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1
ELEC130 Electrical Engineering 1
Week 2Module 1 Introductory Circuit Techniques
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23-Feb-99 Lecture 2 2
Software
Electronic Workbench: Simulation Software Faculty PC’s Rm. ES210 - Go to Diomedes Login: cstudentnumber Password: access keys on students card + daymonth (ddmm)
of birth
TopClass: Class Discussion & Notices
http://www.newcastle.edu.au:86/topclass/ Username: first name.last name Password: date of birth ddmmyy
Email: first name.last name@studentmail
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23-Feb-99 Lecture 2 3
Administration Items
Laboratory & Tutorials start THIS WEEK A couple of corrections have been given to the Tutors
and Laboratory demonstrators
Quiz 1 - Week 3 - Lecture NEXT MONDAY Will cover to the end of Module 1 which will be
completed next lecture before the quiz.
Survey
Subject Home Page: - through Dept. Pages http://www.ee.newcastle.edu.au/ http://www.ee.newcastle.edu.au/undergradcourse.html
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23-Feb-99 Lecture 2 4
Last week
Charge Symbol: Q q(t) Units: Coulombs or C
Current Symbol: I i(t) Units: Amperes or A
Voltage Symbol: V v(t) Units: Volts or V
Power Symbol: P p(t) Units: Watts or W
Resistance Symbol: R Units: Ohms or
(I = Q / t Amps & V = P.t / Q volts)
P = V . I WattsV = R . I Ohms
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23-Feb-99 Lecture 2 5
Conventions
Current - positive charge flow - through element
Voltage - measured across an element
Power
3 A - 3 A=
+
_
I
Circuit or element
+
-
+
v(t)_
I
Absorbing power
Delivering power
I
v(t)
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23-Feb-99 Lecture 2 6
Resistance
Material - resistivity R = .l / A Poor conductor is large e.g. plastics, wood Good conductors is small e.g. copper, gold, aluminium
Resistance - the most common materials used are: carbon composition nickel chromium wire wound (for high power applications)
Can be physically small (10mm long) or large (>1m), can be fixed or variable
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23-Feb-99 Lecture 2 7
Resistance
Common - are small fixed with colour coded values:
Black 0 Green 5 Brown 1%Brown 1 Blue 6 Red 2%Red 2 violet 7 Gold 5%Orange 3 Grey 8 Silver 10%Yellow 4 White 9 Nil 20%
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23-Feb-99 Lecture 2 8
Resistance
Charge tends to flow from a higher voltage (potential) to a lower voltage
Determine direction of the current. If not labelled - GUESS the direction.
Potential of resistor where the current enters is positive and leaves is negative.
(If guess is wrong - just get negative voltage for an answer)
4 V 10
I
+
_
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23-Feb-99 Lecture 2 9
Conductance
Sometimes easier to use inverse of resistance called conductance
Symbol: G Units: Siemens S (mhos)
G = R-1
e.g. 2 = 0.5 S
NB: Useful when resistors are connected in parallel
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23-Feb-99 Lecture 2 10
Some Analogies
Charge Volume (of gas)
Voltage Pressure
Current Flow Rate
Resistance Constriction
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23-Feb-99 Lecture 2 11
Series and Parallel Elements
Series elements have the same current
Share voltage
Parallel elements have the same voltage
Share current
ia(t)
ic(t)
ib(t)i(t)
+ v(t) -
i(t)
+ va(t) - + vb(t) - + vc(t) -
+ v(t) -
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23-Feb-99 Lecture 2 12
Kirchoff’s Voltage Law
The sum of the voltages around a closed path is zero:
(closed path) V = 0
Convention is to move around a closed loop in a clockwise direction
Analogy - Walk around campus
How do you specify the polarity of voltages in the circuit?
