M2
Electric Circuit
1
LECTURE 7
INTRODUCTION TO ELECTRIC CIRCUIT
Outline
2
 Introduction
 Circuit elements
 Circuit terminologies
 Basic laws
 Time response
 Responses: sinusoidal vs. non-sinusoidal excitations
 Complex impedance and frequency response
 Phasors and AC powers
 Three-phase systems
1
Electricity: How they work?
3
Electric Circuit
4
• The battery, places a
net positive charge at
one terminal and a net
negative charge on the
other
• The free electrons
(of negative charge)
will drift toward the
positive terminal
• The negative terminal
is a “supply” of
electrons
R.L. Boylestad, Introductory Circuit Analysis, 11th Ed, Prentice Hall
2
Circuit Elements
Active Elements
Independent
sources
Passive Elements
5
• A dependent
p
source is an active
element in which the source quantity
is controlled by another voltage or
current.
• There are four different types: VCVS,
CCVS, VCCS, CCCS
Dependent
sources
C.K. Alexander and M.N.O. Sadiku, Fundamentals of Electric Circuits, 5th edition, McGraw Hill
A Voltage Source
6
R.L. Boylestad, Introductory Circuit Analysis, 11th Ed, Prentice Hall
3
A Current Source
7
http://www.olympusmicro.com/primer/java/solarcell/
A Power Supply
8
http://www.glentestco.com/product/product_pwrsupply01.htm
4
Resistors
9
http://www.macnn.com/articles/12/05/24/well.designed.adapter.protects.phone.from.damage.malfunction/
http://www.resistorguide.com/metal-film-resistor/
http://www.colourbox.com/image/the-printed-circuit-board-with-computer-chips-resistors-and-condensers-image-2350532
Inductors & Capacitors
10
http://www.splung.com/content/sid/3/page/capacitors
http://www.area51esg.com/inductors-coils-chokes.html
A.H. Robbins, W.C. Miller, Circuit Analysis with Devices: Theory and Practice, 3rd edition, Cengage Learning
5
Circuit Terminologies
11
• A branch represents a single element such as a voltage
source or a resistor
• A node is the point of connection between two or more
branches
• A loop is a closed path (same beginning and end nodes)
with no node passed more than once
• A mesh is a loop which does not contain any other loops
within it
C.K. Alexander and M.N.O. Sadiku, Fundamentals of Electric Circuits, 5th edition, McGraw Hill
The Almighty Laws: Ohm’s Law
12
• George Simon Ohm
• Ge
German
a (Erlangen,
( a ge , Co
Cologne)
og e) ((1789–1854)
789 854)
• Physicist and Mathematician
• Professor of Physics,
• University of Cologne
http://www-history.mcs.st-and.ac.uk/
Mathematicians/Ohm.html
• v-i relationship of a resistor
Note: the negative current and
voltage result in the graph extended
in the 3rd quadrant
C.K. Alexander and M.N.O. Sadiku, Fundamentals of Electric Circuits, 5th edition, McGraw Hill
6
Kirchhoff’s Laws: KCL
13
• Kirchhoff’s current law
http://www.biografiasy
vidas.com/biografia/k/
kirchhoff.htm
• German (Königsberg,
(Königsberg
Berlin) (1824-87)
• Physicist
• Professor of Physics,
• University of
Heidelberg
R.L. Boylestad, Introductory Circuit Analysis, 11th Ed, Prentice Hall
Kirchhoff’s Laws: KVL
14
Kirchhoff’s voltage law (KVL): the algebraic sum of the
potential rises and drops
p
p around a closed loop
p (or
path) is zero.
These laws will be important bases of circuit theorems
and analysis techniques
R.L. Boylestad, Introductory Circuit Analysis, 11th Ed, Prentice Hall
7
Time Response: Resistor
15
There is no limitation on the rate
of change imposed on the
resistor voltage and current
Purely resistive circuit
A.H. Robbins, W.C. Miller, Circuit Analysis with Devices: Theory and Practice, 3rd edition, Cengage Learning
Time Response: R-L
16
A.H. Robbins, W.C. Miller, Circuit Analysis with Devices: Theory and Practice, 3rd edition, Cengage Learning
8
An Inductor and a Fluorescent Lamp
17
http://www.youtube.com/watch?v=z55566ep0Hg
Breaking an Inductive Circuit
18
When the inductor current is interrupted the
field begins to collapse causing a large induced
voltage across the coil.
