝒎 𝑺𝒊𝒏 ω𝒕 = 𝑬𝒎𝑺𝒊𝒏 𝟐π𝒇𝒕 − 𝑷𝒉𝒂𝒔𝒆 𝑨 𝒗𝒐𝒍𝒕𝒂𝒈𝒆
𝒆𝑩𝑵 = 𝑬𝒎𝑺𝒊𝒏 ω𝒕 − 𝟏𝟐𝟎𝟎 = 𝑬𝒎𝑺𝒊𝒏 𝟐π𝒇𝒕 − 𝟏𝟐𝟎𝟎 − 𝑷𝒉𝒂𝒔𝒆 𝑩 𝒗𝒐𝒍𝒕𝒂𝒈𝒆
𝒆𝑪𝑵 = 𝑬𝒎𝑺𝒊𝒏 ω𝒕 − 𝟐𝟒𝟎𝟎 = 𝑬𝒎𝑺𝒊𝒏 𝟐π𝒇𝒕 − 𝟐𝟒𝟎𝟎 − 𝑷𝒉𝒂𝒔𝒆 𝑪 𝒗𝒐𝒍𝒕𝒂𝒈𝒆
•
Em and ω are peak voltage and angular velocity respectively. Same as defined for
single phase system.
Three- phase AC Power – Phasor Representation
• The phasor diagram of the three-phase ac power system is as shown below:
•
•
•
•
𝐸𝑚 𝐴𝑁
( ) = 0.707 𝐸
𝑚(𝐴𝑁 )
2
𝐸
E𝐵𝑁 = 𝑚(𝐵𝑁) = 0.707 𝐸𝑚(𝐵𝑁)
2
𝐸
E𝐶𝑁 = 𝑚(𝐶𝑁) = 0.707 𝐸𝑚(𝐶𝑁)
2
E𝐴𝑁 =
EAN, EBN and 𝐸𝐶𝑁 are the effective value (rms) of each of
the three phase voltages.
Phasor Representations:
• EAN = EAN
• EBN = EBN
• ECN = ECN
00
-1200
-2400