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ICEN 211 – ELECTRICAL ENGINEERING PRINCIPLES I

C
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3
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1
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Many branches of electrical engineering, such as
power, electric machines, control, electronics, communications, and instrumentation, are based
on electric circuit theory
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Circuit theory is also valuable to students
specializing in other branches of the physical sciences because circuits are a good model for the
study of energy systems in general, and because of the applied mathematics, physics, and
topology involved
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To do this requires an interconnection of electrical
devices
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An electric circuit is an interconnection of electrical elements
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System of units

Objectives of study
(i)
(ii)
(iii)

Introduce some common unit systems
Explain the different categories of SI units
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Categories
(i)

The metric system - based on metre
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2
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Derived units – with special name or no special names
Non- SI units that are commonly accepted to use with SI units

The system of units used in engineering and science is the Système Internationale d’Unités
(International system of units), usually abbreviated to SI units, and is based on the metric system
...
Therefore, all business and even household
transactions are conducted in SI units
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1
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Therefore, a table of conversions
from one unit to another is not required
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The system is coherent with the derived units
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3
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g
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Energy is now expressed in
watt-sec rather than in Joule etc
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1
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The following are the considerations for selection of fundamental quantities
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(ii) The measuring units shall he of a practical size
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1
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2
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3
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4
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5
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16 of the thermodynamic temperature of water at which point it is
simultaneously a gas, a liquid and a solid (the trip point)
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Quantity-mol, mol
It is defined as the amount of substance which contains as many elementary particles as there are
atoms in 0
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7
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The supplementary units used for two and three dimensional problem related to geometry are:
2

1
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Solid angle, Steradian Sr
Current is taken as the fundamental quantity
...
It is possible to
derive current from charge and vice versa
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Table 1: The basic units in the SI system are listed below with their symbols:
Quantity

SI base unit

Unit symbol

Length (l)
Mass (m)
Time (t)
Electric current (I)
Thermodynamic
temperature (T)
Luminous intensity (Iv)
Amount of substance (n)

Metre
kilogram
second
ampere
kelvin

m
kg
s
A
K

Symbol for
dimension
L
M
T
I
Ɵ

candela
mole

cd
mol

J
N

1
...
The six most common multiples, with their meaning, are listed below:
Table 2: Multiple or submultiple units

Symbol Name
M
mega multiply
by
1000000
(i
...
×106)
k
kilo
multiply
by
3
1000 (i
...
×10 )
m
milli divide by 1000
(i
...
×10−3)
μ
micro divide by 1 000
000 (i
...
×10−6)
n
nano divide
by
1000000000
(i
...
×10−9)
p
pico
divide
by
1000000000000
((i
...
×10−12)

3

1
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Two examples are:
Velocity – metres per second (m/s)
Acceleration – metres per second squared (m/s2)
Even though it is possible to function with the seven fundamental units mentioned above, yet if a
set of derived units are defined with special names, the resulting equations and calculations are
greatly simplified tables below
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— The unit of force [in the MKS (meter, kilogram, second) system] is the force
which gives to a mass of 1 kilogram an acceleration of 1 meter per second, per second
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— The joule is the work done when the point of application of 1
MKS unit of force [newton] moves a distance of 1 meter in the direction of the force
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— The watt is the power which in one second gives rise to energy of 1
joule
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The Comité International des Poids et Mesures (CIPM) accepts
the following propositions which define the theoretical value of the electric units:
Ampere (unit of electric current)
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Volt (unit of potential difference and of electromotive force)
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Ohm (unit of electric resistance)
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Coulomb (unit of quantity of electricity)
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Farad (unit of capacitance)
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Henry (unit of electric inductance)
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Weber (unit of magnetic flux)
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4

Table 3 Derived SI units (without special name)

Table 4: Derived SI units (with special names)

Table 5: Non-SI units (but acceptable)

5

Table 6: Summary of derived units
Unit

1
2
3
4
5
6
7
8
9
10
11
12
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14
15

Name

Quantity Unit
Symbol
symbol

Capacitance
Conductance
Inductance
Potential difference
Resistance
Energy
Force
Frequency
IL luminance
Luminance flux
Magnetic flux
Magnetic flux density
Power
Pressure/ stress
Quantity of electricity

farad
siemens
henry
volt
ohms
joule
Newton
herz
lux
lumen
weber
tesla
watts
pascal
coulumb

C
G
L
V,E
R
W
F
f
E
Φ
Φ
B
P
p
Q

F
S
H
V
Ω
J
N
Hz
lx
lm
Wb
T
W
Pa
C

Expression
in terms of
other units
C/V
A/V
Wb/A
W/A
V/A
N
...
m/s2
S-1
lm/m2
cd
...
s
Wb/m2
J/s
N/m2
A
...
4

Basic circuit relationships

1
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1 Charge and Current
The most basic quantity in an electric circuit is the electric charge
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24×1018 electrons)
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Thus, charge, in coulombs Q=It where I is the current in amperes and t is the time in seconds
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We also know that the
charge e on an electron is negative and equal in magnitude to 6
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The presence of equal numbers of protons and electrons leaves an atom neutrally charged
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The coulomb is a large unit for charges
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602𝑥10−19 =
6
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Thus realistic or laboratory values of charges are on the order of pC, nC, or
µC
...
According to experimental observations, the only charges that occur in nature are integral
multiples of the electronic charge e = - 1
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The law of conservation of charge states that charge can neither be created nor destroyed, only
transferred
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Electric current
Consider the flow of electric charges
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When a conducting wire (consisting of
several atoms) is connected to a battery (a source of
electromotive force), the charges are compelled to move; positive
charges move in one direction while negative charges move in Figure 1: Electric current due to
the opposite direction
...
It is conventional to take the current flow as the conductor
...
That is, opposite to the flow of
negative charges, as Fig
...
illustrates
...
Although we now know that current in
metallic conductors is due to negatively charged electrons, we will follow the universally
accepted convention that current is the net flow of positive charges
...
Or defined as
the time rate of flow of charge through a certain section
...

