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EET1122/ET
Circuit Analysis
Introduction
Electrical and TelecommunicationsEngineering Technology Department
Professor Jang
Prepared by textbook based on “Introduction to Circuit Analysis”
by Robert Boylestad, Prentice Hall, 10
th
edition.
Acknowl Acknowl
e e
dgementdgement
I want to express my gratitude to Prentice Hall giving me the permissionto use instructor’s material for developing this module. I would like tothank the Department of Electrical and Telecommunications EngineeringTechnology of NYCCT for giving me support to commence andcomplete this module.
I
hope this module is helpful to enhance our
students’ academic performance.
Sunghoon Jang
OUTLINES OUTLINES
Introduction to Electrical Engineering
A Brief History
Units of Measurement
Systems of Units
Operation of a Scientific Calculator
Significant Figures
Introduction
The Electrical/Electronics Engineering
The growing sensitivity to the technologies on Wall Street is clearevidence that the electrical/electronics industry is one that will have asweeping impact on future development in a wide range of areas thataffect our life style, general health, and capabilities.•
Semiconductor Device
Analog & Digital Signal Processing
Telecommunications
Biomedical Engineering
Fiber Optics & Opto-Electronics
Integrated Circuit (IC)
Key Words
: Electrical Engineering, Units, Powers, Calculator
ET162 Circuit Analysis – Introduction
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Figure 1.
Computer chip on
finger. (Courtesy of Intel Corp.)
ET162 Circuit Analysis – Introduction
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Introduction – A Brief History
FIGURE 1.2FIGURE 1.
Time charts: (a)Time charts: (a)
longlong-range; (b) expanded
range; (b) expanded
..
ET162 Circuit Analysis – Introduction
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Units of Measurement
The numerical value substituted into an equation must haveThe unit of measurement specified by the equation
Examples
1 mi = 5280 ft4000 ft = 0.7576 mi1 min = 0.0167 h
d
mi
v
mi
h
t
h
ET162 Circuit Analysis – Introduction
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Systems of Units
The
English
system is based on a single standard, the
metric
is
subdivided into two interrelated standards: the
MKS
and the
CGS
English
Metric
Length: Yard (yd)
Length: Meter (m)
Mass: Slug
Mass: Kilogram (kg)
Force: Pound
Force: Newton (N)
Temperature: Fahrenheit (°F)
Temperature: Kelvin (K)
Energy: Foot-pound (ft-lb)
Energy: Joule (J)
Time: Seconds (s)
Time: Seconds (s)
ET162 Circuit Analysis – Introduction
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6
Systems of Units
FIGURE 1.3FIGURE 1.
Com
p
arison of
Comparison of
Ex. 1-
a.
= [(2)(0.0001)] [(7)(0.000001)]
= (2 × 10
)(7 × 10
= (2)(7) × (
= 14 × 10
a.
= (3.4 × 10
5
)(61 × 10
= (3.4)(61) × (
5
= 207.4 × 10
0
Ex. 1-
a.
3
= (3 × 10
3
= (3 × 10
3
3
× 10
b.
2
= (9.08 × 10
7
2
2
× (
7
2
= 82.4464 × 10
14
ET162 Circuit Analysis – Introduction
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Ex. 1-
12
8 4
8 4
2
5 3
3
5
×
×
×
×
×
×
×
×
−
−
−
− −
−
−
a b
Calculators and Order of Operation
ET162 Circuit Analysis – Introduction
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HW 1-
Perform the following conversions:
a.
1.5 min to seconds
b.
0.04 h to seconds
c.
0.05 s to microseconds
d.
0.16 m to millimeters
e.
0.00000012 s to nanoseconds
f.
3,620,000 s to days
Homework
ET162 Circuit Analysis – Introduction
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EET1122/ET
Circuit Analysis
Current and Voltage
Electrical and TelecommunicationsEngineering Technology Department
Professor Jang
Prepared by textbook based on “Introduction to Circuit Analysis”
by Robert Boylestad, Prentice Hall, 10
th
edition.
