G. Rizzoni and J. Kearns, Principles and Applications of Electrical Engineering, 7th Edition Solutions, Chapter 1
Chapter 1: Fundamentals of Electrical Circuits – Instructor Notes
Chapter 1 has been reorganized to enable students to solve interesting and practical
problems at the very beginning of an introductory course. The first section introduces students to
basic circuit structures (nodes, branches, meshes and loops) and emphasizes the important skill of
identifying and counting nodes. The following three sections cover basic definitions of charge,
current and voltage (Section 1.2), ideal independent and dependent sources (Section 1.3), and
power and the passive sign convention (Section 1.4). A special feature, Focus on Problem Solving:
The Passive Sign Convention (p. 18) along with two examples and two exercises illustrate this
important topic. A second feature that recurs throughout the early chapters is presented in the form
of sidebars. Make The Connection: Hydraulic Analog of a Voltage Source (p. 15), Make The
Connection: Hydraulic Analog of Current Sources (p. 16), and Make The Connection: Hydraulic
Analog of Electrical Resistance (p. 31) present electromechanical analogies.
Section 1.5 introduces Kirchhoff’s laws in multiple forms and further develops problem
solving skill through six examples and three exercises. Two of these examples illustrate simple
yet practical automotive applications.
Section 1.6 covers the concepts of electrical resistance and Ohm’s law and describes the
basic construction of various discrete resistors. Table 1.1 (p. 30) lists the resistance of copper wire
for various gauges while Tables 1.2 (p. 32) and 1.3 (p. 33) summarize the resistivity of common
materials and standard resistor values. Variable resistors and potentiometers are also discussed
along with their practical utility. Resistive power dissipation is introduced here. Finally, a
practical electromechanical analogy of heat transfer in the quenching of an engine crankshaft and
the concept of thermal resistance are discussed at the end of this section. Other analogies are
presented throughout the early chapters.
Sections 1.7 and 1.8 present the Node Voltage and Mesh Current methods. Each section
is supported by highlighted Focus on Problem Solving summaries of the detailed step-by-step
procedure for applying these methods. Seven examples and seven exercises provide thorough
illustrations of the methods, including two examples that introduce MatLab to solve matrix
equations. Section 1.9 details the use of these methods to circuits involving dependent sources.
The presentation of the Node Voltage and Mesh Current methods emphasizes the
importance of consistent and systematic solution methods. The aim of this presentation, which is
perhaps more detailed than usual in a textbook suitable for non-majors, is to develop good habits
early on, with the hope that the orderly approach presented in this chapter will facilitate the
discussion of AC and transient analysis in Chapters 3 and 4.
The homework problems include a variety of practical examples, with emphasis on
automotive batteries and the role of resistance in power dissipation in fuses, cables, lightbulbs
and heating coils. Numerous problems associated with Section 1.2 focus on the charging of
batteries. Problems 1.28, 1.29, 1.33-1.35 and 1.40 focus on resistance and power in lighting
1.1
Copyright 2022 © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw Hill LLC.
,G. Rizzoni and J. Kearns, Principles and Applications of Electrical Engineering, 7th Edition Solutions, Chapter 1
elements; problem 1.41 involves the resistance of heating coils; problem 1.43 involves the role of
wire gauge in power transmission between a generator and an electric motor; problem 1.44
relates the geometry of a thin film resistor to its resistance; and problem 1.45 illustrates the
surprisingly involved analysis of fuses. The remainder of the homework problems are focused
on basic concepts and the development of problem-solving skill.
It has been the authors’ experience that providing students with an early introduction to
practical applications of electrical engineering to their own disciplines can increase the interest
level in the course significantly.
Learning Objectives for Chapter 1
Students will learn to...
1. Identify the principal features of electric circuits or networks: nodes, loops,
meshes, and branches. Section 1.1.
2. Apply definitions of charge, current and voltage. Section 1.2.
3. Identify sources and their i-υ characteristics. Section 1.3.
4. Apply the passive sign convention to compute the power consumed or supplied by
circuit elements. Section 1.4.
5. Apply Kirchhoff’s laws to simple electric circuits. Section 1.5.
6. Apply Ohm’s law to calculate unknown voltages and currents in simple circuits.
Section 1.6.
7. Apply the Node Voltage method to solve for unknown voltages and currents in
resistive networks. Section 1.7.
8. Apply the Mesh Current method to solve for unknown voltages and currents in
resistive networks. Section 1.8.
9. Apply the Node Voltage and Mesh Current methods to solve for unknown
voltages and currents in resistive networks with dependent sources. Section 1.9.
1.2
Copyright 2022 © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw Hill LLC.
, G. Rizzoni and J. Kearns, Principles and Applications of Electrical Engineering, 7th Edition Solutions, Chapter 1
Section 1.2: Charge, Current, and Voltage
Problem 1.1
A free electron has an initial potential energy per unit charge (voltage) of 17 kJ/C and a velocity
of 93 Mm/s. Later, its potential energy per unit charge is 6 kJ/C. Determine the change in
velocity of the electron.
