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- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
A concise and original presentation of the fundamentals for 'new to the subject' electrical engineers This book has been written for students on electrical engineering courses who don't necessarily possess prior knowledge of electrical circuits. Based on the author's own teaching experience, it covers the analysis of simple electrical circuits consisting of a few essential components using fundamental and well-known methods and techniques. Although the above content has been included in other circuit analysis books, this one aims at teaching young engineers not only from electrical and electronics engineering, but also from other areas, such as mechanical engineering, aerospace engineering, mining engineering, and chemical engineering, with unique pedagogical features such as a puzzle-like approach and negative-case examples (such as the unique "When Things Go Wrong..." section at the end of each chapter). Believing that the traditional texts in this area can be overwhelming for beginners, the author approaches his subject by providing numerous examples for the student to solve and practice before learning more complicated components and circuits. These exercises and problems will provide instructors with in-class activities and tutorials, thus establishing this book as the perfect complement to the more traditional texts. * All examples and problems contain detailed analysis of various circuits, and are solved using a 'recipe' approach, providing a code that motivates students to decode and apply to real-life engineering scenarios * Covers the basic topics of resistors, voltage and current sources, capacitors and inductors, Ohm's and Kirchhoff's Laws, nodal and mesh analysis, black-box approach, and Thevenin/Norton equivalent circuits for both DC and AC cases in transient and steady states * Aims to stimulate interest and discussion in the basics, before moving on to more modern circuits with higher-level components * Includes more than 130 solved examples and 120 detailed exercises with supplementary solutions * Accompanying website to provide supplementary materials www.wiley.com/go/ergul4412
