Fundamentals of
Electrical Circuits
MODULE 1
Engr. Prince Sero
Outline
I. Course Description
II. General Policies
III. Units, Contact Hours, Requisites
IV. Grading System
V. Course Outline
VI. References
VII. Basic Concepts
COURSE DESCRIPTION
COURSE DESCRIPTION
This course introduces the fundamental concepts, circuit laws,
theorems, and techniques used in electrical circuit analysis
and transient analysis, as well as its applications. The course
covers circuit topologies and DC excitations, transient
response, AC response, and polyphase circuits. The use of
computer software for circuit simulation and design are
emphasized to expose students to computer-based tools.
General Policies
General Policies
• Attendance will be checked through a SEAT PLAN. You will have a
freedom to choose your place good for the whole semester unless told
otherwise.
• Only missed major exams may be given a special make-up exam with
valid reasons and upon presentation of related documents. Missed
quizzes will be given a score of “0”.
General Policies
• Cheating will be automatically penalized with a final grade of “5.0”.
• Going out of the class during exams is NOT ALLOWED.
• Assignments and seat works have a weight equal to a quiz. NO LATE
SUBMISSION policy is implemented.
Units, Contact Hours,
Requisites
Units
Lecture – 3 units
Laboratory – 1 unit
Hours per week
Lecture – 3 hours/week
Laboratory – 3 hours/week
Pre-requisite
Co-requisite
Physics for Engineers
ECEN2101 / ECEN2013
Grading System
MIDTERM
Lecture
Quizzes (Q)
Quizzes (Q)
Midterm Exam (ME)
Final Exam (FE)
Midterm Grade (MGLec)
Final Grade (FGLec)
MIDTERM
Laboratory
FINALS
FINALS
Experiment Report (ER)
Experiment Report (ER)
Midterm Exam (ME)
Final Exam/Project (FE)
Midterm Grade (MGLec)
Final Grade (FGLec)
Grading System
Course Outline
Course Outline
I. Circuit Topologies and DC Excitations
• Introductory Concepts
• Electrical Properties of Materials
• Passive Elements
• Network Laws and Theorems
• Electric Circuit Theorems
Course Outline
II. Transient Response
• RC Circuits
• RL Circuits
• RLC Circuits
Course Outline
III. AC Response and Polyphase Circuits
• Reactance and Impedance
• Introduction to Single-phase AC
• AC Power Analysis
• Sinusoidal Steady-State Analysis
• Three-Phase Circuits
• Transformers
References
References
• Boylestad, Robert L. 2010. Introductory Circuit Analysis. New
Jersey : Pearson Education, Inc.
• Bird, John. 2010. Electrical Circuit Theory and Technology.
Amsterdam: Elsevier
• Dorf, Richard C. and Svoboda, James A. 2011. Introduction to
Electric Circuits 7th edition. USA: John Wiley & Sons, Inc.
• Edminister, J.A. 2011. Theory and Problems of Electric Circuits,
Schaum’s Outline Series. New York, USA : McGraw-Hill
Basic Concepts
Systems of Units
Quantity
Basic Unit
Symbol
Length
Meter
m
Mass
Kilogram
kg
Time
Second
s
Thermodynamic Temperature
Kelvin
K
Electric Current
Ampere
A
Amount of Substance
Mole
mol
Luminous Intensity
Candela
cd
Basic Concepts
SI Unit Prefixes
Prefix
Multiplier
Symbol
Prefix
Multiplier
Symbol
yotta
x 1024
Y
yocto
x 10-24
y
zetta
x 1021
Z
zepto
x 10-21
z
exa
x 1018
E
atto
x 10-18
a
peta
x 1015
P
femto
x 10-15
f
tera
x 1012
T
pico
x 10-12
p
giga
x 109
G
nano
x 10-9
n
mega
x 106
M
micro
x 10-6
µ
kilo
x 103
k
milli
x 10-3
m
hecto
x 102
h
centi
x 10-2
c
deka
x 101
da
deci
x 10-1
d
Basic Concepts
Scientific Notation
• It is the shifting of the decimal point either to the left or to the right of
the given number until there is only one significant digit to the left of
the decimal point and then multiplying the number with the appropriate
power of 10 to retain its original value.
• A way of expressing a number in terms of the power of 10.
Example: 58, 000 meters = 5.8 x 104 m
Basic Concepts
Engineering Notation
• It is an exponential format of specifying numbers in which the powers
of 10 are limited to the multiples of three so that it corresponds to an S.I.
prefix.
• It is the application of decimal prefixes and their abbreviations to
simplify language when dealing with very small or very large units.
Example: 58, 000 meters = 58 km
Basic Concepts
Electric Circuit
• A closed loop of pathway with electric charges or current flowing
through it.