Solution:
Known quantities:
m
Initial Coulombic potential energy, Vi 17kJ /C ; initial velocity, U i 93M ; final Coulombic
s
potential energy, V f 6kJ /C .
Find:
The change in velocity of the electron.
Assumptions:
PEg PEc
Analysis:
Using the first law of thermodynamics, we obtain the final velocity of the electron:
Qheat W KE PEc PEg ...
Heat is not applicable to a single particle. W=0 since no external forces are applied.
KE PEc
1
me (U 2f Ui2 ) Qe (V f Vi )
2
2Qe
U 2f U i2 (V f Vi )
me
2
93 M
m 2 1.6 10
19
C
6kV 17kV
s 9.11 10 37 g
m2 m2
8.649 10 15 3.864 10 15
s2 s2
m
U f 6.917 10 7
s
m m m
U f Ui 93 M 69.17 M 23.83 M .
s s s
1.3
Copyright 2022 © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw Hill LLC.
, G. Rizzoni and J. Kearns, Principles and Applications of Electrical Engineering, 7th Edition Solutions, Chapter 1
Problem 1.2
The units for voltage, current, and resistance are the volt (V), the ampere (A), and the ohm (),
respectively. Express each unit in fundamental MKS units.
Solution:
Known quantities:
MKSQ units.
Find:
Equivalent units of volt, ampere, and ohm.
Analysis:
Joule J
Voltage Volt V
Coulomb C
Coulomb C
Current Ampere a
second s
Volt Joule second J s
Resistance Ohm 2
2
Ampere Coulomb C
Ampere C 2
Conductance Siemens or Mho
Volt J s
Problem 1.3
A particular fully charged battery can deliver 2.7 x 106 coulombs of charge.
Solution:
Known quantities:
qBattery = 2.7 · 106 C.
Find:
a) The capacity of the battery in ampere-hours
b) The number of electrons that can be delivered.
Analysis:
a) There are 3600 seconds in one hour. Amperage is defined as 1 Coulomb per second
and is directly proportional to ampere-hours.
1ℎ𝑟
2.7 ∙ 106 𝐶 ∙ = 750 𝐴𝐻
3600𝑠
b) The charge of a single electron is -1.602·10-19 C. The negative sign is negligible. Simple
division gives the solution:
2.7 ∙ 106 𝐶 25
⁄1.602 ∙ 10−19 𝐶 = 1.685 ∙ 10 𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛𝑠
1 𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛
1.4
Copyright 2022 © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw Hill LLC.
Chapter 1: Fundamentals of Electrical Circuits – Instructor Notes
Chapter 1 has been reorganized to enable students to solve interesting and practical
problems at the very beginning of an introductory course. The first section introduces students to
basic circuit structures (nodes, branches, meshes and loops) and emphasizes the important skill of
identifying and counting nodes. The following three sections cover basic definitions of charge,
current and voltage (Section 1.2), ideal independent and dependent sources (Section 1.3), and
power and the passive sign convention (Section 1.4). A special feature, Focus on Problem Solving:
The Passive Sign Convention (p. 18) along with two examples and two exercises illustrate this
important topic. A second feature that recurs throughout the early chapters is presented in the form
of sidebars. Make The Connection: Hydraulic Analog of a Voltage Source (p. 15), Make The
Connection: Hydraulic Analog of Current Sources (p. 16), and Make The Connection: Hydraulic
Analog of Electrical Resistance (p. 31) present electromechanical analogies.
Section 1.5 introduces Kirchhoff’s laws in multiple forms and further develops problem
solving skill through six examples and three exercises. Two of these examples illustrate simple
yet practical automotive applications.
Section 1.6 covers the concepts of electrical resistance and Ohm’s law and describes the
basic construction of various discrete resistors. Table 1.1 (p. 30) lists the resistance of copper wire
for various gauges while Tables 1.2 (p. 32) and 1.3 (p. 33) summarize the resistivity of common
materials and standard resistor values. Variable resistors and potentiometers are also discussed
along with their practical utility. Resistive power dissipation is introduced here. Finally, a
practical electromechanical analogy of heat transfer in the quenching of an engine crankshaft and
the concept of thermal resistance are discussed at the end of this section. Other analogies are
presented throughout the early chapters.
Sections 1.7 and 1.8 present the Node Voltage and Mesh Current methods. Each section
is supported by highlighted Focus on Problem Solving summaries of the detailed step-by-step
procedure for applying these methods. Seven examples and seven exercises provide thorough
illustrations of the methods, including two examples that introduce MatLab to solve matrix
equations. Section 1.9 details the use of these methods to circuits involving dependent sources.
The presentation of the Node Voltage and Mesh Current methods emphasizes the
importance of consistent and systematic solution methods. The aim of this presentation, which is
perhaps more detailed than usual in a textbook suitable for non-majors, is to develop good habits
early on, with the hope that the orderly approach presented in this chapter will facilitate the
discussion of AC and transient analysis in Chapters 3 and 4.
