Intended Learning Outcomes
The following are the learning outcomes that will be acquired by
the students after finishing the course:
1. Define and analyze the DC/AC Circuits, basic electrical and
electronic devices.
2. Apply the student’s analytical skills by determining basic
electrical measuring instruments.
3. Evaluate the properties of 3-phase systems and the operation
of transformers, D.C. machines, and induction motors.
What is “Electricity”?
ELECTRICITY
form of energy
Greatest discoveries of man
Come from the greekword “electron” which means amber
Electricity is all about electrons, which are the fundamental
cause of electricity
Static Electricity - involves electrons that are moved from one
place to another, usually by rubbing or brushing
Current Electricity - involves the flow of electrons in a
conductor
FAMOUS CONTRIBUTION ABOUT
ELECTRICITY
WIILIAM GILBERT
 Father of electricity published his studies
 The electric attraction
 The electric force
BENJAMIN FRANKLIN
 In 1752, Franklin proved that lightning and the spark from amber were one and the
same thing. This story is a familiar one, in which Franklin fastened an iron spike to a
silken kite, which he flew during a thunderstorm, while holding the end of the kite
string by an iron key. When lightening flashed, a tiny spark jumped from the key to
his wrist. The experiment proved Franklin's theory, but was extremely dangerous - he
could easily have been killed.
FAMOUS CONTRIBUTION ABOUT
ELECTRICITY
GALVANI AND VOLTA
In 1786, Luigi Galvani, an Italian professor of medicine, found that when the
leg of a dead frog was touched by a metal knife, the leg twitched violently. Galvani
thought that the muscles of the frog must contain electricity.
By 1792, another Italian scientist, Alessandro Volta, disagreed: he realized that the main
factors in Galvani's discovery were the two different metals - the steel knife and the tin
plate - upon which the frog was lying. Volta showed that when moisture comes between
two different metals, electricity is created. This led him to invent the first electric battery,
the voltaic pile, which he made from thin sheets of copper and zinc separated by moist
pasteboard.
In this way, a new kind of electricity was discovered, electricity that flowed
steadily like a current of water instead of discharging itself in a single spark or shock.
Volta showed that electricity could be made to travel from one place to another by wire,
thereby making an important contribution to the science of electricity. The unit of
electrical potential, the Volt, is named after him.
FAMOUS CONTRIBUTION ABOUT
ELECTRICITY
MICHAEL FARADAY
The credit for generating electric current on a practical scale goes
to the famous English scientist, Michael Faraday. Faraday was greatly
interested in the invention of the electromagnet, but his brilliant mind took
earlier experiments still further. If electricity could produce magnetism,
why couldn't magnetism produce electricity?
In 1831, Faraday found the solution. Electricity could be produced
through magnetism by motion. He discovered that when a magnet was
moved inside a coil of copper wire, a tiny electric current flows through
the wire. Of course, by today's standards, Faraday's electric generator was
crude (and provided only a small electric current), but he had discovered
the first method of generating electricity by means of motion in a
magnetic field.
FAMOUS CONTRIBUTION ABOUT
ELECTRICITY
JAMES WATT
When Edison's generator was coupled with Watt's steam engine, large
scale electricity generation became a practical proposition. James Watt, the
Scottish inventor of the steam condensing engine, was born in 1736. His
improvements to steam engines were patented over a period of 15 years, starting
in 1769 and his name was given to the electric unit of power, the Watt.
ANDRE MARIE AMPERE
Andre Marie Ampere, a French mathematician who devoted himself to
the study of electricity and magnetism, was the first to explain the electrodynamic theory. A permanent memorial to Ampere is the use of his name for the
unit of electric current.
FAMOUS CONTRIBUTION ABOUT
ELECTRICITY
GEORGE OHM
George Simon Ohm, a German mathematician and physicist, was a
college teacher in Cologne when in 1827 he published, "The Galvanic
Circuit Investigated Mathematically". His theories were coldly received
by German scientists, but his research was recognized in Britain and he
was awarded the Copley Medal in 1841. His name has been given to the
unit of electrical resistance.
HOW ELECTRICITY PRODUCED
 Electricity Produced from Frictional Energy
(Static Electricity)
 Electricity produced from Pressure
 Electricity Produced from Heat
 Electricity Produced from Chemical
Reaction
 Electricity Produced from Light
 Electricity Produced from Magnetism
CONDUCTORS
 In conductors, electric charges are free to move through
the material. In insulators, they are not.
 In conductors:
 The charge carriers are called free electrons
 Only negative charges are free to move
 When isolated atoms are combined to form a metal,
outer electrons of the atoms do not remain attached to
individual atoms but become free to move throughout
the volume of the material
CONDUCTORS
Other Types of Conductors
 Electrolytes
 Both negative and positive charges can move
 Semiconductors
 In-between conductors and insulators in their ability to
conduct electricity
 Conductivity can be greatly enhanced by adding small
amounts of other elements
 Requires quantum physics to truly understand how they
work
INSULATORS
Insulators on the other hand are the exact opposite of
conductors. They are made of materials, generally non-metals,
that have very few or no “free electrons” float about within
their basic atom structure because the electrons in the outer
valence shell are strongly attached by the positively charge
inner nucleus. So if a potential voltage is applied to the
material no current will flow as there are no electrons to move
which gives these materials their insulating properties.
Insulators plat an important tool within electrical and
electronics because without them electrical circuit would not
short together and not work.
ELECTRIC CHARGE
 Most basic quantity of electric circuit
 Is an electrical property of an atomic particle which
matter consists, measured in Coulombs (C)
 Like charges repel while unlike charges attract.
NOTE:
1e= -1.602x10^-19
1P= 1.602x10^-19
1coulomb (C) = 6.25x1018 electrons or
protons; named after a French Physicist
Charles
SI PREFIXES
BASIC ELECTRICAL CIRCUIT (DC)
VOLTAGE (V), CURRENT (I),
RESISTANCE (R)
VOLTAGE
 Also known as electromotive force (emf); electric pressure; potential difference.