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23-Feb-99 Lecture 2 13
Kirchoffs Voltage Law - example
+
-
IR1
R2
V1
+
_
V2
+
_
Vs
021 sVVV
Example: If Vs = 12 V and R1= R2 , then V1 = V2
= 6 V
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23-Feb-99 Lecture 2 14
Series Resistance
Vs = V1 + V2 + …….+ Vn where e.g. V1 = R1 I by
Ohm’s Law
Vs = R1 I + R2 I + …….+ Rn I
Vs = (R1 + R2 + …….+ Rn)I
Thus Req = R1 + R2 + …….+ Rn
I
+ -Vs
+ Vn -
Rn
+ V2 -
R2
+ V1 -
R1
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23-Feb-99 Lecture 2 15
Lecture Exercise
I
VX
+
-
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23-Feb-99 Lecture 2 16
Kirchoff’s Current Law
Total charge (current) accumulating at a node is zero:
(entering) I - (leaving) I = 0
Convention is current entering a node is positive and leaving a node is negative
Analogy - road intersection
How do you specify the direction of current if it is not given?
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23-Feb-99 Lecture 2 17
Kirchoff’s Current Law - example
I1 + I3 - I2 = 0
nodeI1 I2
I3
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23-Feb-99 Lecture 2 18
Parallel resistance
Is = I1 + I2 + …..+ In
[ I = V. 1/R = V G ]
Is = VG1 + VG2 +... + VGn
Is = V (G1 + G2 +... + Gn)
Is = V Geq
Geq = G1 + G2 +... + Gn
1/Req = 1/R1+ 1/R2+...+ 1/Rn
Is R2R1
+
V
_
Rn
I1 I2 In
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23-Feb-99 Lecture 2 19
Two Parallel Resistors
1/Req = 1/R1 + 1/R2
= (R1 + R2)/ R1.R2
Req = R1.R2 / (R1 + R2)
Vs R2R1
I1 I2
+
-
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23-Feb-99 Lecture 2 20
Current Division
NB: more current flows through path of lesser resistance
R2R1
I1 I2
+
-Vs
+
_
ss
ss
ss
IRR
RI
GG
GI
GGG
IGVI
GG
IV
21
2
21
11
121
11
21
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23-Feb-99 Lecture 2 21
Voltage Division
Vs
+
-
IR1
R2
V1
+
_
V2
+
_
s
s
s
VRR
RV
VRR
RIRV
RR
VI
2!
22
2!
111
2!
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23-Feb-99 Lecture 2 22
Series Sources
Ideal independent voltage sources in series add algebraically
NB cases of parallel voltage sources are not resolvable. WHY?
+ - + - + - + -I V1 V2 V3
Vn
- VR +
RI
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23-Feb-99 Lecture 2 23
Parallel Sources
Ideal independent current sources in parallel add algebraically
NB cases of series current sources are not resolvable. WHY?
In
I3I2I1
R
+
V
_
IT
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23-Feb-99 Lecture 2 24
Example
R2 and R3 are effectively open circuited and therefore can be omitted
R7 and R8 are short circuited, and can be omitted
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23-Feb-99 Lecture 2 25
Example continues
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23-Feb-99 Lecture 2 26
Wye Delta Transformations
Need to find equivalent resistance to determine current. HOW?(They are not in series, not in parallel)
Use Y to transformation
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23-Feb-99 Lecture 2 27
Equating Resistance's
Resistance between X - Y
In Ra // (Rb + Rc)
In Y R1 + R3
RbRa
Rc
R1 R2
R3
XX
Y
Y
Z
Z
31)(
)(RR
RRR
RRRR
cba
cbaXY
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23-Feb-99 Lecture 2 28
Solving simultaneously ….
To obtain R1, R2, R3 in terms of Ra, Rb, Rc
and vice versa
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23-Feb-99 Lecture 2 29
Example cont.
X
Y Z
Y
X Z
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23-Feb-99 Lecture 2 30
Linearity
A linear circuit is one that contains only linear elements.
Resistors, Voltage & Current sources, Inductors and Capacitors are linear elements.
An example of a nonlinear element is a lamp or a diode. A diode allows current to flow freely in one direction, but blocks the flow of current in the other.
Power is not linear due to V2 or I2 !
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23-Feb-99 Lecture 2 31
Superposition
What to do when there is more than one source in a circuit?
SUPERPOSITION - If a linear circuit is excited by more than one independent source, then the total response is simply the sum of the responses of the individual sources.
How do you temporarily remove sources? Voltage source by a short circuit Current sources by an open circuit
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23-Feb-99 Lecture 2 32
Superposition example
+
-Vs
R1
R2R3 Is
IR2