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Table of Contents
Cover
Title Page
Copyright
Dedication
Important Units
Conventions with Examples
Preface
About the Companion Website
Chapter 1: Introduction
1.1 Circuits and Important Quantities
1.2 Resistance and Resistors
1.3 Independent Sources
1.4 Dependent Sources
1.5 Basic Connections of Components
1.6 Limitations in Circuit Analysis
1.7 What You Need to Know before You Continue
Chapter 2: Basic Tools: Kirchhoff's Laws
2.1 Kirchhoff's Current Law
2.2 Kirchhoff's Voltage Law
2.3 When Things Go Wrong with KCL and KVL
2.4 Series and Parallel Connections of Resistors
2.5 When Things Go Wrong with Series/Parallel Resistors
2.6 What You Need to Know before You Continue
Chapter 3: Analysis of Resistive Networks: Nodal Analysis
3.1 Application of Nodal Analysis
3.2 Concept of Supernode
3.3 Circuits with Multiple Independent Voltage Sources
3.4 Solving Challenging Problems Using Nodal Analysis
3.5 When Things Go Wrong with Nodal Analysis
3.6 What You Need to Know before You Continue
Chapter 4: Analysis of Resistive Networks: Mesh Analysis
4.1 Application of Mesh Analysis
4.2 Concept of Supermesh
4.3 Circuits with Multiple Independent Current Sources
4.4 Solving Challenging Problems Using the Mesh Analysis
4.5 When Things Go Wrong with Mesh Analysis
4.6 What You Need to Know before You Continue
Chapter 5: Black-Box Concept
5.1 Thévenin and Norton Equivalent Circuits
5.2 Maximum Power Transfer
5.3 Shortcuts in Equivalent Circuits
5.4 When Things Go Wrong with Equivalent Circuits
5.5 What You Need to Know before You Continue
Chapter 6: Transient Analysis
6.1 Capacitance and Capacitors
6.2 Inductance and Inductors
6.3 Time-Dependent Analysis of Circuits in Transient State
6.4 Switching and Fixed-Time Analysis
6.5 Parallel and Series Connections of Capacitors and Inductors
6.6 When Things Go Wrong in Transient Analysis
6.7 What You Need to Know before You Continue
Chapter 7: Steady-State Analysis of Time-Harmonic Circuits
7.1 Steady-State Concept
7.2 Time-Harmonic Circuits with Sinusoidal Sources
7.3 Concept of Phasor Domain and Component Transformation
7.4 Special Circuits in Phasor Domain
7.5 Analysis of Complex Circuits at Fixed Frequencies
7.6 Power in Steady State
7.7 When Things Go Wrong in Steady-State Analysis
7.8 What You Need to Know before You Continue
Chapter 8: Selected Components of Modern Circuits
8.1 When Connections Are via Magnetic Fields: Transformers
8.2 When Components Behave Differently from Two Sides: Diodes
8.3 When Components Involve Many Connections: OP-AMPs
8.4 When Circuits Become Modern: Transistors
8.5 When Components Generate Light: LEDs
8.6 Conclusion
Chapter 9: Practical Technologies in Modern Circuits
9.1 Measurement Instruments
9.2 Three-Phase Power Delivery
9.3 AD and DA Converters
9.4 Logic Gates
9.5 Memory Units
9.6 Conclusion
Chapter 10: Next Steps
10.1 Energy Is Conserved, Always!
10.2 Divide and Conquer Complex Circuits
10.3 Appreciate the Package
10.4 Consider Yourself as a Circuit Element
10.5 Safety First
Chapter 11: Photographs of Some Circuit Elements
Appendix A
A.1 Basic Algebra Identities
A.2 Trigonometry
A.3 Complex Numbers
Appendix B: Solutions to Exercises
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Index
End User License Agreement
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Guide
cover
Table of Contents
Preface
Begin Reading
List of Illustrations
Chapter 1: Introduction
Figure 1.1 A simple circuit involving a bulb connected to a battery. The connection between the bulb and battery is shown via simple lines.
Figure 1.2 A circuit involving connections of four components labeled from
to
. From the circuit-analysis perspective, connection shapes are not important, and these three representations are equivalent.
Figure 1.3 Electric field lines created individually by a positive charge and a negative charge. An electric field is assumed to be created whether there is a second test charge or not. If a test charge is located in the field, repulsive or attractive force is applied on it.
Figure 1.4 Movement of a charge in an electric field created by external sources. The energy absorbed or released by the charge does not depend on the path but depends on the potentials at the start and end points. The electric potential (voltage) is always defined between two points, while selecting a reference point as a ground enables unique voltage definitions at all points.
Figure 1.5 On a metal wire, the conventional current direction, which is defined as positive charge flow, is the opposite of the actual electron movements. In a circuit, voltages are defined at the nodes, as well as across components, using the sign convention.
Figure 1.6 Power of a device for given current and voltage across it.
Figure 1.7 Transient state and steady state in DC and AC signals.
Figure 1.8 Structure of a general coaxial cable and a representation of the drift velocity of an electron under an electric field.
Figure 1.9 The resistance of a rod with conductivity
is often approximated as
, where
and
are the length and cross-section area, respectively, of the rod. In circuit analysis, a resistor is a two-terminal device that usually consumes energy.
Figure 1.10 Short circuit and open circuit can be interpreted as special cases of resistors, with zero and infinite resistance values, respectively.
Figure 1.11 There are alternative symbols to show voltage and current sources; circular representations are used in this book. For any source, the polarity should be clearly indicated. In addition to sources with constant values (DC sources), the source values
and
may depend on time (AC sources).
Figure 1.12 Dependent sources have fixed voltage/current values, depending on some other voltage/current values in the circuit.
Figure 1.13 Series and parallel connections, where the current and voltage are common values, respectively, for the components.
Figure 1.14 Some possible and impossible configurations using ideal components.
Figure 1.15 Some possible circuits involving only one or two components that are connected consistently. In the first and second circuits, where there is a current and a voltage source, the sources do not produce any power. However, they still provide the current and voltage values, in accordance with their definitions. In the third circuit, the voltage source absorbs power (100 W), while the current source delivers power (100 W).
Figure 1.16 Two simple circuits that can be interpreted incorrectly as impossible. In fact, both two circuits are possible and they involve consistent voltage and current values. In the first circuit, a voltage drop (by an amount of
V) exists across the resistor. In the second circuit, a nonzero current (
A) flows through the resistor. These values can easily be found by applying Kirchhoff's laws, as described in the next chapter.
Chapter 5: Black-Box Concept
Figure 5.1 Thévenin and Norton equivalent circuits.
Figure 5.2 Open-circuit and short-circuit cases to find the values in a Thévenin equivalent circuit.