 The energy required to move a unit charge through an element, measured in volts (V)
Types of Voltage
DC Voltage
 commonly produce by batteries
where: W = work done (Joule)
Q = charge (coulomb)
AC Voltage
 produced by electric generator
ELECTRIC CURRENT
 Such movement of free electrons creates an electric current
 Materials with large numbers of free electrons are called electrical conductors.
They conduct electrical current.
 Rate of flow of electron or electric charge through a conductor or circuit (crkt)
elements
 Measured in amperes (A) or coulumbs/sec
Two common types of Current
where: Q = charge (coulomb)
t = time (second)
 Direct Current – current remains constant at
all times
 Alternating Current – current varies
sinusoidally with time
EXAMPLE 1
1. A battery can deliver 10 Joules of energy to move 5 coulombs of charge.
What is the potential difference between the terminals of the battery?
2. What current must flow if 0.24 coulombs is to be transferred in 15ms?
3. If a current of 10A flows for four minutes, find the quantity of electricity
transferred.
4. The current in an electric lamp is 5 amperes. What quantity of electricity
flows towards the filament in 6 minutes?
5. A constant current of 4A charges a capacitor. How long will it take to
accumulate a total charge of 8 coulombs on the plate?
SOLUTIO
N:
RESISTANCE
 The electrical resistance of an electrical conductor is a measure of the
difficulty to pass an electric current through that conductor, measured in
ohms (Ω)
 Oppose current flow.
 Named after the German Physicist, George S. Ohm.
 Depends upon the kind of material, length of material, cross sectional area
and temperature
LAW OF RESISTANCE
 its varies directly as its length (l)
 its varies inversely as the cross-sectional (A) of the conductor
 it depends on the nature of the material
 it depends on the temperature of the conductor
RESISTANCE AND RESISTIVITY
SPECIFIC RESISTANCE OR RESISTIVITY (ρ)
 The resistance of electrical materials in terms of unit dimensions length and crosssectional area.
 The amount of change of resistance in a material per unit change in temperature.
 The unit is ohm-circular mils per foot.
The resistance is directly proportional
to the conductor length. The resistance
is inversely proportional to the crosssectional area.
RESISTANCE AND RESISTIVITY
So, to find the resistance of any conductor, providing that its dimensions and its
resistivity are known, the formula is given by:
Where: 𝜌 is the resistivity, in 𝛺 - 𝐶𝑀/𝑓𝑡
L is the length of the conductor, in 𝑚, 𝑐𝑚, 𝑓𝑡
A is the cross-sectional area of the conductor, in 𝐶𝑀
V is the volume of the conductor
RESISTIVITY OF COMMON ELEMENTS AT 20℃
CROSS – SECTIONAL AREA
AREA in Circular Mil
AREA in Square Mil
Where: d = diameter in mil
Where: d = diameter in mil
Circular Mil (CM)
Area of a circle having a diameter of one mil
1 in = 1,000 mils
1 MCM = 1,000 CM
CONVERSION BETWEEN
CIRCULAR MIL & SQUARE MIL
EXAMPLE 2
Using the given particulars, calculate the resistances
of the following conductors at 20ºC.
a. Material – Copper Annealed, Length –
1000ft., CM – 3220 circular mils
b. Material – Aluminum, Length – 4 miles,
Diameter – 262mils
SOLUTIO
N:
68, 644 mil^2
68, 644 mil^2
ANS: R = 5.2305 ohms
EXAMPLE 3
1.
The substation bus bar is made up of 2 inches
round copper bars 20ft. long. What is the
resistance of each bar if resistivity is 1.724x10-6
ohm-cm?
2.
Determine the resistance of a bus bar made of
copper if the length is 10m long and the cross
section is 4x4 cm2. Use 1.724x10-6 ohm-cm as
the resistivity.
ANYONE
??
TEMPERATURE EFFECTS ON RESISTANCE
Experiments have shown that the resistance of all wires generally used in practice in
electrical systems, increases as the temperature increases.
The temperature-resistance effect is given by the equation;
EXAMPLE 4
A coil of copper wire has a resistance of 62 ohm, at a
room temperature of 24ºC. What will be its resistance at?
a. 80ºC
b. -20ºC
SOLUTIO
N:
RESISTOR COLOR CODING
RESISTOR COLOR CODING
Brown, Black, Orange, Gold
RESISTOR COLOR CODING
RESISTOR COLOR CODING
CONDUCTANCE
 reciprocal of resistance
 permits the flow of electron through a conductor or an element
 measured in mho (Ʊ), siemens (S)
Siemens (mho) - unit of conductance. Named after the german engineer, Earnst Werner von
Siemens (1816-1892)
Conductivity (δ) – reciprocal of resistivity
where:
δ = conductivity (siemens per meter)
L = length (meter)
A = cross sectional area (square meter)
G = conductance (siemens)
R = resistance
𝝆 = specific resistance (resistivity, ohm-meter)
POWER
 is the time rate of expending or absorbing energy
 measured in watts (W) or J/s
 Named after the British Engineer and inventor James Watt.
where:
P = electrical power (watt)
V = voltage (volt)
I = current (ampere)
R = resistance (ohm)
Passive Sign (+)
 Power is being delivered to the load
Negative Sign (-)
 Power is being supplied by the load
ELECTRICAL ENERGY
Energy is the capacity to do work.
W = Pt
where:
W = electrical energy (Joule)
P = electrical power (watt)
t = time (second)
kilowatt-hour (kW-hr)
Unit in which electrical energy is sold to a consumer.
EXAMPLE 5
1. A 100W electric light bulb is connected to a 250V
supply. Determine:
a. the current flowing in the bulb
b. the resistance of the bulb
2. Electrical equipment in an office takes a current of
13A from a 240V supply. Estimate the cost per week
of electricity if the equipment is used for 30 hours
each week and 1kWh of energy costs 7 pesos.
SOLUTIO
N:
THANK YOU!
BASIC ELECTRIC CIRCUIT
Electric circuit: It is a closed loop of pathway with electric charges flowing
through it. It is the sum of all electric components in the closed loop of
pathway with flowing electric charges. An example of an electric circuit
includes resistors, capacitors, inductors, power sources, wires, switches, etc.