A.H. Robbins, W.C. Miller, Circuit Analysis with Devices: Theory and Practice, 3rd edition, Cengage Learning
9
Breaking an Inductive Circuit
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http://www.youtube.com/watch?v=INbS-71KSz0
Charging a Capacitor
20
http://www.youtube.com/watch?v=IvFVu7Jxa2I
10
Discharging a Capacitor
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http://www.youtube.com/watch?v=5D2cLj28Pc8
Time Response: RC
22
A.H. Robbins, W.C. Miller, Circuit Analysis with Devices: Theory and Practice, 3rd edition, Cengage Learning
11
Time Response: RC
23
A.H. Robbins, W.C. Miller, Circuit Analysis with Devices: Theory and Practice, 3rd edition, Cengage Learning
A Sinusoidal Waveform
24
R.L. Boylestad, Introductory Circuit Analysis, 11th Ed, Prentice Hall
12
Periodic Functions
25
Squarewave signal
Sawtooth signal
Full-wave signal
Triangular signal
R.L. Boylestad, Introductory Circuit Analysis, 11th Ed, Prentice Hall
https://www.projectrhea.org/rhea/index.php/HW1.4_Ben_Laskowski_-_Periodic_and_Non-Periodic_Functions_ECE301Fall2008mboutin
Fourier Series
26
http://www2.math.umd.
edu/~dlevy/photos2/ph
otos/mathematical_line
age/jeanbaptiste_fourier.html
French (Auxerre, Grenoble, Paris) (1768–1830)
Mathematician, Egyptologist, and Administrator
y
q
Professor of Mathematics,, École Polytechnique
R.L. Boylestad, Introductory Circuit Analysis, 11th Ed, Prentice Hall
13
27
R.L. Boylestad, Introductory Circuit Analysis, 11th Ed, Prentice Hall
Phasor
28
A phasor is a rotating line whose projection on a vertical
axis can be used torepresent sinusoidally varying quantities
A.H. Robbins, W.C. Miller, Circuit Analysis with Devices: Theory and Practice, 3rd edition, Cengage Learning
14
Phasor Illustration
29
http://www.ceb.cam.ac.uk/pages/impedance-analysis-basics.html
A.H. Robbins, W.C. Miller, Circuit Analysis with Devices: Theory and Practice, 3rd edition, Cengage Learning
Resistance and Sinusoidal Excitation
• Response in time domain
30
• Phasor (frequency) domain
A.H. Robbins, W.C. Miller, Circuit Analysis with Devices: Theory and Practice, 3rd edition, Cengage Learning
15
Inductance and Sinusoidal Excitation
• Response in time domain
31
• Phasor domain
A.H. Robbins, W.C. Miller, Circuit Analysis with Devices: Theory and Practice, 3rd edition, Cengage Learning
Capacitance and Sinusoidal Excitation
• Response in time domain
32
• Phasor domain
A.H. Robbins, W.C. Miller, Circuit Analysis with Devices: Theory and Practice, 3rd edition, Cengage Learning
16
Resonance
33
Resonant condition
R.L. Boylestad, Introductory Circuit Analysis, 11th Ed, Prentice Hall
Resonance
34
Practical implication: Capacitor and inductor voltages can be much
larger than the supplied voltage
R.L. Boylestad, Introductory Circuit Analysis, 11th Ed, Prentice Hall
17
An Application of a Resonant Circuit
35
• Induction heating
f = 15 kHz
R.L. Boylestad, Introductory Circuit Analysis, 11th Ed, Prentice Hall
One-Port vs. Two-Port Networks
36
Two-port network One-port network
R.L. Boylestad, Introductory Circuit Analysis, 11th Ed, Prentice Hall
18
37
Power
38
• Instantaneous power
A.H. Robbins, W.C. Miller, Circuit Analysis with Devices: Theory and Practice, 3rd edition, Cengage Learning
19
Power
39
• Inductor
• Observation
1) Average power is zero
2) The power alternately flows into and out of the inductor
(also known as reactive power: Q)
A.H. Robbins, W.C. Miller, Circuit Analysis with Devices: Theory and Practice, 3rd edition, Cengage Learning
Power
40
• Capacitor
• Observation (similar to the inductor)
1) Average power is zero
2) The power alternately flows into and out of the inductor
(also known as reactive power: Q)
A.H. Robbins, W.C. Miller, Circuit Analysis with Devices: Theory and Practice, 3rd edition, Cengage Learning
20
Complex Power
41
S  V I  V I  θ v  θ i
 S  V I cos (θ v  θ i )  j V I sin (θ v  θ i )
S = P
+ j Q
• Power triangle
C.K. Alexander and M.N.O. Sadiku, Fundamentals of Electric Circuits, 5th edition, McGraw Hill
Why Rated VA?
42
• Using only active power
• Reactive power is in the
picture
A.H. Robbins, W.C. Miller, Circuit Analysis with Devices: Theory and Practice, 3rd edition, Cengage Learning
21
Three-Phase Systems
43
http://www.ece.umn.edu/users/riaz/animations/alternator.html
Three-Phase System
44
Wye connection
Delta connection
R.L. Boylestad, Introductory Circuit Analysis, 11th Ed, Prentice Hall
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