Figure 5.3 Open-circuit and short-circuit cases to find the values in a Norton equivalent circuit.
Chapter 7: Steady-State Analysis of Time-Harmonic Circuits
Figure 7.1 Steady-state equivalents of capacitors and inductors when only DC sources are involved.
Figure 7.2 A representation of passage from transient to steady state in an AC circuit.
Figure 7.3 Sinusoidal voltage and current sources.
Figure 7.4 A resistor connected to a sinusoidal voltage source.
Figure 7.5 A capacitor connected to a sinusoidal voltage source.
Figure 7.6 A capacitor connected to a sinusoidal current source at different frequencies.
Figure 7.7 An inductor connected to a sinusoidal current source.
Introduction to Electrical Circuit Analysis
Özgür Ergül
Middle East Technical University, Ankara, Turkey
This edition first published 2017
© 2017 John Wiley and Sons Ltd
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by law.Advice on how to obtain permision to reuse material from this title is available at http://www.wiley.com/go/permissions.
The right of Özgür Ergül to be identified as the author of this work has been asserted in accordance with law.
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Library of Congress Cataloging-in-Publication data applied for
ISBN: 9781119284932
Cover design by Wiley
Cover image: (Circuit Board) © ratmaner/Gettyimages; (Electronic Components)
© DonNichols/Gettyimages; (Formulas) © Bim/Gettyimages
For my wife Ayça, three cats (Boncuk, Pepe, and Misket), and the dog, who all suffered during the writing of this book
Important Units
Ampere (A)
Coulomb (C)
Farad (F): C/V
Henry (H): weber/A
Hertz (Hz): 1/s
Joule (J): N m
kg
/s
kilo (k
):
meter (m)
micro (
):
milli (m
):
Newton (N): kg m/s
Conventions with Examples
Fractions:
A
A
A
Irrational numbers:
A
A
A
Approximation:
A
A
Scientific notation:
Preface
Since the first known electricity experiments more than 25 centuries ago by Thales of Miletus, who believed that there should be better ways than mythology to explain physical phenomena, humankind has worked hard to understand and use electricity in many beneficial ways. The last three centuries have seen rapid developments in understanding electricity and related concepts, leading to constantly accelerating technology advancements in the last several decades. Today, most of us simply cannot live without electricity, and it is almost ubiquitous in daily life. We are so attached to and dependent on electricity that there are even post-apocalyptic fiction movies and film series based on sudden electrical power blackouts. And they are terrifying.
Electricity is one of a few subjects with which we have a strange relationship. The more we use it, less we know about it. Electrical and electronic devices, where electricity is somehow used to produce beneficial outputs, are a closed book to most of us, until we open them (not a suggested activity!) and see that they contain incredibly small but highly intelligent parts. These parts, some of which once had huge dimensions and even filled entire rooms, are now so tiny that we are able to place literally billions of them (at the time of writing) in a smartphone microprocessor. One billion is a huge number; at a rate of one a second, it takes 31 years to count. And we are able to put these uncountable (OK, countable, but not feasibly so) numbers of components together and make them work in harmony for our enjoyment. Yet most of us know little about how they actually work.
The topic of circuit analysis has naturally developed in parallel with electrical circuits and devices starting from centuries ago. To provide some intuition, Ohm's law has been known since 1827, while Kirchhoff's laws were described in 1845. Nodal and mesh analysis methods have been developed and used for systematically applying Kirchhoff's laws. Phasor notation is borrowed from mathematics to deal with time-harmonic circuits. These fundamental laws have not changed, and they will most probably remain the same in the coming years. In general, basic laws describe everything when they are wisely used. Hence, more and more sophisticated circuits in future technologies will also benefit from them, independent of their complexity.
Circuit analysis is naturally linked to all other technologies involving electricity, including medical, automotive, computer, energy, and aerospace industries, as well as all subcategories of electrical and electronic engineering. Interestingly, with the rapid development of technology, we tend to learn fundamental laws more superficially. One can identify two major factors, among many:
As circuits become more complicated and specialized, we are attracted and guided to focus on higher-level representations, such as inputs and outputs of microchips with well-defined functions, without spending time on fundamental laws.