A basic electric circuit contains three components: the power supply, the
electrical load, and the wires (conductors)
BASIC ELECTRIC CIRCUIT
Wires connect the power supply and the load, and carry electric charges
through the circuit.
A power supply (power source) is a device that supplies electrical energy to
the load of the circuit; it can convert other forms of energy to electrical
energy. The electric battery and generator are examples of power supply.
BASIC ELECTRIC CIRCUIT
 The battery converts chemical energy into electrical energy.
 The hydroelectric generator converts hydro energy (the energy of
moving water) into electrical energy.
 The thermo power generator converts heat energy into electrical
energy.
 The nuclear power generator converts nuclear energy into electrical
energy.
 The wind generator converts wind energy into electrical energy.
 The solar generator converts solar energy into electrical energy.
BASIC ELECTRIC CIRCUIT
An electrical load is a device that is usually connected to the output terminal of an
electric circuit.
 The load consumes or absorbs electrical energy from the source.
 The load may be any device that can receive electrical energy and convert it
into other forms of energy.
Examples of electric loads:
 Electric lamp converts electrical energy into light energy.
 Electric stove converts electrical energy into heat energy.
 Electric motor converts electrical energy into mechanical energy.
 Electric fan converts electrical energy into wind energy.
 Speaker converts electrical energy into sound energy.
 Solar cell converts sunlight into electrical energy.
 Microphone converts sound energy into electrical energy.
CIRCUIT SYMBOLS
CIRCUIT SYMBOLS
For example, both the battery and the direct current (DC) generator can
convert other energy forms into electrical energy and produce DC
voltage. Therefore, they are represented by the same circuit symbol—
the DC power supply E.
CIRCUIT ELEMENTS
CIRCUIT ELEMENTS
CIRCUIT ELEMENTS
NODE, BRANCHES AND LOOPS
Since the elements of an electric circuit can be interconnected
in several ways, there are basic terms and concepts of network
topology to be understood. To differentiate between a circuit
and a network, we may regard a
Network as an interconnection of elements or
devices
whereas a
Circuit is a network providing one or more closed
paths
BRANCH
A branch represents a
single element such as a
voltage source or a
resistor.
In other words, a branch
represents
any
two
terminal element. The
circuit has five branches,
namely, the 10-V voltage
source, the 2-A current
source, and the three
resistors
NODE
A node is the point of
connection between two or more
branches.
A node is usually indicated by a
dot in a circuit. If a short circuit
(a connecting wire) connects two
nodes, the two nodes constitute a
single node. The circuit in the
figure has three nodes a, b, and c.
The three points that form node
b are connected by perfectly
conducting wires and therefore
constitute a single point. The
same is true of the four points
forming node c.
NODE
LOOP
A loop is any closed path in a
circuit.
A loop is a closed path formed
by starting at a node, passing
through a set of nodes, and
returning to the starting node
without passing through any
node more than once. A loop is
said to be independent if it
contains a branch which is not
in any other loop. Independent
loops or paths result in
independent sets of equations.
For example, the closed path
bcb contains 3-Ω resistor and a
2A current source.
OHM’S LAW
In 1828, George Simon Ohm, a German physicist, derived a
relationship between electric current and potential difference.
This relationship is known as Ohm’s law. As a result of his
pioneering work, the term Ohm was adopted as the unit of
electrical resistance.
Ohm’s law states that “the current flowing through a conductor is
directly proportional to the potential difference applied across its
ends, provided the temperature and other physical conditions
remain unchanged.” The resistance, measured in ohms, is the
constant of proportionality between the voltage and current.
EXAMPLE 6
1. A 100 V battery is connected across a resistor and causes
a current of 5 mA to flow. Determine the resistance of
the resistor. If the voltage is now reduced to 25 V, what
will be the new value of the current flowing?
2. Determine the voltage which must be applied to a 2 kΩ
resistor in order that a current of 10 mA may flow.
SOLUTIO
N:
SERIES CIRCUIT
A series circuit has more than one resistor (anything that uses
electricity to do work) and gets its name from only having one
path for the charges to move along.
Resistor in Series – the total resistance (effective resistance or
resultant resistance) is equal to the sum of the individual resistance.
RT = R1 + R 2 + R3
+…Rn
Current in Series Circuit – a series circuit has only one path in
which charge can flow. The current are same everywhere.
IT = I1 = I2 = I3 = …
In
Voltage in Series Circuit – Total voltage in a series circuit is
equal to the sum of the individual voltage drops.
V1 = V2 + V3 + V4 + ....
Vn
PARALLEL CIRCUIT
A parallel circuit has more than one resistor and gets its name from having parallel
paths to move along. Charges can move through any of several paths. If one of the items
in the circuit is broken then no charge will move through that path, but other paths will
continue to have charges flow through them.
Resistor in Parallel – The reciprocal of the total resistance
(effective resistance of resultant resistance) is equal to the sum of
the reciprocal of individual resistance.
Current in Parallel Circuit – A parallel circuit has more than
one path for the current to flow. The total current is equal to the
sum of the sub-currents.
IT = I1 + I2 + I3 + …
In
Voltage in Parallel Circuit – Components in a parallel circuit
share the same voltage.
V1 = V2 = V3 = V4 = ....
Vn
SERIES – PARALLEL COMBINATION
CIRCUIT
A series-parallel circuit is a combinational circuit which when
simplified will result into a series circuit.
PARALLEL – SERIES COMBINATION
CIRCUIT
A parallel-series circuit is a combinational circuit which when
simplified will result into a parallel circuit.
EXAMPLE 7
1. A 3-ohm resistor and a 6-ohm resistor are connected in series
across a DC supply. If the voltage drop across the 3-ohm
resistor is 4V, what is the voltage of the supply?
2. A 5-ohm resistance is connected in parallel with a 10-ohm
resistance. What is the equivalent resistance?
3. Two resistance of 10 and 15 ohms each respectively are
connected in parallel. The two are then connected in series with
a 5-ohm resistance. What is the equivalent resistance?
