Transcript lecture2

ELEC130
Electrical Engineering 1
Week 2
Module 1
Introductory Circuit Techniques
1
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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Lecture 2
2
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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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
(I = Q / t
Amps
Units: Ohms or 
& V = P.t / Q volts)
P = V . I Watts
V = R . I Ohms
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Conventions
 Current - positive charge flow - through element
=
-3A
3A
 Voltage - measured across an element
 Power
I
+
v(t)
_
+ Circuit
v(t) or
_
+
-
Delivering
power
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I
element
I
Lecture 2
Absorbing
power
5
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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Resistance
 Common - are small fixed with colour coded values:
Black
Brown
Red
Orange
Yellow
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0
1
2
3
4
Green
Blue
violet
Grey
White
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5
6
7
8
9
Brown
Red
Gold
Silver
Nil
1%
2%
5%
10%
20%
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Resistance
 Charge tends to flow from a
higher voltage (potential) to a
lower voltage
I
+
 Determine direction of the
current. If not labelled - GUESS
the direction.
4V
10
_
 Potential of resistor where the
current enters is positive and
leaves is negative.
 (If guess is wrong - just get
negative voltage for an answer)
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Conductance
 Sometimes easier to use inverse of resistance called
conductance
 Symbol:
 Units:
G
Siemens S (mhos)
 G = R-1
 e.g. 2  = 0.5 S
 NB: Useful when resistors are connected in parallel
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Some Analogies
 Charge
Volume (of gas)
 Voltage
Pressure
 Current
Flow Rate
 Resistance
Constriction
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Series and Parallel Elements
 Series elements have the
same current
 Share voltage
 Parallel elements have
the same voltage
 Share current
ia(t)
i(t)
i(t)
+ va(t)
+
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-
+ vb(t)
v(t)
-
+ vc(t)
-
ib(t)
ic(t)
-
+
Lecture 2
v(t)
11
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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Kirchoffs Voltage Law example
+
I
V1
V1  V2  Vs  0
_
+
Vs
R1
-
+
R2
 Example: If Vs = 12 V and
R1= R2 , then V1 = V2 = 6 V
V2
_
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Series Resistance
R1
I
+ V1
R2
-
+ V2
Rn
-
+ Vn
-
Vs
+ Vs = V1 + V2 + …….+ Vn
 Vs = R1 I + R2 I + …….+ Rn I
 Vs = (R1 + R2 + …….+ Rn)I
where e.g.
V1 = R1 I
by Ohm’s Law
 Thus Req = R1 + R2 + …….+ Rn
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Lecture Exercise
I
+
VX
-
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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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Kirchoff’s Current Law - example
I1
node
I2
I 1 + I3 - I 2 = 0
I3
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Parallel resistance
+
Is
R1
R2
I1
I2
 Is = I1 + I2 + …..+ In
 [ I = V. 1/R = V G ]
V R
n
_
In  Is = VG1 + VG2 +... + VGn
 Is = V (G1 + G2 +... + Gn)
 Is = V Geq
 Geq = G1 + G2 +... + Gn
 1/Req = 1/R1+ 1/R2+...+ 1/Rn
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Two Parallel Resistors
 1/Req = 1/R1 + 1/R2
+
= (R1 + R2)/ R1.R2
-
 Req = R1.R2 / (R1 + R2)
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Lecture 2
Vs
R1
R2
I1
I2
19
Current Division
Is
Vs 
G1  G2
+
+
-
Vs
_
R1
R2
I1
I2
Is
I1  Vs G1 
G1
G1  G2
G1
R2
I1 
Is 
Is
G1  G2
R1  R2
 NB: more current flows through
path of lesser resistance
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Voltage Division
I
R1
V1
R1
V1  IR1 
Vs
R!  R2
_
+
Vs
Vs
I
R!  R2
+
-
+
R2
R2
V2 
Vs
R!  R2
V2
_
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Series Sources
 Ideal independent voltage sources in series add
algebraically
+-
+-
+-
+-
I
V1
V2
V3
Vn
I
R
-
VR
+
 NB cases of parallel voltage sources are not resolvable. WHY?
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Parallel Sources
 Ideal independent current sources in parallel add
algebraically
IT
+
V
_
In
R
I1
I2
I3
 NB cases of series current sources are not resolvable. WHY?
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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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Example continues
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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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Equating Resistance's
 Resistance between X - Y
 In   Ra // (Rb + Rc)
X
Ra
Y
Rb
Rc
 In Y  R1 + R3
RXY
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X
Z
R1
R2
Z
R3
Y
Ra ( Rb  Rc )

 R1  R3
Ra  ( Rb  Rc )
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Solving simultaneously ….
To obtain R1, R2, R3 in terms of Ra, Rb, Rc
and vice versa
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Example cont.
X
X
Y
Z
Z
Y
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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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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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Superposition example
R1
Vs
+
-
R2
R3
Is
I R2
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