The homework problems include a variety of practical examples, with emphasis on
automotive batteries and the role of resistance in power dissipation in fuses, cables, lightbulbs
and heating coils. Numerous problems associated with Section 1.2 focus on the charging of
batteries. Problems 1.28, 1.29, 1.33-1.35 and 1.40 focus on resistance and power in lighting
1.1
Copyright 2022 © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw Hill LLC.
,G. Rizzoni and J. Kearns, Principles and Applications of Electrical Engineering, 7th Edition Solutions, Chapter 1
elements; problem 1.41 involves the resistance of heating coils; problem 1.43 involves the role of
wire gauge in power transmission between a generator and an electric motor; problem 1.44
relates the geometry of a thin film resistor to its resistance; and problem 1.45 illustrates the
surprisingly involved analysis of fuses. The remainder of the homework problems are focused
on basic concepts and the development of problem-solving skill.
It has been the authors’ experience that providing students with an early introduction to
practical applications of electrical engineering to their own disciplines can increase the interest
level in the course significantly.
Learning Objectives for Chapter 1
Students will learn to...
1. Identify the principal features of electric circuits or networks: nodes, loops,
meshes, and branches. Section 1.1.
2. Apply definitions of charge, current and voltage. Section 1.2.
3. Identify sources and their i-υ characteristics. Section 1.3.
4. Apply the passive sign convention to compute the power consumed or supplied by
circuit elements. Section 1.4.
5. Apply Kirchhoff’s laws to simple electric circuits. Section 1.5.
6. Apply Ohm’s law to calculate unknown voltages and currents in simple circuits.
Section 1.6.
7. Apply the Node Voltage method to solve for unknown voltages and currents in
resistive networks. Section 1.7.
8. Apply the Mesh Current method to solve for unknown voltages and currents in
resistive networks. Section 1.8.
9. Apply the Node Voltage and Mesh Current methods to solve for unknown
voltages and currents in resistive networks with dependent sources. Section 1.9.
1.2
Copyright 2022 © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw Hill LLC.
, G. Rizzoni and J. Kearns, Principles and Applications of Electrical Engineering, 7th Edition Solutions, Chapter 1
Section 1.2: Charge, Current, and Voltage
Problem 1.1
A free electron has an initial potential energy per unit charge (voltage) of 17 kJ/C and a velocity
of 93 Mm/s. Later, its potential energy per unit charge is 6 kJ/C. Determine the change in
velocity of the electron.
Solution:
Known quantities:
m
Initial Coulombic potential energy, Vi 17kJ /C ; initial velocity, U i 93M ; final Coulombic
s
potential energy, V f 6kJ /C .
Find:
The change in velocity of the electron.
Assumptions:
PEg PEc
Analysis:
Using the first law of thermodynamics, we obtain the final velocity of the electron:
Qheat W KE PEc PEg ...
Heat is not applicable to a single particle. W=0 since no external forces are applied.
KE PEc
1
me (U 2f Ui2 ) Qe (V f Vi )
2
2Qe
U 2f U i2 (V f Vi )
me
2
93 M
m 2 1.6 10
19
C
6kV 17kV
s 9.11 10 37 g
m2 m2
8.649 10 15 3.864 10 15
s2 s2
m
U f 6.917 10 7
s
m m m
U f Ui 93 M 69.17 M 23.83 M .
s s s
1.3
Copyright 2022 © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw Hill LLC.
, G. Rizzoni and J. Kearns, Principles and Applications of Electrical Engineering, 7th Edition Solutions, Chapter 1
Problem 1.2
The units for voltage, current, and resistance are the volt (V), the ampere (A), and the ohm (),
respectively. Express each unit in fundamental MKS units.
Solution:
Known quantities:
MKSQ units.
Find:
Equivalent units of volt, ampere, and ohm.
Analysis:
Joule J
Voltage Volt V
Coulomb C
Coulomb C
Current Ampere a
second s
Volt Joule second J s
Resistance Ohm 2
2
Ampere Coulomb C
Ampere C 2
Conductance Siemens or Mho
Volt J s
Problem 1.3
A particular fully charged battery can deliver 2.7 x 106 coulombs of charge.
Solution:
Known quantities:
qBattery = 2.7 · 106 C.
Find:
a) The capacity of the battery in ampere-hours
b) The number of electrons that can be delivered.
Analysis:
a) There are 3600 seconds in one hour. Amperage is defined as 1 Coulomb per second
and is directly proportional to ampere-hours.
1ℎ𝑟
2.7 ∙ 106 𝐶 ∙ = 750 𝐴𝐻
3600𝑠
b) The charge of a single electron is -1.602·10-19 C. The negative sign is negligible. Simple
division gives the solution:
2.7 ∙ 106 𝐶 25
⁄1.602 ∙ 10−19 𝐶 = 1.685 ∙ 10 𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛𝑠
1 𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛
1.4
Copyright 2022 © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior
written consent of McGraw Hill LLC.