OUTLINESOUTLINES
Resistance and Conductance
Ohmmeters
Current and Voltage
Ammeters and Voltmeters
Key Words
: Resistance, Ohmmeter, Current, Voltage, Ammeter, Voltmeter
ET162 Circuit Analysis –Current and Voltage
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At a fixed temperature of 20
C (room temperature), the resistance is
related to the other three factor by
l
R
=
ρ
(ohms,
ρ
A
: resistivity of the sample (CM-ohms/ft at T=
C)
l
: the length of the sample (feet)
A
: cross-sectional area of the sample (circular mils (CM))
FIGURE 1.
Factors affecting the
resistance of a conductor.
ET162 Circuit Analysis –Current and Voltage
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Introduction to Resistance
The flow of charge through any materialencounters an opposing force similar inmany aspect to mechanical friction. Thisopposition, due to the collisions betweenelectrons and other atoms in the material, which converts electrical energy intoanother form of energy such as heat
, is
called the
resistance
of the material. The
Figure 1.
Resistance symbol and
unit of measurement of resistance is the ohm
notation.
ET162 Circuit Analysis –Current and Voltage
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a.
Conductance
Ex. 1-
Find the range in which a resistor having the following color bands must
exist to satisfy the manufacturer’s tolerance:
±10%
10
-
= 0.
9
3
No color
Silver
Gold
White
Orange
5
th
Band
4
th
Band
3
rd
Band
2
nd
Band
1
st
Band
b
.
a. 82
Ω
±
5% (1% reliability)
Since 5% of 82 = 4.10, the resistor should be within the range of 82
, or between 77.90 and 86.
b. 3.
Ω
±
10% =
The resistor should be somewhere between 3.51 and 4.
Ω
.
ET162 Circuit Analysis –Current and Voltage
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The quantity of how well the material will conduct electricityis called
conductance
(S).
1
G
=
R
(siemens, S)
Indicating that increasing
A
the area or decreasing
G
=
(S)
either the length or the
l
resistivity will increase the Conductance
ET162 Circuit Analysis –Current and Voltage
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Ex. 1-
What is the relative increase or decrease in conductivity of a conductor if
Ohmmeters
the area is reduced by 30% and the length is increased by 40%? The resistivity is fixed.
The ohmmeter is an instrument used to perform the following tasks
and several other useful functions.
i
i
i
l
A
G
ρ
Measure the resistance of individual or combined elements
Direct open-circuit (high-resistance) and short-circuit (low
(siemens, S)
resistance) situations
Check continuity of network connections and identify wires of a multi-lead cable
with the subscript
i
for the initial value. Using the subscript
n
for
Test some semiconductor devices
new value :
i
i
i
i
i
i
i
i
n
n
n
n
G
G
l
A
l
A
l
A
G
ET162 Circuit Analysis –Current and Voltage
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FIGURE 1.
Checking the continuity of
a connection.
FIGURE 1.
Measuring the resistance of
a single element.
FIGURE 1.11 Terminalcharacteristics: (a)ideal voltagesource; (b) idealcurrent source.
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16
Ex 1-
In Figure, three conductors of different materials are presented.
a.
Without working out the numerical solution, determine which section wouldappear to have the most resistance. Explain.
b.
Find the resistance of each section and compare with the result of (a) (T = 20
°
C)
Voltage
The
voltage
across an element is the work (energy) required to move
a unit positive charge from the
terminal to the + terminal. The unit
of voltage is the volt,
V
A
potential difference
of 1 volt (V) exists between two points if 1 joul
(J)
of energy is exchanged in moving 1 coulomb (C) of charge
between the two points.
a. R
silver
> R
copper
> R
aluminum
(
)(
)
(
)(
)
(
)(
)
min
CM
ft
l A
R
um
Alu
CM
ft
A
l
R
Copper
CM
ft
A
l
R
Silver
ET162 Circuit Analysis –Current and Voltage
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In general, the potential difference betweentwo points is determined by:
V = voltage (V)Q = coulombs (C)W = potential energy (J)
V
W
Q
FIGURE 1.
Defining the unit of measurement for
voltage.