SOLUTIO
N:
EXAMPLE 8
1. A load of 10-ohms was connected to a 12-volt battery. The current
drawn was 1.18 amperes. What is the internal resistance of the
battery?
2. Three resistors R1, R2 and R3 are connected in parallel and take a
total current of 7.9A from a dc source. The current through R1 is
half of that through R2. If R3 is 36-ohms and takes 2.5A, determine
the values of R1 and R2.
3. Two resistance of 10 and 15 ohms each respectively are connected
in series. The two are then connected in parallel with a 5-ohm
resistance. What is the equivalent resistance?
ANYONE
??
WYE DELTA TRANSFORMATION
Situations often arise in circuit
analysis when the resistors are neither
in parallel nor in series. For example,
consider the bridge circuit shown. The
combination of branch R6 and branch
R5 is not series since a node is between
them. Also, combination of branch R1
through R6 are neither in series nor in
parallel.
Many circuits of the type can be simplified by using three-terminal equivalent
networks. These are the wye (Y) or tee (T) network shown figure (a) and the delta
(Δ) or pi (π) network shown in figure (b). These networks occur by themselves or as
part of a larger network. They are used in three-phase networks, electrical filters,
and matching networks.
DELTA TO WYE CONVERSION
Considering the network below, each resistor in the Y network is the product of the
resistors in the two adjacent Δ branches, divided by the sum of the three Δ resistors.
WYE TO DELTA CONVERSION
The circuit below shows that each resistor in the Δ network is the sum of all possible
products of Y resistors taken two at a time, divided by the opposite Y resistor.
EXAMPLE 9
1. A circuit consisting of three resistors rated 10 ohms, 15 ohms and 20 ohms are
connected in delta. What would be the resistance of the equivalent wye
connected load?
2. A circuit consisting of three resistors rated 10 ohms, 15 ohms and 20 ohms are
connected in wye. What would be the resistance of the equivalent delta
connected load?
3. A 5Ω resistance is connected in parallel with 10Ω resistance. Another set, a 6Ω
and 8Ω resistances are also connected in parallel. Two sets are connected in
series. What is the equivalent resistance?
SOLUTIO
N:
THANK YOU!
“MODULE 2”
RESISTIVE CIRCUITS
(PART II)
ENGR. SARAH JANE F. FRUELDA,
Intended Learning Outcomes
1. Describe an electric circuit and Ohm’s Law
2. Use Ohm’s law to calculate the voltages and currents in electric circuits.
3. Analyze single-loop and single-node-pair circuits to calculate the voltages and
currents in an electric circuit.
4. Determine the equivalent resistance of a resistor network where the resistors
are in series and parallel.
5. Calculate the voltages and currents in a simple electric circuit using voltage
and current division.
6. Transform the basic wye resistor network to a delta resistor network, and visa
versa.
7. Analyze electric circuits to determine the voltages and currents in electric
circuits that contain dependent sources.
8. Apply Kirchhoff’s current law and Kirchhoff’s voltage law to determine the
voltages and currents in an electric circuit.
SERIES CIRCUIT
A series circuit has more than one resistor (anything that
uses electricity to do work) and gets its name from only
having one path for the charges to move along.
Resistor in Series – the total resistance (effective resistance
or resultant resistance) is equal to the sum of the individual
resistance.
RT = R1 + R2 + R3
+…Rn
Current in Series Circuit – a series circuit has only one path
in which charge can flow. The current are same everywhere.
IT = I1 = I2 = I3 = …
In
Voltage in Series Circuit – Total voltage in a series circuit
is equal to the sum of the individual voltage drops.
V1 = V2 + V3 + V4 + ....
Vn
PARALLEL CIRCUIT
A parallel circuit has more than one resistor and gets its name from having
parallel paths to move along. Charges can move through any of several paths. If
one of the items in the circuit is broken then no charge will move through that
path, but other paths will continue to have charges flow through them.
Resistor in Parallel – The reciprocal of the total resistance
(effective resistance of resultant resistance) is equal to the
sum of the reciprocal of individual resistance.
Current in Parallel Circuit – A parallel circuit has more
than one path for the current to flow. The total current is
equal to the sum of the sub-currents.
IT = I1 + I2 + I3 + …
In
Voltage in Parallel Circuit – Components in a parallel
circuit share the same voltage.
V1 = V2 = V3 = V4 = ....
Vn
SERIES – PARALLEL COMBINATION CIRCUIT
A series-parallel circuit is a combinational circuit which
when simplified will result into a series circuit.
PARALLEL – SERIES COMBINATION CIRCUIT
A parallel-series circuit is a combinational circuit which when
simplified will result into a parallel circuit.
EXAMPLE 2.9
A 3-ohm resistor and a 6-ohm resistor are connected in series
across a DC supply. If the voltage drop across the 3-ohm resistor
is 4V, what is the voltage of the supply?
Solution:
EXAMPLE 2.10
Three resistors R1, R2 and R3 are connected in parallel and take a
total current of 7.9A from a dc source. The current through R1 is
half of that through R2. If R3 is 36-ohms and takes 2.5A, determine
the values of R1 and R2.
Solutio
n:
EXAMPLE 2.11
Determine the total resistance of the circuit shown.
Solution:
EXAMPLE 2.12
Solve for Rac, Rab and Rcd for the circuit shown.
ANYONE?
THANK YOU!
Intended Learning Outcomes
1. Describe an electric circuit and Ohm’s Law
2. Use Ohm’s law to calculate the voltages and currents in electric circuits.
3. Analyze single-loop and single-node-pair circuits to calculate the voltages and
currents in an electric circuit.
4. Determine the equivalent resistance of a resistor network where the resistors are in
series and parallel.
5. Calculate the voltages and currents in a simple electric circuit using voltage and
current division.
6. Transform the basic wye resistor network to a delta resistor network, and visa versa.
7. Analyze electric circuits to determine the voltages and currents in electric circuits that
contain dependent sources.
8. Apply Kirchhoff’s current law and Kirchhoff’s voltage law to determine the voltages
and currents in an electric circuit.
