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PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING
THIRD EDITION
C H A P T E R
2
Fundamentals of Electrical Circuits
McGraw-Hill
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GIORGIO RIZZONI
© The McGraw-Hill Companies, Inc. 2000
PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING
THIRD EDITION
Figure 2.4 (a) Automotive circuits
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GIORGIO RIZZONI
© The McGraw-Hill Companies, Inc. 2000
PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING
THIRD EDITION
Figure 2.4 (b) Equivalent electrical circuit
Ibatt
Ihead
Itail
Istart
I fan
I locks
Idash
+
Vbatt
–
(b)
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GIORGIO RIZZONI
© The McGraw-Hill Companies, Inc. 2000
PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING
THIRD EDITION
Figure 2.8 (a) Electrical vehicle battery pack
Vbatt1 Vbatt2
Vbattn
12 V 12 V 12 V
12 V 12 V
DC-AC converter
(electric drive)
AC motor
(a)
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GIORGIO RIZZONI
© The McGraw-Hill Companies, Inc. 2000
PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING
THIRD EDITION
Figure 2.8 (b) Illustration of KVL
vbatt2 vbatt3 vbatt31
+ –+ – + –
+
vbatt1
+
Power
converter
and motor
–
vdrive
–
(b)
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GIORGIO RIZZONI
© The McGraw-Hill Companies, Inc. 2000
PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING
THIRD EDITION
i
i
+
v
–
+
v
Load
Source
Figure 2.10 Various representations of an
electrical system
i
Power flow
(a) Conceptual
representation
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VS _+
R
–
+
–
Car
battery
(b) Symbolic (circuit)
representation
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GIORGIO RIZZONI
Headlight
(c) Physical
representation
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PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING
THIRD EDITION
Figure 2.18 Volt-ampere characteristic of a
tungsten light bulb
i (amps)
0.5
0.4
0.3
0.2
0.1
–60 –50 –40 –30 –20 –10 0
– 0.1
Current
meter
i
Variable
voltage
source
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–0.2
+
–0.3
v
–0.4
–
10 20 30 40 50 60 v (volts)
–0.5
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GIORGIO RIZZONI
© The McGraw-Hill Companies, Inc. 2000
PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING
THIRD EDITION
Figure 2.20 The resistance element
i
i
+
l R=
l
A
R
v
1/R
–
A
v
Physical resistors
with resistance R.
Typical materials are
carbon, metal film.
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Circuit symbol
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GIORGIO RIZZONI
i-v characteristic
© The McGraw-Hill Companies, Inc. 2000
PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING
THIRD EDITION
Figure 2.22 Resistor color code
b
4
b
b
3
2
b
1
Color bands
black
brown
red
orange
yellow
green
0
1
2
3
4
5
blue
violet
gray
white
silver
gold
6
7
8
9
10%
5%
Resistor value = ( b 1 b 2 )
10 b 3;
b 4 = % tolerance in actual value
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GIORGIO RIZZONI
© The McGraw-Hill Companies, Inc. 2000
PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING
THIRD EDITION
Figure 2.30
R
+ v
1.5 V
_+
i
– v
The current i flows through each of
the four series elements. Thus, by
KVL,
–
+
+
v
–
R
1.5 = v1+ v 2+ v3
R
N
R
n
R
EQ
R3
N series resistors are equivalent to
a single resistor equal to the sum of
the individual resistances.
R2
R1
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GIORGIO RIZZONI
© The McGraw-Hill Companies, Inc. 2000
PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING
THIRD EDITION
Figure 2.32 Parallel circuits
KCL applied at this node
iS
+
i1
i2
i3
R1
R2
R3 v
R1 R2 R3 Rn RN
–
The voltage v appears across each parallel
element; by KCL, i S = i1 + i2 + i 3
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REQ
N resistors in parallel are equivalent to a single equivalent
resistor with resistance equal to the inverse of the sum of
the inverse resistances.