Great advancements in circuit-solver software “eliminate” the need to fully understand fundamental laws and appreciate their importance in everyday life, reducing circuit analysis to numbers.
Unfortunately, without absorbing fundamental laws, we tend to make major conceptual mistakes. Most instructors have had a student who offers infinite energy by rotating something (usually a car wheel if s/he is a mechanical engineering student), disregarding the conservation of energy. It is often a confusing issue for a biomedical student to appreciate the necessity of grounding for medical safety. And it is probably a computational mistake but not a new technology if a circuit analyzer program provides a negative resistor value. The aim of this book is to gradually construct the basics of circuit analysis, even though they are not new material, while accelerating our understanding of electrical circuits and all technologies using electricity.
This is intended as an introductory book, mainly designed for college and university students who may have different backgrounds and, for whatever reason, need to learn about circuits for the first time. It mainly focuses on a few essential components of electrical components, namely,
resistors,
independent voltage and current sources,
dependent sources (as closed components, not details),
capacitors, and
inductors.
On the other hand, transistors, diodes, OP-AMPs, and similar popular and inevitable components of modern circuits, which are fixed topics (and even starting points) in many circuit books, are not detailed. The aim of this book is not to teach electrical circuits, but rather to teach how to analyze them. From this perspective, the components listed above provide the required combinations and possibilities to cover the fundamental techniques, namely,
Ohm's and Kirchhoff's laws,
nodal analysis,
mesh analysis,
the black-box approach and Thévenin/Norton equivalent circuits.
This book also covers the analysis methods for both DC and AC cases in transient and steady states.
To sum up, the technology that is covered in this book is well established. The analysis methods and techniques, as well as components, listed above have been known for decades. However, the fundamental methods and components need to be known in sufficient depth in order to understand how electrical circuits work, including state-of-the-art devices and their ingredients. Many books in this area are dominated by an increasing number of new electrical and electronic components and their special working principles, while the fundamental techniques are squeezed into short descriptions and limited to a few examples. Therefore, the purpose of this book is to provide sufficient basic discussion and hands-on exercises (with solutions at the back of the book) before diving into modern circuits with higher-level properties.
Enjoy!
About the Companion Website
This book is accompanied by a companion website:
www.wiley.com/go/ergul4412
The website includes:
Exercise sums and solutions
Videos
Chapter 1Introduction
We start with the iconic figure (Figure 1.1), which depicts a bulb connected to a battery. Whenever the loop is closed and a full connection is established, the bulb comes on and starts to consume energy provided by the battery. The process is often described as the conversion of the chemical energy stored in the battery into electrical energy that is further released as heat and light by the bulb. The connection between the bulb and battery consists of two wires between the positive and negative terminals of the bulb and battery. These wires are shown as simple straight lines, whereas in real life they are usually coaxial or paired cables that are isolated from the environment.
Figure 1.1 A simple circuit involving a bulb connected to a battery. The connection between the bulb and battery is shown via simple lines.
The purpose of this first chapter is to introduce basic concepts of electrical circuits. In order to understand circuits, such as the one above, we first need to understand electric charge, potential, and current. These concepts provide a basis for recognizing the interactions between electrical components. We further discuss electric energy and power as fundamental variables in circuit analysis. The time and frequency in circuits, as well as related limitations, are briefly considered. Finally, we study conductivity and resistance, as well as resistors, independent sources, and dependent sources as common components of basic circuits.
1.1 Circuits and Important Quantities
An electrical circuit is a collection of components connected via metal wires. Electrical components include but are not limited to resistors, inductors, capacitors, generators (sources), transformers, diodes, and transistors. In circuit analysis, wire shapes and geometric arrangements are not important and they can be changed, provided that the connections between the components remain the same with fixed geometric topology. Wires often meet at intersection points; a connection of two or more wires at a point is called a node. Before discussing how circuits can be represented and analyzed, we first need to focus on important quantities, namely, electric charge, electric potential, and current, as well as energy and power.
Figure 1.2 A circuit involving connections of four components labeled from to . From the circuit-analysis perspective, connection shapes are not important, and these three representations are equivalent.