CIRCUITS WITH DEPENDENT SOURCES
As discussed in the previous module (Module 1), the dependent sources generate a
voltage or current that is determined by a voltage or current at a specified location in
the circuit. These sources are very important because they are an integral part of the
mathematical models used to describe the behavior of many electronic circuit elements.
Problem-Solving Strategy for solving Circuits with dependent sources
1. When writing the KVL and/or KCL equations for the network, treat the dependent
source as though it were an independent source.
2. Write the equation that specifies the relationship of the dependent source to the
controlling parameter.
3. Solve the equations for the unknowns. Be sure that the number of linearly
independent equations matches the number of unknowns.
EXAMPLE 2.17
Determine the voltage Vo in the circuit.
Solution:
EXAMPLE 2.18
The network shown contains a voltage-controlled voltage source. Find 𝑉𝑜.
Solution:
THANK YOU!
INTRODUCTION
This part will be about the analysis of circuits in which the
source voltage or current is time-varying or sinusoidally timevarying excitation, or simply, excitation by a sinusoid. A sinusoid is
a signal that has the form of the sine or cosine function.
A sinusoidal current is usually referred to as alternating
current (ac). This current reverses at regular time intervals and has
alternately positive and negative values. Circuits driven by
sinusoidal current or voltage sources are called ac circuits.
INTRODUCTION
This section will be divided into:
 Origins of AC and DC current
 Difference between direct current and alternating current
system
 Generation of alternating current and voltage
 Waveform and vector representation of voltage and current
 Identifying different types of AC circuits (series), and their
corresponding wave and vector representation
ORIGINS OF ALTERNATING CURRENT AND
DIRECT CURRENT
A magnetic field near a wire causes electrons to flow in a single
direction along the wire, because they are repelled by the negative side of a
magnet and attracted toward the positive side. This is how DC power from a
battery was born, primarily attributed to Thomas Edison’s work.
In late 1800s, the battle of direct current versus alternating current
began. Both had their own advantages. However, ac generators gradually
replaced Edison’s dc battery system because ac is more efficient and
economical to transmit over long distances. In ac, instead of applying the
magnetism along the wire steadily, scientist Nikola Tesla used a rotating
magnet.
DIFFERENCE BETWEEN DC AND
AC SYSTEM
Electricity flows in two ways: either in an alternating current
(AC) or in a direct current (DC). The chart below shows the
comparison between the two.
DIFFERENCE BETWEEN DC AND
AC SYSTEM
Note: Power factor is the ratio of the real power that is used to do
work and the apparent power that is supplied to the circuit.
GENERATION OF ALTERNATING
CURRENT AND VOLTAGE
Alternating voltage may be generated (a) by rotating a coil
in a magnetic field or (b) by rotating a magnetic field
within a stationary coil, as shown in the figure below.
GENERATION OF ALTERNATING
CURRENT AND VOLTAGE
Operation principle of generating alternating voltage is based on Electromagnetic Induction,
which is defined by Faraday’s Law, which states:
Eemf
dΦ
= −N
dt
The electromotive force, Eemf, induced in a coil is proportional to the number of
turns N, in the coil and the rate of change, dΦ/dt of the number of magnetic flux lines
passing through the surface enclosed by the coil. The emf is the voltage produce when a
conductor winding in a magnetic field or by altering the direction of flux.
The value of the voltage generated depends, in each case, upon the number of turns
in the coil, strength of the field and the speed at which the coil or magnetic field rotates. It
changes:
 In magnitude from instant to instant as varying flux are cut per second; and
 In direction as coil sides changes positions under north and south poles, implies
that an alternating emf is generated.
WAVEFORM AND VECTOR DIAGRAM REPRESENTATION
OF ALTERNATING CURRENT AND VOLTAGE
AC Waveform
A wave is a disturbance. Unlike water waves, electrical waves
cannot be seen directly but they have similar characteristics. All
periodic waves can be constructed from sine waves, which is why sine
waves are fundamental. While waveform is the resulting graph of an
alternating current plotted to a base of time.
Therefore, AC waveform is defined as one that varies in both
magnitude and direction in more or less an even manner with respect
to time. It also refers to a time-varying waveform known as a
sinusoidal wave or a generated sine wave.
WAVEFORM AND VECTOR DIAGRAM REPRESENTATION
OF ALTERNATING CURRENT AND VOLTAGE
Types of Waveform
 Sinusoidal wave
 Half wave
 Triangular wave
 Semi-circular wave
 Trapezoidal wave
 Square wave
WAVEFORM AND VECTOR DIAGRAM REPRESENTATION
OF ALTERNATING CURRENT AND VOLTAGE
Cycle
One complete series of values is called a cycle. One complete
cycle is equivalent to one revolution.
Time Period
The time taken in seconds for an alternating quantity to complete
one cycle is called the period or the periodic time, T, of the waveform.
Which can be expressed mathematically,
2π
T=
ω
where
ω
= the angular velocity in radian/s, which is equal to 2πf
WAVEFORM AND VECTOR DIAGRAM REPRESENTATION
OF ALTERNATING CURRENT AND VOLTAGE
Frequency
The number of cycles completed per second is called the
frequency, f, of the supply and is measured in hertz, Hz. Also, it is the
reciprocal of time period. The standard frequency of the electricity
supply in the Philippines is 60 Hz.
PN
1
f=
=
120
T
where
P
N
T
= the number of pole/s
= speed in revolution per minute
= time period in seconds
EXAMPLE 7
1. Determine the periodic time for frequencies of (a)
50 Hz and (b) 20 kHz
2. Determine the frequencies for periodic times of (a)
4 ms, (b) 4 μs
3. An alternating current completes 5 cycles in 8 ms.
What is its frequency?
WAVEFORM AND VECTOR DIAGRAM REPRESENTATION
OF ALTERNATING CURRENT AND VOLTAGE
Peak value or maximum value or crest value or amplitude
This is largest value reached in a half cycle (during positive or
negative) of the waveform. Such values are represented by Vm, Im, etc.