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ET162 Circuit Analysis –Current and Voltage
Fixed (dc) Supplies
The terminology
dc
is an
abbreviation
for
direct current
, which
encompasses the various electrical systems in which there is aunidirectional (“one direction”) flow of charge.
DC Voltage Sources
Dc voltage sources can be divided into three broad categories:
Batteries
(chemical action), (2)
generators
(electro-mechanical),
and (3)
power supplies
(rectification).
Ex. 1-
Find the potential difference between two points in an electrical system
if 60 J of energy are expended by a charge of 20 C between these two points.
V
C
J
Q
W
V
J
J
V
V
Q
W
×
×
Ex. 1-
Determine the energy expended moving a charge of 50
μ
C through a
potential difference of 6 V.
ET162 Circuit Analysis –Current and Voltage
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FIGURE 1.
Symbol
for a dc voltage source. ET162 Circuit Analysis –Current and Voltage
EET1122/ET
Circuit Analysis
Ohm’s Law
Electrical and TelecommunicationsEngineering Technology Department
Professor Jang
Prepared by textbook based on “Introduction to Circuit Analysis”
by Robert Boylestad, Prentice Hall, 10
th
edition.
Acknowl Acknowl
e e
dgementdgement
I want to express my gratitude to Prentice Hall giving me the permissionto use instructor’s material for developing this module. I would like tothank the Department of Electrical and Telecommunications EngineeringTechnology of NYCCT for giving me support to commence andcomplete this module.
I
hope this module is helpful to enhance our
students’ academic performance.
Sunghoon Jang
OUTLINES OUTLINES
Introduction to Ohm’s Law
Plotting Ohm’s Law
Power
Key Words
: Ohm’s Law, Current, Voltage, Power
Introduction to Ohm’s Law
Figure 4.
Basic Circuit.
Ohm’s law
clearly reveals that
a fixed resistance, the greaterthe voltage across a resistor,the more the current, the morethe resistance for the samevoltage, the less the current.
V
R
I
)
,
(
)
,
(
)
,
(
Ω
= =
ohms
I E
R
V
volts
R
I
E
A
amperes
R E
I
ET162 Circuit Analysis – Ohm’s Law
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ET162 Circuit Analysis – Ohm’s Law
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2
Ex. 4-
Determine the current resulting from the application of a 9-V battery
across a network with a resistance of 2.
Ω
.
I
E R
V
A
=
=
=
9
2 2
4 09
.
.
Ω
Ex. 4-
Calculate the resistance of a 60-W bulb if a current of 500 mA results
from an applied voltage of 120 V.
R
E I
V
A
=
=
×
=
−
120
500
10
240
3
Ω
ET162 Circuit Analysis – Ohm’s Law
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For an isolated resistive element, the polarity of the voltage dropis as shown in Fig. 4.2(a) for the indicated current direction. Areversal in current will reverse the polarity, as shown in Fig.4.2(b). In general, the flow of charge is from a high (+) to a low (–)potential.
FIGURE 4.
Defining polarities.
ET162 Circuit Analysis – Ohm’s Law
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I
E R
V
mA
=
=
×
=
16
2
10
8
3
Ω
Ex. 4-
Calculate the current through the 2-k
Ω
resistor of Fig. 4.3 if the voltage
drop across it is 16 V. Ex. 4-
Calculate the voltage that must be applied across the soldering iron of
Fig. 4.5 to establish a current of 1.5 A through the iron if its internal resistance is 80
Ω
.
(
)(
)
E
I
R
A
V
=
⋅
=
=
15
80
120
.
Ω
FIGURE 4.
Example
ET162 Circuit Analysis – Ohm’s Law
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FIGURE 4.
Example 4.
Plotting Ohm’s Law
Graph, characteristics, plots play an important role in every technicalfield as a mode through which the broad picture of the behavior orresponse of a system can be conveniently displayed. It is thereforecritical to develop the skills necessary both to read data and to plotthem in such a manner that they can be interpreted easily. For most sets of characteristicsof electronic devices, the currentis represented by the verticalaxis, and the voltage by thehorizontal axis, as shown in Fig.4.5.
