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Electrical Engineering
Principles & Applications

Chapter 1- Introduction

Slide 1

Electrical Engineering Subdivisions
• Communication systems
– Cellular, radio, satellite,
Internet

• Computer systems
– Process & store information
in digital form

• Control systems
– Gather information with
sensors and use electrical
energy to control a physical
process

• Electromagnetics
– Study and applications of
electric and magnetic fields

• Electronics
– Study and applications of
materials, devices, and
circuits in amplifying and
switching electrical
signals

• Photonics
– Controlling photons
rather than electrons

• Power systems
– Convert energy to and
from electrical form and
transmit energy

• Signal Processing
– Extract info from
electrical signals
Slide 2

Why Study Electrical Engineering?
• To pass the Fundamentals of Engineering (FE)
Examination
• So you can lead projects in your own field
• To be able to operate and maintain electrical systems
• To communicate with electrical engineering consultants
More importantly
To meet the course requirements for your degree ☺
Slide 3

Objectives
Electrical circuits are the basis of all branches of electrical
engineering

Electrical systems have two main objectives:
• To gather, store, process, transport, and present
information
• To distribute and convert energy between various
forms

We will
1
...
Solve for currents, voltages, and powers in simple circuits
3
...
Calculate power and energy and determine whether energy
is supplied or absorbed by a circuit element
Slide 4

Example: Headlight circuit

Slide 5

Electric Circuit
• Connection of several circuit elements in closed
paths by conductors

Slide 6

Electrical Current
• Electrical current:
– Flow of electrons through a wire or other
electrical conductor
• Electrons are negatively charged particles

– The time rate of flow of electrical charge through
a conductor or circuit element
– The units are amperes (A), which are equivalent to
coulombs per second (C/s)

• The charge per electron is -1
...
01sin(200t) C
Find the current as a function of time
Slide 8

Some Definitions
• A Circuit:
– Typically consists of a power source, connecting wires or
conductors, and a device that uses the electrical energy
– The device that uses the energy is called the load
– For current to flow in an electric circuit, there must be a
complete path from the negative terminal of the power
source, through the connecting wires and load, back to the
positive terminal of the source
– If a complete path does not exist, no current will flow, and
the circuit is called an open circuit

• A Bus:
– An electrical conductor that serves as a common connection
for two or more electrical circuits
– A path where electricity follows
Slide 9

Direct Current (DC) & Alternating Current (AC)

When current is constant with time, we say
that we have direct current, abbreviated
as DC
...
time


...
The units of
voltage are volts (V), which are equivalent to
joules per coulomb (J/C)

Slide 12

Voltage Polarity Indicates Direction of
Energy Flow

Positive charge

a circuit element

Energy absorbed by element appears as heat, mechanical
energy, stored chemical energy, etc
Slide 13

Reference Directions
• Initial directions may be not known in advance
– Start by assigning current variables
– Arbitrarily select a reference direction for each current
– After solving for the currents, we may find currents with
negative values
actual current is opposite to assumed
direction

i2 = 1A

Slide 14

i3 = -3A

Double-Subscript Notation for Currents

iab = -iba

Slide 15

Reference Polarities
• Initial polarities for voltage may not be known in advance
• Start by assigning voltage variables
• Arbitrarily select a reference polarity for each voltage
• After solving for the voltages, we may find voltages
with negative values
actual polarity is opposite to
assumed polarity

Slide 16

Double-Subscript Notation for Voltages

vab = -vba

Slide 17

Power & Energy
Recall that:
Current is the rate of flow of charge and voltage is the
energy transferred per unit of charge
current × voltage is the rate of energy transfer which
is called power

p (t ) = v (t )i(t )
t

w =

2

∫

p ( t ) dt

t1

Volts × Ampere = (joules/coulomb) × (coulombs/second)
= joules/second
= watts
Slide 18

Passive Reference Configuration
Does the power p = vi represent energy supplied or
absorbed by the element?
In the figure on the right, current enters the
positive polarity of voltage
called passive
reference configuration
+ve power

energy absorbed by element

-ve power

energy supplied by element

Slide 19

Example: Power Calculations

(a)
P = 12 x 2 = 24 W
Absorbed by element
Slide 20

(b)
P = 12 x (-1) = -12 W
Supplied by element

(c)
P = 12 x (-3) = -36 W
Supplied by element

Example: Energy Calculations
Given that

v(t ) = 12V and i (t ) = 2e − t A
Find the power and compute the energy from t1 = 0 to t2 = ∞
Solution:

−t

p (t ) = v (t )i (t ) = 24 e W
∞

∞

0

0

−t

energy = ∫ p(t )dt = ∫ 24e dt
= [−24e−t ]∞ = −24e−∞ − (−24e0 ) = 24J
0
Positive energy
Slide 21

absorbed by element

Prefixes
Prefix

Scale Factor

tera-

T

1012

giga-

G

109

meg- or mega-

M

106

kilo-

k

103

milli-

m

10-3

micro-

µ

10-6

nano-

n

10-9

pico-

p

10-12

femtoSlide 22

Abbreviation

f

10-15

Kirchhoff’s Current Law (KCL)
• A node is a point at which two or more circuit
elements are joined together
• KCL: The net current entering a node is zero
• Alternatively, the sum of the currents entering a
node equals the sum of the currents leaving a node

Slide 23

Kirchhoff’s Current Law (KCL)
i1 + i2 − i3 = 0

i1

i3

i2
i3

− i3 + i4 = 0

Slide 24

i4

Series Circuits
• Two elements are connected in series if there is no
other element connected to the node joining them
• The elements have the same current going through
them

