Introduction
ELEC 308
Elements of Electrical Engineering
Dr. Ron Hayne
Images Courtesy of Allan Hambley and Prentice-Hall
Admin
 Course materials available online
 http://ece.citadel.edu/hayne/

Students are encouraged to print lecture slides in
advance and use them to take notes in class
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Electrical Engineering
 Two main objectives:
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To gather, store, process, transport, and present
INFORMATION
To distribute, store, and convert ENERGY between
various forms
 Subdivisions:
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Communication systems
Computer systems
Control systems
Electromagnetics
Electronics
Photonics
Power systems
Signal processing
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Why Electrical Engineering?
 Why You Need to Study Electrical Engineering
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FE Exam
Broad knowledge base
Technological advances in CEE tools
Communication with ECE consultants
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Electrical Circuits
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Fluid Flow Analogy
Electrical Circuits
Fluid Flow
Battery
Pump
Charge
Fluid
Conductors (no resistance)
Pipes (frictionless)
Current
Flow rate
Voltage
Pressure differential
Switches
Valves
Resistance
Constriction in pipe (turbulence, heat)
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Electrical Circuits
 Electrical Circuit
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 Voltage Sources
Various types of circuit
elements connected in closed
paths by conductors
 Circuit elements
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Resistances, inductances,
capacitances, voltage
sources, etc.
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Induce flow of electrons
(charge) through conductors
and other circuit elements
Energy is transferred
between circuit elements,
resulting in a useful function
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Electrical Circuit Analysis
 Steps
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Model physical components mathematically
Voltage or current sources
 Resistors, inductors, capacitors,
 Diodes, transistors, transformers, electric motors
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Determine system of equations for unknown
element characteristics
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Solve using linear algebra methods
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Electrical Current
 Time rate of flow of electrical charge
through a conductor or circuit element
 Units are amperes (A)
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1 A = 1 coulombs per second (C/s)
One electron has charge -1.602×10-19 C
 Net charge flowing through cross section as a
function of time is q(t)
 Electrical current flowing cross section is i(t)
and is given by
dq(t)
i(t) 
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dt
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Current - Reference Directions
 Arbitrarily assign a reference direction
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May not be ACTUAL direction of current flow
Positive current flow: Reference matches Actual
Negative current flow: Reference opposite Actual
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DC vs. AC
 Current constant with time
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Direct current, or DC
 Current varies with time
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Alternating current, or AC
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Voltage
 Energy transferred as charges moves through
circuit element
 Units are volts (V)
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1 V = 1 joule per coulomb (J/C)
 Voltage is measured ACROSS a circuit
element
 Current is measured THROUGH a circuit
element
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Voltage Polarities
 Assign polarities to indicate the direction of
energy flow
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Voltage – Reference Polarities
 Arbitrarily assign a reference polarity
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May not be ACTUAL voltage polarity
Positive voltage: Reference matches Actual
Negative voltage: Reference opposite Actual
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DC vs. AC
 Voltage constant with time
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Direct current, or DC
Example: v1(t) = 10 V
 Voltage varies with time
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Alternating current, or AC
Example: v2(t) = 10sin(200πt)
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Electrical Power
 Power is energy per unit time
 Consider the units of the product of voltage
and current:
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volts × amperes = (J/C) × (C/s) = J/s = watts = W
 The rate of energy transfer IN to or OUT of a
circuit element can be calculated from the
current and voltage
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p = vi
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Passive Reference Configuration
 Positive Power
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Energy being absorbed by
the circuit element
Current enters the positive
polarity of the voltage
 Negative Power
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Energy being supplied by
the circuit element
Current enters the negative
polarity of the voltage
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Energy
 To calculate the energy delivered to or from
a circuit element over a specific interval of
time, we must know the power over that
interval:
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Power = J/s
Must integrate power over time interval:
t2
w   p t dt
t1
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Energy has units joules (J)
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Node
 Point at which 2 or more circuit elements are
joined together
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Kirchhoff’s Current Law (KCL)
 KCL: The net current
entering a node is zero.
 Also, the net current
leaving a node is zero.
 In other words, the total
amount of current
ENTERING a node must
equal the total amount of
current LEAVING a
node.
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Understanding KCL
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KCL Examples
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Series Circuit Elements
 When elements are
connected end to end,
they are connected in
SERIES
 All circuit elements
have IDENTICAL
Currents
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Series Circuit Elements
 Identify the groups of circuit elements that
are connected in series
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Kirchhoff’s Voltage Law (KVL)
 KVL: The algebraic
sum of the voltages
equals zero for any
closed path (loop) in an
electrical circuit.
 To add voltages
algebraically,
we must be consistent:
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Understanding KVL
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KVL: Conservation of Energy
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Parallel Circuit Elements
 When both ends of one element are
connected to corresponding ends of another,
they are connected in PARALLEL
 All circuit elements have IDENTICAL
Voltages
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Parallel Circuit Elements
 Identify the groups of circuit elements that
are connected in parallel
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Basic Circuit Elements
 Conductors
 Voltage sources
 Current sources
 Resistors
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Conductors
 Ideal conductors
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Represented by unbroken lines between ends of other
circuit elements
Voltage between ends of an ideal conductor is zero,
REGARDLESS of the current
All points connected by ideal connector can be
considered a single NODE
Two points in circuit connected by ideal conductor are
SHORTED together (SHORT Circuit)
No conductor or other elements connected between two
parts of a circuit is an OPEN Circuit

How much current flows through an OPEN Circuit?
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Voltage Sources
 Ideal Independent Voltage Source
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Maintains a specified voltage across its terminals,
independent of other circuit elements
Good DC example is a battery
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Ideal vs. Reality
 What’s the conflict here?
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Current Sources
 Ideal Independent Current Source
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Maintains a specified current through itself,
independent of other circuit elements
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Ideal Resistors
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Ohm’s Law
 Voltage, v, across a
resistor with resistance,
R, is proportional to the
current, I, through the
resistor
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v = iR
 Units of resistance are
V/A, or ohms (Ω)
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Resistors
 Can be constructed of may different types of
conductive materials
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Physical Resistance Parameters
 Consider resistors that contain conductive
material in a form that has uniform crosssectional area, A
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Resistance is approximately R = ρL/A
 where ρ is the RESISTIVITY of the material.
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Classification of Materials
 Conductors
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Lowest resistivity
Easily conduct electrical current
 Insulators
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High resistivity
Conduct very little electrical current
 Semiconductors
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Somewhere in between
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Resistance Power Calculations
 Remember p = vi and Ohm’s Law, v = iR
 Substituting these two equations, we can get:
p = Ri2 = v2/R
 Notice that power is ALWAYS positive for
resistances
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Thus power is ALWAYS supplied or absorbed
for resistances??
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Resistors vs. Resistances
 Resistance
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Describes a circuit property for which voltage is
proportional to current
For example:
Many speakers have resistances of 4Ω or 8Ω
 Many antennas have resistances of 50Ω
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 Resistor
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Two-terminal device composed of a conductive
material
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Summary
 Electrical Parameters
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Current
Voltage
Power
Energy
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 Tools
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 Electrical Circuits
Series
Parallel
Short Circuit
Open Circuit
 Circuit Elements
KCL
KVL
Ohm’s Law
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Voltage Sources
Current Sources
Resistors
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