Average or mean value
This is the average value measured over a half cycle (since
over a complete cycle the average value is zero). Mathematically, in
general,
area under the curve
Average or mean value =
base
WAVEFORM AND VECTOR DIAGRAM REPRESENTATION
OF ALTERNATING CURRENT AND VOLTAGE
Effective value
This is the current which will produce the same heating effect
as an equivalent direct current. It is sometimes called as root mean
square (rms) value and whenever an alternating quantity is given, it is
assumed to be the rms value.
Form factor (ff) and peak factor (pf),
form factor =
rms value
average value
peak factor =
maximum value
rms value
WAVEFORM AND VECTOR DIAGRAM REPRESENTATION
OF ALTERNATING CURRENT AND VOLTAGE
The values of form and peak factor gives an indication of the shape of
waveforms. For sine wave, form factor is equivalent to 1.11 while 1.41
for the peak factor.
EXAMPLE 8
1. Calculate the rms value of a sinusoidal current of
maximum value of 20 A
2. A supply voltage has a mean value of 150 V.
Determine its maximum value and its rms value.
SOLUTIO
N:
WAVEFORM AND VECTOR DIAGRAM REPRESENTATION
OF ALTERNATING CURRENT AND VOLTAGE
Instantaneous values
Instantaneous values are the values of the alternating
quantities at any instant of time or angle of rotation. They are
represented by small letter. Consider the sinusoidal voltage
𝐞 = 𝐄𝐦 𝐬𝐢𝐧(𝛚𝐭 ± ∅)
Similarly, the equation of induced alternating current
𝐢 = 𝐈𝐦 𝐬𝐢𝐧(𝛚𝐭 ± ∅)
WAVEFORM AND VECTOR DIAGRAM REPRESENTATION
OF ALTERNATING CURRENT AND VOLTAGE
where
Em
Im
ωt
ø
f
= the amplitude or maximum value of the
sinusoidal voltage in volt
= the amplitude or maximum value of the
sinusoidal current in ampere
= the argument of the sinusoid
= the angle of lag or lead in degree
= frequency of rotation of the coil in hertz
PHASE RELATIONSHIP OF A SINUSOIDAL
WAVEFORM
Note: Assume that the reference waveform is sine wave at 0 deg.
PHASOR DIAGRAM OF A SINUSOIDAL
WAVEFORM
PHASOR DIAGRAM OF A SINUSOIDAL
WAVEFORM
Two or more sine waves of the same frequency can be shown on the
same vector diagram because the various vectors representing different
waves all rotate counter-clockwise at the same frequency and maintain a
fixed position relative to each other.
SINE AND COSINE WAVEFORM AND
PHASOR RELATIONSHIP
cos 𝜔𝑡 = sin(𝜔𝑡 + 90°)
sin 𝜔𝑡 = cos 𝜔𝑡 − 90°
EXAMPLE 9
Calculate the phase difference between e1 =
-10 cos(ωt + 50°) and e2 = 12 sin(ωt - 10°).
State which sinusoid is leading. Draw the
waveform and phasor diagram.
SOLUTIO
N:
SOLUTIO
N:
EXAMPLE 10
Find the phase angle between i1 = -4 sin(377t +
25°) and i2 = 5 cos(377t - 40°). Does i1 lead or
lag i2? Draw the waveform and phasor diagram.
SOLUTIO
N:
EXAMPLE 11
Determine the (a) instantaneous current equations and (b)
draw the vector and wave diagram. Assume I1 = I2 = I3 =
I4 = 5 A and the reference vector is I1.
I2 leads I1 by 45°
I3 leads I1 by 30°
I4 lags I3 by 60°
ANYONE
??
SUMMATION OF IN – PHASE
SINUSOIDAL WAVES
When two or more sinusoidal voltage or current waves are in-phase and
having the same frequency, they may be added to yield a sine wave of the
same frequency. The total value is equal to the arithmetic sum of the
maximum values of the component wave.
EXAMPLE 12
1. Two voltages of 50 volts and 25 volts respectively
are in-phase, determine the total voltage and the
instantaneous voltage.
2. Find the total instantaneous voltage equation of
the given data: v1 = 20 sinωt, v2 = 15 cos(ωt - 90),
v3 = -10 cos(ωt+90) and v4 = -20 sin(ωt+180).
SOLUTIO
N:
SUMMATION OF OUT – OF – PHASE
SINUSOIDAL WAVES
When two or more sinusoidal voltage or current waves are out-of-phase
and having the same frequency, they maybe added to yield a sine wave of
the same frequency
SUMMATION OF OUT – OF – PHASE
SINUSOIDAL WAVES
Out-of-phase sinusoidal quantities can be added or subtracted in two ways:
 The addition or subtraction of two or more values start with finding
their vector representation, the vertical and horizontal directions, and
from this the calculation of the vertical and horizontal components
can be attained for the resultant “R” vector, which is the total value.
Example, A + B
X – component = A cos(ø) + B cos(ø)
Y – component = A sin(ø) + B sin(ø)
R =
X2
+ Y2
∅=
tan−
Y
X
EXAMPLE 13
1. Add the following currents: i1 = 7 sin ωt and i2 =
10 sin (ωt + π/3).
2. Two alternating voltages are represented by e1 =
50 sin ωt and e2 = 100 sin (ωt - π/6)V. Draw the
phasor diagram and find, by calculation, a
sinusoidal expression to represent e1 + e2.
SOLUTIO
N:
SOLUTIO
N:
EXAMPLE 14
Find the total/resultant effective voltage, given the
following:
e1 = 10 sin ωt
e2 = -15 cos (ωt – π/3)
e3 = 10 cos ωt
e4 = -20 sin (ωt– π/3)
ANYONE
??
SUMMATION OF OUT – OF – PHASE
SINUSOIDAL WAVES
 Transform the given sinusoid into complex form:
A = Amcos(ø) ± j Am sin(ø)
where ± = depends on the sign of the angle
Then add or subtract the two vectors, A and B using the generalized
expression is as follows:
A = x + jy
B = w + jz
A + B = (x + w) + j(y+z)
After adding or subtracting the two vectors, transform the complex
form into sinusoidal expression.