FIGURE 4.
Plotting Ohm’s
law
ET162 Circuit Analysis – Ohm’s Law
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Ex. 4-
Find the power delivered to the dc motor of Fig. 4.11.
P
V I
V
A
W
kW
FIGURE 4.
Example 4.6.
Ex. 4-
What is the power dissipated by a 5-
Ω
resistor if the current is 4 A?
P = I
2
R = (4 A)
2
W
ET162 Circuit Analysis – Ohm’s Law
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FIGURE 4.
The nonlinear I-V characteristics of
Ex. 4-8 a 75-W light bulb.
The I-V characteristics of a light bulb are powered in Fig. 4.12. Note the
nonlinearity of the curve, indicating a wide range in resistance of the bulb withapplied voltage as defined by the earlier discussion. If the rated voltage is 120 V,find the wattage rating of the bulb. Also calculate the resistance of the bulbunder rated conditions.
A
t
V
I
A
P
V I
V
A
W
At
V
R
V
I
V
A
ET162 Circuit Analysis – Ohm’s Law
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HW 4-
A stereo system draws 2.4 A at 120 V. The audio output power is 50 W.
a.
How much power is lost in the form of heat in the system?
b.
What is the efficiency of the system?
Sometimes the power is given and the current or voltage must bedetermined.
P
I
R
I
P R
or
I
P R
ampere
=
⇒
=
=
2
2
(
)
P
V
R
V
PR
or
V
PR
volts
2
2
a
P
i
EI
V
A
W
P
P
P
P
P
P
W
W
W
i
o
lost
lost
i
0
P
0
W
b
η
×
P
i
W
Ex. 4-
Determine the current through a 5-k
Ω
resistor when the power dissipated
by the element is 20 mW.
I
P R
W
A
mA
× ×
×
×
−
−
−
3
3
6
3
Homework
ET162 Circuit Analysis – Ohm’s Law
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ET162 Circuit Analysis – Ohm’s Law
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EET1122/ET162 Circuit Analysis
Series Circuits
Electrical and TelecommunicationsEngineering Technology Department
Professor Jang
Prepared by textbook based on “Introduction to Circuit Analysis”
by Robert Boylestad, Prentice Hall, 10
th
edition.
Acknowl Acknowl
e e
dgementdgement
I want to express my gratitude to Prentice Hall giving me the permissionto use instructor’s material for developing this module. I would like tothank the Department of Electrical and Telecommunications EngineeringTechnology of NYCCT for giving me support to commence andcomplete this module.
I
hope this module is helpful to enhance our
students’ academic performance.
Sunghoon Jang
OUTLINES OUTLINES
Introduction to Series Circuits
Kirchhoff’s Voltage Law
Voltage Divider Rule
Interchanging Series Elements
Series Circuits – Notation
Ideal dc Voltage Sources vs. Non-ideal Sources
Voltage Regulation
Key Words
: Series Circuit, Kirchhoff’s Voltage Law, Voltage Divider Rule
ET162 Circuit Analysis – Series Circuits
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Series Circuits - Introduction
Two types of current are available to the consumer today. One is
direct
current (dc),
in which ideally the flow of charge (current) does not
change in magnitude with time. The other is sinusoidal
alternating
current (ac),
in which the flow of charge is continually changing in
magnitude with time.
FIGURE 5.
Introducing the basic components of an electric circuit.
V (volt) = E (volt)
ET162 Circuit Analysis – Series Circuits
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E
T
= E
1
+ E
2
+ E
3
= 10V + 6V + 2V = 18V
E
T
= E
2
+ E
3
– E
1
= 9V +3V – 4V = 8V
FIGURE 5.
Reducing series dc
voltage sources to a single source.
Voltage Sources in Series
Voltage sources can be connected in series, as shown in Fig. 5.7, to increaseor decrease the total voltage applied to a system. The net voltage isdetermined simply by summing the sources with the same polarity andsubtracting the total of the sources with the opposite polarity.