1.1.1 Electric Charge
Electric charge is a fundamental property of matter to describe force interactions among particles. According to Coulomb's law, there is an attractive (negative) force between a proton and an electron given by
which is significantly larger than (around times) the gravity between these particles. In the above, is the distance between the proton and electron, given in meters (m). This law can be rewritten by using Coulomb's constant
as
where
are the electrical charges of the proton and electron, respectively, in units of coulombs (C). Coulomb's constant enables the generalization of the electric force between any arbitrary charges and as
where and are assumed to be point charges (theoretically squeezed into zero volumes), which are naturally formed of collections of protons and electrons.
The definition of the electric force above requires at least two charges. On the other hand, it is common to extend the physical interpretation to a single charge. Specifically, a stationary charge is assumed to create an electric field (intensity) that can be represented as
where is now the distance measured from the location of the charge. This electric field is in the radial direction, either outward (positive) or inward (negative), depending on the type (sign) of the charge. Therefore, we assume that an electric field is always formed whether there is a second test charge or not. If there is at a distance , the electric force is now measured as
either as repulsive (if and have the same sign) or attractive (if and have different signs).
Figure 1.3 Electric field lines created individually by a positive charge and a negative charge. An electric field is assumed to be created whether there is a second test charge or not. If a test charge is located in the field, repulsive or attractive force is applied on it.
The definition of the electric field is so useful that, in many cases, even the sources of the field are discarded. Consider a test charge exposed to some electric field . The force on can be calculated as
without even knowing the sources creating the field. This flexibility further allows us to define the electric potential concept, as discussed below.
1.1.2 Electric Potential (Voltage)
Consider a charge in some electric field created by external sources. Moving the charge from a position to another position may require energy if the movement is opposite to the force due to the electric field. This energy can be considered to be absorbed by the charge. If the movement and force are aligned, however, energy is extracted from the charge. In general, the path from to may involve absorption and release of energy, depending on the alignment of the movement and electric force from position to position. In any case, the net energy absorbed/released depends on the start and end points, since the electric field is conservative and its line integral is path-independent.
Figure 1.4 Movement of a charge in an electric field created by external sources. The energy absorbed or released by the charge does not depend on the path but depends on the potentials at the start and end points. The electric potential (voltage) is always defined between two points, while selecting a reference point as a ground enables unique voltage definitions at all points.
Electric potential (voltage) is nothing but the energy considered for a unit charge (1 C) such that it is defined independent of the testing scheme. Specifically, the work done in moving a unit charge from a point to another point is called the voltage between and . Conventionally, we have
as the voltage between and , corresponding to the work done in moving the charge from to . If , then work must be done to move the charge (the energy of the charge increases). On the other hand, if , then the work done is negative, indicating that energy is actually released due to the movement of the charge. The unit of voltage is the volt (V), and 1 volt is 1 joule per coulomb (J/C).
A proper voltage definition always needs two locations and a polarity definition. Considering three separate points , , and , we have
and
The equality above is a result of the conservation of the electric energy (conservative electric field). On the other hand, , , and are not yet uniquely defined. In order to simplify the analysis in many cases, a location can be selected as a reference with zero potential. In circuit analysis, such a location that corresponds to a node is called ground, and it allows us to define voltages at all other points uniquely. For example, if in the above, we have .
1.1.3 Electric Current
A continuous movement of electric charges is called electric current. Conventionally, the direction of a current flow is selected as the direction of movement of positive charges. The unit of current is the ampere (A), and 1 ampere is 1 coulomb per second (C/s). Formally, we have
where and represent charge and time, respectively. The current itself may depend on time, as indicated in this equation. But, in some cases, we only have steady currents, , where does not depend on time.
Different types of current exist, as discussed in Section 1.2.1. In circuit analysis, however, we are restricted to conduction currents, where free electrons of metals (e.g., wires) are responsible for current flows. Since electrons have negative charges and an electric current is conventionally defined as the flow of positive charges, electron movements and the current direction on a wire are opposite to each other. Indeed, when dealing with electrical circuits, using positive current directions is so common that the actual movement of charges (electrons) is often omitted.