EXAMPLE 15
1. Add the following currents: i1 = 7 sin ωt and i2 =
10 sin (ωt + π/3).
2. Two alternating voltages are represented by e1 =
50 sin ωt and e2 = 100 sin (ωt - π/6)V. Draw the
phasor diagram and find, by calculation, a
sinusoidal expression to represent e1 + e2.
SOLUTIO
N:
EXAMPLE 16
Find the total/resultant effective voltage, given the
following:
e1 = 10 sin ωt
e2 = -15 cos (ωt – π/3)
e3 = 10 cos ωt
e4 = -20 sin (ωt– π/3)
ANYONE
??
THANK YOU!
NETWORK LAWS, THEOREMS AND
PRINCIPLES
1.
2.
3.
4.
5.
6.
7.
8.
9.
Kirchhoff’s Laws
Maxwell’s “Mesh” Analysis
Nodal Analysis
Millman’s Theorem
Source Transformation
Superposition Theorem
Thevenin’s Theorem
Norton’s Theorem
Maximum Power Transfer
KIRCHHOFF’S LAW
In 1845, German physicist Gustav Kirchhoff first described two laws that
became central to electrical engineering- the Kirchhoff's Current Law
(also known as Kirchhoff's Junction Law, and Kirchhoff's First Law) and
the Kirchhoff’s Voltage Law.
These laws are extremely useful in real life because they describe the
relation of values of currents that flow through a junction point and
voltages in an electrical circuit loop. They describe how electrical current
flows in all of the billions of electric appliances and devices, as well as
throughout homes and businesses, that are in use continually on Earth.
KIRCHHOFF'S CURRENT LAW
The algebraic sum of currents at any node (or in general, any closed surface in an
electrical network) is zero. Here, currents entering and current leaving the node must be
assigned opposite algebraic signs.
The sum of currents entering a node must equal the sum of currents leaving this node.
a
KIRCHHOFF'S VOLTAGE LAW
When the current flows in an element from
the lower potential point towards a higher
potential point, a voltage rise is
encountered. Voltage drop is encountered
when the current flows in an element from
the higher potential terminals toward the
lower potential terminals, as in the case of
current flow through a load.
The algebraic sum of all voltage around
any closed loop in an electric circuit is
zero. Here a voltage rise may be taken
with a positive sign while a voltage drop
would be taken with a negative sign or
vice versa.
EXAMPLE 1
Determine each branch current using Kirchhoff’s laws.
SOLUTIO
N:
EXAMPLE 2
Find the value of currents and voltages in each resistance shown in the
circuit below using Kirchhoff’s Law.
SOLUTIO
N:
48 V
EXAMPLE 3
Find the value of currents and voltages in each
resistance shown in the circuit below using
Kirchhoff’s Law.
ANYONE
??
MESH ANALYSIS
The solution of complex networks are frequently be simplified by using a
system of loop or mesh current instead of branch currents of the frequently
(Kirchhoff’s Law) procedure. First proposed by James Clerk Maxwell. This
method involves a set of independent loop or mesh currents assigned to as
many meshes as exists in the circuit. The magnitude of the current passing
through in each resistor is the algebraic sum of the mesh currents passing
through it. This method is only applicable to a circuit that is planar.
A mesh is a loop which does not contain any other loops within it.
A super mesh results when two meshes have a (dependent or independent)
current source in common.
EXAMPLE 4
Find the currents and voltages in the circuit using
Maxwell Mesh Analysis.
SOLUTIO
N:
EXAMPLE 5
For the circuit shown. Find V1 and V2 using Maxwell
Mesh Analysis.
SOLUTIO
N:
EXAMPLE 6
Find the value of I1, I2, and I3 using Maxwell Mesh
Analysis.
ANYONE
??
THANK YOU!
MODULE 3
SINGLE PHASE SERIES AC CIRCUIT
EE – 420 Basic Electrical and Electronics Engineering
Engr. Sarah Jane F. Fruelda, REE, RME
IMPEDANCE
Impedance (Z) is the effective resistance of an electric circuit or component to alternating
current, arising from the combined effects of ohmic resistance and reactance. It can be
represented by a complex form, either in rectangular or polar form.
Rectangular form:
Polar form:
Z = R ± jX
Z = Zm ∠ϕ
Also, the impedance Z of a circuit is the ratio of the phasor voltage E to the phasor current I,
measured in ohms (Ω). It represents the opposition which the circuit exhibits to the flow of
sinusoidal current.
E
Z=
I
IMPEDANCE
Frequently, for solving the impedance, impedance triangle is used. It is the right-angled triangle
formed by the vectors representing the resistance drop, the reactance drop, and the impedance
drop of a circuit carrying an alter. Example of an impedance triangle is shown below:
where:
R = resistance in ohm
X = reactance in ohm
Zm = magnitude of impedance in ohm,
= R2 ± X 2
Ø = angle in degree
RESISTANCE AND REACTANCE
Resistance
Resistance is an electrical quantity that measures how the device or
material reduces the electric current flow through it. The resistance is
measured in units of ohms(Ω)
Reactance
Reactance is the opposition of a circuit element to a change in
current or voltage, due to that element’s inductance or capacitance. It is
the property of inductor or capacitor which opposes the flow of current.
POWER FACTOR
Power factor
Power factor is a measure of the electrical systems efficiency. It
is defined as the ratio of the resistance and impedance or it is the
cosine of the angle between the impressed voltage and the current.
Like all ratio measurements, power factor (pf) is a unitless quantity.
However, for ac supply it is necessary to determine if the power
factor is leading or lagging.
DIFFERENT TYPES OF SERIES
AC CIRCUIT
PURELY RESISTIVE AC CIRCUIT
A pure resistance circuit takes a current in phase with the impressed voltage. This
implies that the power factor is unity. Therefore, the applied voltage has to supply the
ohmic voltage drop only. Hence,
e = iR
where:
e = Em sinωt
= instantaneous voltage in volt
E
i = Im sinωt = m sinωt = instantaneous current in ampere
𝑅
PURELY RESISTIVE AC CIRCUIT
The instantaneous power,
p = ei = Em Im sin2 ωt
The average power,
Pave = EI
The impedance for pure resistance is,
E
Z = I = R + j0
PURELY INDUCTIVE AC CIRCUIT
A pure inductance circuit takes the current IL that lags the applied voltage EL by 90°.