ET162 Circuit Analysis – Series Circuits
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Kirchhoff’s Voltage Law
Kirchhoff’s voltage law (KVL) states that the algebraic sum of thepotential rises and drops around a closed loop (or path) is zero. A
closed loop
is any continuous path that leaves a point in one direction
and returns to that same point from another direction without leaving thecircuit.
V = 0
(Kirchhoff’s voltage law
in symbolic form)
FIGURE 5.
Applying Kirchhoff’s
voltage law to a series dc circuit.
E – V
1
– V
2
or E = V
1
+ V
2
V
rises
V
drops
ET162 Circuit Analysis – Series Circuits
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Ex. 5-
For the circuit of Figure 5.9:
a. Determine V
2
using Kirchhoff’s voltage law.
b. Determine I.c. Find R
1
and R
2
.
b
.
A
V
R
V
I
2 2
3
3
1
1
V A
I
V
R
V A
I
V
R
c
.
a
. Kirchhoff’s voltage law (clockwise direction): - E + V
3
2
1
= 0
or
E = V
1
2
3
and
V
2
= E – V
1
3
= 54V – 18V – 15 V = 21V
FIGURE 5.
ET162 Circuit Analysis – Series Circuits
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10
Ex. 5-
Find V
1
and V
2
for the network of Fig. 5.10.
1
1
V
V
V
and
V
V
For path 1, starting at point a in a clockwise direction:
For path 2, starting at pointa in a clockwise direction:
V
V
and
V
V
2
2
FIGURE 5.
ET162 Circuit Analysis – Series Circuits
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−
−
=
=
60
40
30
0
50
V
V
V
V
and
V
V
x
x
Ex. 5-
Using Kirchhoff’s voltage law, determine the unknown voltage for
the network of Fig. 5.11.
6
14
2
0
18
V
V
V
V
and
V
V
x
x
−
=
= −
FIGURE 5.
Ex. 5-
For the circuit of Fig. 5.12.
a. Determine V
2
using Kirchhoff’s voltage law.
b. Determine I.c. Find R
1
and R
3
.
a
K
irchhoff
s
voltage law
clockwise directionV
V
V
V
or
V
V
2
2
−
b
I
V
R
V
A
2 2
c
R
V
I
V
A
R
V
I
V
A
1
1
3
3
FIGURE 5.
ET162 Circuit Analysis – Series Circuits
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ET162 Circuit Analysis – Series Circuits
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Voltage Divider Rule (VDR)
The voltage divider rule (VDR) can be derived by analyzing the network of Fig. 5.15.
The voltage across the resistive elements will divide as the magnitude of the resistance levels.
R
T
= R
1
+ R
2
The voltages across the resistive elements of Fig. 5.13 are provided. Since the resistance level of R
1
is 6 times that of R
3
, the voltage across R
1
is 6 times that of
and
I = E/R
T
R
3
. The fact that the resistance level of R
2
is 3 times that of R
1
results in three times
the voltage across R
2
. Finally, since R
1
is twice R
2
, the voltage across R
1
is twice
Applying Ohm’s law:
that of R
2
. If the resistance levels of all resistors of Fig. 5.13 are increased by the
same amount, as shown in Fig. 5.14, the voltage levels will all remain the same.
T
T
T
T
R
E
R
R
R
E
IR
V
R
E
R
R
R
E
IR
V
2
2
2
2
1
1
1
1
FIGURE 5.
Developing the voltage divider rule.
FIGURE 5.
Revealing how the voltage
will divide across series resistive elements.
FIGURE 5.
The ratio of the resistive values
determines the voltage division of a series dc circuit.
T x
x
R
E
R
V
=
ET162 Circuit Analysis – Series Circuits
(voltage divider rule)
Boylestad
15
Floyd
In Fig. 5.31, V
a
is the voltage from
point a to ground. In this case it isobviously 10V since it is right acrossthe source voltage E. The voltage V
b
is
the voltage from point b to ground.Because it is directly across the 4-
resistor, V
b
= 4V.
A single-subscript notation can be employed that provides the voltage at apoint with respect to ground.
FIGURE 5.
Defining the use of single-
subscript notation for voltage levels.