• A basic electric circuit contains three components: the power supply,
the load, and the wires.
• Wires connect the power supply and the load.
• Power supply is a device that supplies electrical energy to the load of the circuit.
• Load is a device that is usually connected to the output terminal of an electric
circuit.
Basic Concepts
Electric Circuit
Basic Concepts
Schematic Symbols
Component
Circuit Symbol
DC Power Supply
AC Power Supply
Fixed Resistor
Variable Resistor
Basic Concepts
Schematic Symbols
Component
Circuit Symbol
Capacitor
Inductor
Switch
Basic Concepts
Electric Current
• Electric current is measured by the amount of electric charge that flows
past a given point at a certain time interval in an electric circuit.
𝐶𝑢𝑟𝑟𝑒𝑛𝑡 =
𝐶ℎ𝑎𝑟𝑔𝑒
𝑇𝑖𝑚𝑒
𝐼=
𝑄
𝑇
• Electric current is also expressed by the derivative:
𝑑𝑞
𝑖=
𝑑𝑡
Basic Concepts
Electric Current
Similarly expressed as:
𝑡
𝑄 = න 𝑖 𝑑𝑡
𝑡0
Here, we represent current as i because there can be several types of
current; that is, charge can vary with time in several ways. If the current
does not change with time but remains constant, we call it direct current
(DC). Otherwise, we call it alternating current (AC).
Basic Concepts
DIRECT CURRENT (DC) is a current ALTERNATING CURRENT (AC) is a
that remains constant with time.
current that varies sinusoidally with
time.
Basic Concepts
Electric Current
Quantity
Quantity Symbol
Unit
Unit Symbol
Charge
Q
Coulombs
C
Time
t
Seconds
s
Current
I
Amperes
A
1 Coulomb = 6.25 x 1018 electrons, e1 electron = - 1.602 x 10-19 Coulomb, C
Basic Concepts
1 Coulomb = 6.25 x 1018 electrons, e1 electron = - 1.602 x 10-19 Coulomb, C
Electric Current
1 Ampere = 1 Coulomb / 1 second
Basic Concepts
Ammeter
Ammeter is an instrument that can be
used to measure current, and its
symbol is
It must be connected in series with
the circuit to measure current, as
shown in the figure.
Basic Concepts
Direction of Electric Current
There are two methods to express the direction of electric current.
Conventional Current Flow
Electron Flow
Basic Concepts
Direction of Electric Current
Conventional Current Flow
The assumed direction of the flow of current, which is opposite from the
electron flow, that is from the positive of the source to the negative of
the source.
Electron flow
Actual flow of current since electrons are the moving charges therefore
it moves from the negative of the source going to the positive of the
source.
Basic Concepts
SAMPLE PROBLEMS
Sample Problems
1. How much charge is represented by 4,600 electrons?
Ans. -7.369 x 10-16 C
2. The total charge entering the terminal is given by q = 5t sin 4πt mC. Calculate
the current at t = 0.5 s.
Ans. 31.42 mA
3. Determine the total charge entering a terminal between t = 1 s and t = 2 s if the
current passing the terminal is i = (3t2 – t ) A.
Ans. 5.5 C
4. If in problem number 2, q = (10 – 10e-2t) mC, find the current at t = 1.0 s.
Ans. 2.707 mA
Basic Concepts
Electric Voltage
Voltage / Electromotive Force ( V or E )
• EMF is an electric pressure or force that is supplied by a voltage
source, which causes electric current to flow in a circuit.
• Voltage is responsible for the pushing and pulling of electrons or
current through an electric circuit.
• In a linear circuit of fixed resistance, if we increase the voltage, the
current goes up, and similarly, if we decrease the voltage, the current
goes down.
Basic Concepts
Potential Difference
Potential difference/voltage is the amount of energy or work
required to move electrons between two points and is expressed by the
formula:
𝑉𝑜𝑙𝑡𝑎𝑔𝑒 =
𝑊𝑜𝑟𝑘
𝐶ℎ𝑎𝑟𝑔𝑒
𝑉=
𝑊
𝑄
Voltage is also expressed by the derivative:
𝑑𝑤
𝑣=
𝑑𝑞
Basic Concepts
Electric Voltage
Quantity
Quantity Symbol
Unit
Unit Symbol
Voltage
V
Volt
V
Work (Energy)
W
Joule
J
Charge
Q
Coulomb
C
Basic Concepts
Potential Difference Explained
Basic Concepts
Potential Difference Explained
Assuming there are two water tanks
A and B.
Water will flow from tank A to B
because tank A has a higher water
level than tank B
It is the water-level difference that
produces the potential energy for
tank A, and work is done when water
flows from tank A to B.
Basic Concepts
Potential Difference Explained
Basic Concepts
Electric Voltage
• Current will flow between two points in an electric circuit only when
there is an electrical potential difference.