In a purely inductive circuit the opposition to the flow of alternating current is called
the inductive reactance, XL
EL
xL =
= 2πfL Ω
IL
where
EL
IL
f
L
= the voltage across the inductance in volt (V)
= the current through the inductance in ampere (A)
= the supply frequency in hertz (Hz)
= the inductance in henry (H)
PURELY CAPACITIVE AC CIRCUIT
A pure capacitance circuit takes a current IC that leads the applied voltage EC by 90°.
In a purely capacitive circuit the opposition to the flow of alternating current is called
the capacitive reactance, XC
EC
1
xC =
=
Ω
IC 2πfC
where
EC
IC
f
C
= the voltage across the capacitance in volt (V)
= the current through the capacitance in ampere (A)
= the supply frequency in hertz (Hz)
= the capacitance in farad (F)
SAMPLE PROBLEMS:
1.
(a) Calculate the reactance of a coil of inductance 0.32 H when it is connected to a
50 Hz supply. (b) A coil has a reactance of 124 ohms in a circuit with a supply of
frequency 5 kHz. Determine the inductance of the coil.
2.
A coil has an inductance of 40 mH and negligible resistance. Calculate its inductive
reactance and the resulting current if connected to (a) a 240 V, 50 Hz supply, and
(b) a 100 V, 1 kHz supply
3.
Determine the capacitive reactance of a capacitor of 10 μF when connected to a
circuit of frequency (a) 50 Hz (b) 20 kHz.
SOLUTION:
SERIES RL CIRCUIT
In an ac circuit containing inductance L and
resistance R, the applied voltage E is the phasor sum
of ER and EL and thus the current I lags the applied
voltage E by an angle lying between 0° and 90°.
SERIES RC CIRCUIT
In an ac circuit containing capacitance C and
resistance R, the applied voltage E is the phasor sum
of ER and EC and thus the current I leads the applied
voltage E by an angle lying between 0° and 90°.
SERIES RLC CIRCUIT
In an ac series circuit containing resistance R,
inductance L and capacitance C, the applied voltage
E is the phasor sum of ER, EL and EC. EL and EC are
anti-phase, displaced by 180°, and there are three
diagrams possible – each depending on the relative
values of EL and EC.
SAMPLE PROBLEMS:
1.
In a series R-L circuit the potential difference across the resistance R is 12 V and the potential
difference across the inductance L is 5 V. Find the supply voltage and the phase angle between the
current and voltage.
2.
A coil has a resistance of 4 Ω and an inductance of 9.55 mH. Calculate (a) the reactance, (b) the
impedance, and (c) the current taken from a 240 V, 50 Hz supply. Determine also the phase angle
between the supply voltage and current.
3.
A coil takes a current of 2 A from a 12 V dc supply. When connected to a 240 V, 50 Hz supply the
current is 20 A. Calculate the resistance, impedance, inductive reactance and inductance of the coil.
4.
A resistor of 25 Ω is connected in series with a capacitor of 45 μF. Calculate (a) the impedance, and (b)
the current taken from a 240 V, 50 Hz supply. Find also the phase angle between the supply voltage and
the current.
SOLUTION:
SAMPLE PROBLEMS:
5. A capacitor C is connected in series with a 40 Ω resistor across a supply of frequency
60 Hz. A current of 3 A flows and the circuit impedance is 50 Ω. Calculate (a) the value
of capacitance, (b) the supply voltage, (c) the phase angle between the supply voltage
and current, (d) the potential difference across the resistor and (e) the potential
difference across the capacitor. Draw the phasor diagram.
6. A coil resistance 5 Ω and inductance of 120 mH in series with a 100 μF capacitor, is
connected to a 300 V, 50 Hz supply. Calculate (a) the current flowing, (b) the phase
difference between the supply voltage and the current, (c) the voltage across the coil
and (d) the voltage across the capacitor.
ANYONE?
THANK YOU!
Single Phase Series AC
Circuit
More Examples
Recall:
1. If the emf in a circuit is given by e= 100 sin 628t , the
maximum value of the voltage and frequency is?
2. What is the complex expression for a given alternating
current i=250 sin(t-25) ?
3. A circuit has a resistance of 20  and a reactance of 30
.What is the power factor of the circuit?
4. A two-element series circuit with R= 15 , L= 20 mH has
an impedance of 30  .What is the frequency in Hz?
5. What are the two elements in a series circuit connection
having a current and voltage of i= 13.42 sin(500t-53.4) A
and v= 150 sin (500t+10) V?
6. A capacitor in series with 200  resistor draws a current
of 0.3 ampere from 120 V,60 hz source.What is the value of
capacitor in microfarad?
7. Reactances are connected in series: Xc1= 100 , Xc2= 40
, XL1= 30 , XL2= 70 ,What is the net reactance?
8. A series RLC circuit has elements R= 50  ,L=8 mH and
C= 2.22 F. What is the equivalent impedance of the circuit
if the frequency is 796 Hz?
9. A 25  resistor is connected in series with a coil of 50 
resistance and 150mH inductance. What is the power factor
of the circuit?
10. . A capacitor C is connected in series with a 40 Ω resistor across
a supply of frequency 60 Hz. A current of 3 A flows and the circuit
impedance is 50 Ω. Calculate (a) the value of capacitance, (b) the
supply voltage, (c) the phase angle between the supply voltage and
current, (d) the potential difference across the resistor and (e) the
potential difference across the capacitor. Draw the phasor diagram.
11. A coil resistance 5 Ω and inductance of 120 mH in series with a
100 μF capacitor, is connected to a 300 V, 50 Hz supply. Calculate
(a) the current flowing, (b) the phase difference between the supply
voltage and the current, (c) the voltage across the coil and (d) the
voltage across the capacitor.