The single-subscript notation V
a
specifies the voltage at point a with respect
to ground (zero volts). If the voltage is less than zero volts, a negative signmust be associated with the magnitude of V
a
V
ab
= V
a
– V
b
= 10V – 4V = 6V
Single-Subscript Notation
FIGURE 5.
Example 5.14.
General Comments
A particularly useful relationship can now be established that will haveextensive applications in the analysis of electronic circuits. For the abovenotational standards, the following relationship exists:
V
ab
= V
a
– V
b
Ex. 5-
Find the voltage V
ab
for the conditions of Fig. 5.32.
V
V
V
V
V
V
ab
a
b
ET162 Circuit Analysis – Series Circuits-Notation
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Ex. 5-
Find the voltage V
b
, V
c
and V
ac
for the network of Fig. 5.36.
Starting at Ground, we proceedthrough a rise of 10 V to reachpoint a and then pass through adrop in potential of 4 V to point b.
The result is that the meter
will read
V
b
= +10V – 4V = 6V
ET162 Circuit Analysis – Series Circuits-Notation
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20
FIGURE 5.
Ex. 5-
Find the voltage V
a
for the configuration of Fig. 5.33.
V
V
V
V
V
V
V
V
V
ab
a
b
a
ab
b
V
V
V
V
V
V
V
V
ab
a
b
Ex. 5-
Find the voltage V
ab
for the configuration of Fig. 5.34.
FIGURE 5.
8
FIGURE 5.
The
impact of positive andnegative voltages on thetotal voltage drop.
If we then proceed to point c,there is an additional drop of20V, result in
V
c
= V
b
– 20V – 6V
= 6V – 20V = – 14V
FIGURE 5.
The voltage V
ac
can be obtained
V
ac
= V
a
– V
c
= 10V – (–14V)= 24 V
ET162 Circuit Analysis – Series Circuits-Notation
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23
ies Circuits
Floyd
I
E
E
R
V
V
V
A
and
V
V
V
V
V
V
T
ab
cb
c
1
2
ET162 Circuit Analysis – Ser
24
Ex. 5-
Determine V
ab
, V
cb
and V
c
for the network of Fig. 5.37.
FIGURE 5.
Redrawing the circuit of Fig.
5.37 using dc voltage supply symbols.
I
V
A
V
I R
A
V
V
I R
A
V
V
E
V
ab cb c
2
1
1
The other approach is to redraw the network as shownin Fig. 5.37 to clearly establish the aiding effect of E
1
and E
2
and then solve the resulting series circuit.
There are two ways to approach this problem. The first is thatthere is a 54-V drop across the series resistors R
1
and R
2
.
FIGURE 5.
3
Redrawing the network with standardbattery symbol will result in thenetwork of Fig.5.40. Applying thevoltage divider rule,
FIGURE 5.
Ex. 5-
Using the voltage divider rule, determine the voltages V
1
and V
2
for of
Fig. 5.39.
V
R E
R
R
V
V
V
R
E
R
R
V
V
1
1
1
2
2
2
1
2
FIGURE 5.
ET162 Circuit Analysis – Series Circuits-Notation
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25
FIGURE 5.
Ex. 5-
For the network of Fig. 5.40:
a. Calculate V
ab
.
b. Determine V
b
.
c. Calculate V
c
.
a
Voltage divider rule
V
R E
R
V
V
ab
T
1
b
Voltage divider rule
V
V
V
R
R
E
R
V
V
or
V
V
V
E
V
V
V
V
b
R
R
T
b
a
ab
ab
2
3
2
3
c. V
c
= ground potential = 0V
ET162 Circuit Analysis – Series Circuits-Notation
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Ideal Voltage Sources vs. Non-ideal Voltage Sources
Every source of voltage, whether a generator, battery, or laboratory supply asshown in Fig. 5.41(a), will have some
internal resistance (know as the non-
ideal voltage source)
. The equivalent circuit of any source of voltage will
therefore appear as shown in Fig. 5.41(b).
FIGURE 5.
(a) Sources of dc voltage; (b) equivalent circuit.
ET162 Circuit Analysis – Series Circuits-Notation
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