• For example, if 1 J of energy is used to move a 1 C charge from point a
to b, it will have a 1 V potential difference or voltage across two points.
Basic Concepts
Electric Voltage
”The charge will not move unless you apply the potential difference.”
Voltage drop occurs when a voltage across a component when current
flows from a higher potential point to a lower potential point.
Voltage rise occurs when a voltage across a component when current
flows from a lower potential point to a higher potential point.
Basic Concepts
Voltmeter
Voltmeter is an instrument that can
be used to measure voltage. Its
symbol is
The voltmeter should be connected
in parallel with the circuit component
to measure voltage.
Basic Concepts
Resistance
Resistor
• “Resists” the flow of electrical current.
• The higher the value of resistance, the smaller the current will be.
Resistance
• The property of a material or circuit elements to oppose the flow of
electrons.
• Expressed in ohms (Ω).
Basic Concepts
Factors Affecting Resistance
•
•
•
•
Length
Cross-sectional Area
Nature of the Material
Temperature
Basic Concepts
Factors Affecting Resistance
Cross-sectional area of the wire (A)
The larger the diameter of the wire, the greater the cross-sectional
area, the less the resistance in the wire and the more the flow of
current.
Length (L)
The longer the wire, the more the resistance and the more the time
taken for the current to flow.
Basic Concepts
Factors Affecting Resistance
Resistivity (ρ)
It is a measure for the opposition to flowing current through a
material of wire, or how difficult it is for current to flow through a
material. The different materials have different resistivity, i.e. more or
less resistance in the materials.
Temperature (T)
Resistivity of a material is dependent upon the temperature
surrounding the material. Resistivity increases with an increase in
temperature for most materials.
Basic Concepts
Resistance
Since,
𝑅∝
𝐿
𝐴
𝜌𝐿
𝐴
Then,
𝑅=
But,
𝑉 = 𝐴𝐿 ;
Then,
Therefore,
𝐿=
𝑅=
where:
;
𝑉
𝑉
and 𝐴 =
𝐴
𝐿
𝜌𝑉
𝜌𝐿2
=
𝐴2
𝑉
;
𝝆 = resistivity or specific resistance
of a given material at a certain
temperature (Ω-m)
L = length (m)
A = cross-sectional area (m2)
V = volume (m3)
For constant temperature only.
Basic Concepts
Resistivity of Copper at 20°C
• Standard Annealed Copper
𝝆 = 1.7241 x 10-8 Ω - m
𝝆 = 1.7241 x 10-6 Ω - cm
𝝆 = 10.37 Ω - cmil / ft
• Hard - Drawn Copper
𝝆 = 1.77 x 10-8 Ω - m
𝝆 = 1.77 x 10-6 Ω – cm
𝝆 = 10.65 Ω - cmil / ft
Basic Concepts
Mil (mil)
A unit of length equivalent to one thousandth of an inch.
1 mil = 1 x 10-3 in
Square mil (mil2)
A cross sectional area of a square whose side is equivalent to 1 mil.
Circular mil (cmil)
A cross sectional area of a circle whose diameter is equivalent to 1 mil.
𝜋
1 𝑐𝑚𝑖𝑙 = 𝑠𝑞𝑢𝑎𝑟𝑒 𝑚𝑖𝑙
4
𝐴𝑟𝑒𝑎 𝑖𝑛 𝑐𝑚𝑖𝑙 = 𝐷2 = 𝐷1 2 𝑥 106
where:
D = diameter in mils
D1 = diameter in inch
Basic Concepts
END
Basic Concepts
SAMPLE PROBLEMS
Sample Problems
1. Calculate the voltage required to accelerate an electron to a kinetic
energy of 8x10-15 Joules?
2. A car battery supplies a current of 50A to the starter motor. How
much charge passes through the starter in half a minute?
3. A positively charged dielectric has a charge of 2 coulombs. If
12.5x1018 free electrons are added to it, what will be the net charge
on the said dielectric?
4. A cloud of 2.5x1019 electrons move past a given point every two
seconds. How much is the intensity of the electron flow?
Sample Problems
5. A conductor has an area of 40,000 circular mils. What is the
diameter of this conductor in inches?
6. What is the area in circular mils (CM) of a conductor whose
diameter is 0.25 inch?
7. Determine the resistance of the copper wire with a length of 10
meters and a cross sectional of 4 cm by 4 cm.
8. A copper wire has a diameter of 2 inches and a length of 20 feet.
What is the resistance of the wire?
9. An electric conductor 1 m long with a cross sectional area of 1 mm2
has a resistance of 0.017 Ω, what is the resistance of a 50 m wire of
the same material with a cross-sectional of 0.25 mm2?