Slide 25

Examples
Example:
Use KCL to determine the values of the unknown currents

Example:
Identify the groups of elements connected in series

Slide 26

Kirchhoff’s Voltage Law (KVL)
• A loop is a closed path around a circuit starting at a node
and eventually returning to the starting node
• KVL: The algebraic sum of the voltages equals zero for any
closed path (loop) in an electrical circuit

Slide 27

Example
Write KVL for the loops identified in the circuit below

Loop1 : −va + vb + vc = 0
Loop2 : −vc − vd + ve = 0
Loop3 : va − ve + vd − vb = 0
Slide 28

Parallel Circuits
• Two elements are connected in parallel if both ends of
one element are connected directly to corresponding
ends of the other

The voltage across parallel elements are equal (both magnitude and
polarity)

Slide 29

Exercise
Use KVL to find vc and ve

Slide 30

Circuit Elements
•
•
•
•

Conductors
Voltage Sources
Current Sources
Resistors

Slide 31

Conductors
• An ideal conductor has no voltage drop across the
ends
• Represented by unbroken lines between ends of other
circuit elements
• Two points are shorted when they are connected by
an ideal conductor
• All points in a circuit connected by ideal conductors
are considered as a single node

Slide 32

Independent Voltage Sources
• Maintains a specified voltage across its terminals
independent of other elements on the circuit and of
the current flowing through it

v
12V

i

Slide 33

Independent Voltage Sources

vx = 0 due to short circuit
but vx = 12 due to supply!

Caution: Don’t short circuit a battery or a supply since a
large current will pass in a short period of time
Too much heat: burn the conductors and destroy the
battery or supply
Slide 34

Dependent (Controlled) Voltage Sources

•

Very useful in constructing circuit models for real-world devices such as
transistors and amplifiers
For a voltage controlled source: V = K1vx , K1 is a gain parameter with no units
For a current controlled source: V = K2ix, K2 is a gain parameter with units
[V/A]
Slide 35

Independent Current Sources
• Forces a specific current to flow through
itself independent of the elements connected
to it and of the voltage across it

v

2A

Slide 36

i

Dependent (Controlled) Current Sources

•

Very useful in constructing circuit models for real-world devices such
as transistors and amplifiers
For a voltage controlled source: I = K3vx, K3 is a gain parameter with units
[A/V]

For a current controlled source: I = K4ix, K4 is a gain parameter with no units
Slide 37

Resistors
A resistor is a passive element characterized by an algebraic relation
between the voltage across its terminals and the current through it

+ v(t ) −

Standard Multiples of Ohm
MΩ
kΩ

i (t )

Mega Ohm (10 6 Ω)
Kilo Ohm (103 Ω)

A linear resistor obeys Ohm’s Law

v(t ) = R i (t )
The constant, R, is called the resistance of the component and is
measured in units of Ohm (Ω)
From a dimensional point of view, Ohms is a derived unit of Volt/Amp
Slide 38

Resistors
+ v(t ) −
i (t )
Conductance
Instead of expressing voltage as a function of current one can
express current in terms of voltage
...

i
+
v

Two special resistor values
Notice passive sign
convention

R

−

+
v=0

Circuit Represent ation
Circuit Representation
i

−
Short

“A touch of
reality”

Circuit
R=0
G=∞

i=0

Open
Circuit
R=∞
G=0

Linear approximation

v

Linear range
Actual v-I relationship
Slide 41

Ohm’s Law is a valid approximation
when voltages and currents remain
in the Linear Range

Ohm’s Law Problem Solving Tip

v = Ri

i = Gv OHM' s Law

One equation and three variables
...

Combining Ohm’s law and the
expressions for power we can derive
several useful expressions

P = vi

(Power)

v = Ri , or i = Gv (Ohm' s Law)

Given v, R

Given P , i
v=

P
v
,R =
i
i

Given

i, R

v = Ri , P = vi = Ri 2

i=

2

v
v
, P = vi =
R
R

A matter of units
Working with the units Volt, Ampere
Watt, Ohm, there is never a problem
...


EXAMPLE : R = 40 kΩ, i = 2mA
The basic strategy is to express
all given variables in SI units

v = (40 *103 Ω) * (2 *10 −3 A) = 80[V ]
P = Ri 2 = (40 *103 Ω) * (2 *10 −3 A) 2 =

Given P, R
P
i=
, v = Ri = PR
R

If not given, the reference direction for voltage or current
can be chosen and the other is given by the passive sign
convention
Slide 45

160 *10 −3 [W ]

Using KVL, KCL, and Ohm’s Law to Solve a
Circuit Problem
Example:
Find the source voltage in the following circuit

Slide 46

Example (cont
...
5ix = i y
ix = 2 A
Slide 47

v x = 10ix = 20 V
Vs = v x + 15

Vs = 35 V

Another Example
Find Vx

Slide 48

Circuit Elements
Passive Elements
Voltage
dependent
sources

Absorb energy (may store)
Independent Sources

Current
dependent
sources

Slide 49

Supply energy

How Many KCL or KVL Equations are Needed?
In the circuit define
N

Number of nodes

B

Number of branches

N −1

Linearly Independent
KCL Equations

B − ( N − 1) Linearly Independent
KVL Equations

EXAMPLE:
For the circuit shown we have
N = 6, B = 7
...


•

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