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GIORGIO RIZZONI
© The McGraw-Hill Companies, Inc. 2000
PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING
THIRD EDITION
Figure 2.36 Wheatstone bridge circuits
c
R1
+
_
vS
R3
va v b
a
b
R2
Rx
d
(a)
c
vS
+
_
R1
a va
R2
vb
R3
b
Rx
d
(b)
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GIORGIO RIZZONI
© The McGraw-Hill Companies, Inc. 2000
PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING
THIRD EDITION
Figure 2.37 A force-measuring instrument
F
c
ia
+
R2 , R3 bonded
to bottom surface
R1
R3
vS
va
R4
h
w
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vb
–
R2
Beam cross section
ib
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GIORGIO RIZZONI
d
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PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING
THIRD EDITION
Figure 2.38 Practical voltage source
rS
Practical
voltage
source
iS
+
vS
_+
vL
RL
–
iS =
lim i S =
RL
rS
iS
0
vS
rS + R L
vS
rS
max
+
vS
+
_
vL
–
The maximum (short circuit)
current which can be supplied
by a practical voltage source is
iS max = vS
rS
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GIORGIO RIZZONI
© The McGraw-Hill Companies, Inc. 2000
PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING
THIRD EDITION
Figure 2.39 Practical current source
A model for practical current
sources consists of an ideal source
in parallel with an internal
resistance.
Maximum output
voltage for practical
current source with
open-circuit load:
vS
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max
+
iS
rS
vS
RL
–
+
iS
r
S
v
S
–
= i S rS
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GIORGIO RIZZONI
© The McGraw-Hill Companies, Inc. 2000
PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING
THIRD EDITION
Figure 2.41 Measurement of current
R1
R1
A
A
vS +
_
R2 vS +_
i
Symbol for
ideal ammeter
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A series
circuit
i
R2
Circuit for the measurement
of the current i
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GIORGIO RIZZONI
© The McGraw-Hill Companies, Inc. 2000
PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING
THIRD EDITION
Figure 2.42 Measurement of voltage
R1
R1
+
vS +
_
v2 R2
i –
A series
circuit
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V
Ideal
voltmeter
vS +
_
+
+
v2 R2 V v2
–
–
i
Circuit for the measurement
of the voltage v 2
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GIORGIO RIZZONI
© The McGraw-Hill Companies, Inc. 2000
PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING
THIRD EDITION
Figure 2.43 Models for practical ammeter
and voltmeter
rm
V
Practical
voltmeter
A
rm
Practical
ammeter
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GIORGIO RIZZONI
© The McGraw-Hill Companies, Inc. 2000
PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING
THIRD EDITION
Figure 2.44 Measurement of power
i
i
R1
R1
W
A
+
vS _+
v2 R2
–
Measurement of the power
dissipated in the resistor R2:
P2 = v2 i
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+
vS +
_
V
v 2 R2
–
Internal wattmeter connections
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GIORGIO RIZZONI
© The McGraw-Hill Companies, Inc. 2000
PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING
THIRD EDITION
Figure 2.45 Definition of a branch
a
i
+
A
Branch v
voltage
Branch R
current
–
rm
A branch
b
Ideal
resistor
A battery
Practical
ammeter
Examples of circuit branches
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GIORGIO RIZZONI
© The McGraw-Hill Companies, Inc. 2000
PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING
THIRD EDITION
Figure 2.47 Definition of a node
Node a
Node c
Node a
iS
vS
Node
Node b
Node b
Examples of nodes in practical circuits
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GIORGIO RIZZONI
© The McGraw-Hill Companies, Inc. 2000
PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING
THIRD EDITION
Figure 2.48 Definition of a loop
Note how two different loops
in the same circuit may include some of the same elements or branches.
Loop 1
R
R2
iS
1-loop circuit
3-loop circuit
(How many nodes in
this circuit?)
Loop 2
Loop 3
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R1
vS
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GIORGIO RIZZONI
© The McGraw-Hill Companies, Inc. 2000
PRINCIPLES AND APPLICATIONS OF ELECTRICAL ENGINEERING
THIRD EDITION
Figure 2.49 Definition of a mesh
How many loops can you identify in this four-mesh circuit? (Answer: 14)
R4
R3
Mesh 3
Mesh
4
R1
+
vS
_
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Mesh
1
R2
Mesh
3
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GIORGIO RIZZONI
R5
iS
© The McGraw-Hill Companies, Inc. 2000