Yet another method of defining electric current (1 amp) is as the constant electric current in two
infinite parallel conductors separated from each other by 1 m, experience a force of 2 x 10-9 N/m
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An atom has positive charges
(protons) in its nucleus and an equal number of electrons (negative charges) surround the nucleus
making the atom neutral
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The basic unit of charge is the charge on an
electron e = 1
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Mathematically, the relationship between current i, charge q, and time t is
𝑑𝑞
𝑖 = 𝑑𝑡 ……………
...
(1)
...
(1) suggests that current need not be a constant-valued
function
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If the current does not change with time, but remains
constant, we call it a direct current (dc)
...
By convention the symbol I is used to
represent such a constant current
...
A
common form of time-varying current is the sinusoidal
current or alternating current (ac)
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Such current is used in your household, to run the air
conditioner, refrigerator, washing machine, and other
electric appliances
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Current
being
the Figure 2: (a) direct current (dc), (b)
alternating current (ac)
movement of charge, we
expect current to have an
associated direction of flow
...
Based on this convention, a current of 5 A
may be represented positively or negatively as shown in Fig
...
In
Figure 3: Convection current flow: (a)
other words, a negative current of -5 A flowing in one direction
positive current flow, (b) negative
as shown in Fig
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the opposite direction
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4
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However,
its form can be converted i
...
, energy can be converted from one form of energy to another e
...

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Electromechanical energy conversion, Electro-chemical energy conversion, photoelectric energy
conversion etc
...
e
...
The movement of charges contribute to current and the amount
of work done per unit charge is the potential difference between the two points
...

Basically to move the electron in a conductor in a particular direction requires some work or
energy transfer
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1
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The voltage between
two points a and b in an electric circuit is the energy (or work) needed to move a unit charge
from a to b; mathematically,
𝑑𝑤
𝑉𝑎𝑏 = 𝑑𝑞 ………
...
The voltage or simply v
is measured in volts (V), i
...

Figure 4 shows the voltage across an element (represented by a
rectangular block) connected to points a and b
...
The vab can
be interpreted in two ways: (1) point a is at a potential of vab volts higher
than point b, or (2) the potential at point a with respect to point b is Vab
...
(4)
For example, in Fig
...

Figure 4: Polarity of
In Fig
...
5(b), point b is V above voltage Vab
...
We may say that in Fig
...
In other words,
a voltage drop from a to b is equivalent to a voltage rise from b to
a
...

The common term signal is used for an electric quantity such as a
current or a voltage (or even electromagnetic wave) when it is used
for conveying information
...
Like electric
current, a constant voltage is called a dc voltage and is represented
Figure 5: Two equivalent
representations of the same
by V, whereas a sinusoidally time-varying voltage is called an ac
voltage Vab: point a is 9 V above
voltage and is represented by v
...


9

NB
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Example 1
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
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5 𝐶

1
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3 Power and Energy
Although current and voltage are the two basic variables in an electric circuit, they are not
sufficient by themselves
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We all know from experience that a 100-watt bulb gives more light than a 60watt bulb
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Thus, power and energy
calculations are important in circuit analysis
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𝑑𝑤
We write this relationship as power, 𝑝 = 𝑑𝑡 …………………
...
From Eqs
...
(6)
or

𝑝 = 𝑣𝑖 ………………………………
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(7) is a time-varying quantity and is called the instantaneous power
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If the power has a + sign, power is being delivered to or absorbed by the element
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But how do we know when the power has a negative
or a positive sign?
Current direction and voltage polarity play a major role in
determining the sign of power
...
6(a)
...
6(a) in order for the power to
have a positive sign
...

By the passive sign convention, current enters through the
positive polarity of the voltage
...
However, if p = -vi
or vi < 0, as in Fig
...

Passive sign convention is satisfied when the current enters through the positive terminal of
an element and p = + vi
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For this reason,
the algebraic sum of power in a circuit, at any instant of time, must be zero:
∑ 𝒑 = 𝟎 …………………
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From Eq
...
(9)
Energy is the capacity to do work, measured in joules (J)
...
If 2
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Example 3

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1
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An electric circuit is simply an
interconnection of the elements
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There are two types of elements found in electric circuits: passive elements and active elements
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Examples of
passive elements are resistors, capacitors, and inductors
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Active elements
...
There are two kinds of sources: independent and dependent
sources
...
i
...
Delivers to the circuit whatever current is
necessary to maintain its terminal voltage
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Figure 7 shows the
symbols for independent voltage sources
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7
...
7
...

An ideal independent current source is an active element that
provides a specified current completely independent of the voltage
across the source
...
The
symbol for an independent current source is displayed in Fig
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An ideal dependent (or controlled) source is an active element in which the source quantity is
controlled by another voltage or current
...
9
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A voltage-controlled voltage source (VCVS)
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A current-controlled voltage source (CCVS)
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A voltage-controlled current source (VCCS)
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A current-controlled current source (CCCS)
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6
Applications
Electricity Bills
The second application deals with how an electric utility company charges their customers
...
(Other factors that affect the cost
include demand and power factors; we will
ignore these for now
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As energy consumption increases, the
cost per kWh drops
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Example
A homeowner consumes 600 kWh in January
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00
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Next 200 kWh per month at 10 cents/kWh
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