When charges move, they interact with each other differently such that they cannot be modeled only with an electric field. For example, two parallel wires carrying currents in opposite directions attract each other, even though they do not possess any net charges considering both electrons and protons. Similar to the interpretation that electric field leads to electric force, this attraction can be modeled as a magnetic field created by a current, which acts as a magnetic force on a test wire. Electric and magnetic fields, as well as their coupling as electromagnetic waves, are described completely by Maxwell's equations and are studied extensively in electromagnetics.
Figure 1.5 On a metal wire, the conventional current direction, which is defined as positive charge flow, is the opposite of the actual electron movements. In a circuit, voltages are defined at the nodes, as well as across components, using the sign convention.
1.1.4 Electric Voltage and Current in Electrical Circuits
In electrical circuit analysis, charges, fields, and forces are often neglected, while electric voltage and electric current are used to describe all phenomena. This is completely safe in the majority of circuits, where individual behaviors of electrons are insignificant (because the circuit dimensions are large enough with respect to particles), while the force interactions among wires and components are negligible (because the circuit is small enough with respect to signal wavelength). The behavior of components is also reduced to simple voltage–current relationships in order to facilitate the analysis of complex circuits. The limitations of circuit analysis using solely voltages and currents are discussed in Section 1.6.
In an electrical circuit, voltages are commonly defined at nodes, while currents flow through wires and components. A wire is assumed to be perfectly conducting (see Section 1.2.4) such that no voltage difference occurs along it, that is, the voltage is the same on the entire wire. This is the reason why their shapes are not critical. On the other hand, a voltage difference may occur across a component, depending the type of the component and the overall circuit. For unique representation of a node voltage, a reference node should be selected as a ground. However, the voltage across a component can always be defined uniquely since it is based on two or more (if the component has multiple terminals) points.
In circuit analysis, voltages and currents are usually unknowns to be found. Since they are not known, in most cases, their direction can be arbitrarily selected. When the solution gives a negative value for a current or a voltage, it is understood that the initial assumption is incorrect. This is never a problem at all. For consistency, however, it is useful to follow a sign convention by fixing the voltage polarity and current direction for any given component. In the rest of this book, the current through a component is always selected to flow from the positive to the negative terminal of the voltage.
1.1.5 Electric Energy and Power of a Component
Consider a component with a current and voltage , defined in accordance with the sign convention. If , one can assume that positive charges flow from the positive to the negative terminal of the component. In addition, if , these positive charges encounter a drop in their potential values, that is, they release energy. This energy must be somehow used (consumed or stored) by the component. Formally, we define the energy of the component as
where the time integral is used to account for all charges passing during , assuming that the component is used from time . If , it is understood that the component consumes net energy during the time interval . On the other hand, if , the component produces net energy in the same time interval. We note that the unit of energy is the joule, as usual.
Energy as defined above provides information in selected time intervals. In many cases, however, it is required to know the behavior (change of the energy) of the component at a particular time. For a device with a current and voltage , this corresponds to the time derivative of the energy, namely the power of the device, defined as
Specifically, for a given component, its power is defined as the product of its voltage and current. The unit of power is the watt (W), where 1 watt is 1 volt ampere (V A) or 1 joule per second (J/s). If , the component absorbs energy at that specific time. Otherwise (i.e., if ), the component produces energy.
Example 1
Electric power and energy are often underestimated. Consider an 80 W bulb, which is on for 24 hours. Using the energy spent by the bulb, how many meters can a 1000 kg object be lifted?
Solution
The energy spent by the bulb is
Then, assuming m/s, and using for the potential energy, we have
Example 2
There are approximately bulbs on earth. Assuming an average on period of 6 hours and 50 W average power, find the amount of coal required to produce the same amount of energy for 1 day. Assume that the thermal energy of coal is J/kg and the efficiency of the conversion of the energy is .
Solution
The required energy for the bulbs per day is
The corresponding amount of coal can be found as
Example 3
The voltage and current of a device are given by V and A, respectively, as functions of time. Find the maximum power of the device.
Solution
We have
as the power of the device. We note that
In order to find the maximum point for the power, we use
leading to
Then the maximum power is
Figure 1.6 Power of a device for given current and voltage across it.
Exercise 1
A device has a power of 60 W when it is active and 10 W when it is on standby. An engineer measures that it spends a total of 2664 kJ energy in 24 hours. How many hours was the device actively used?
1.1.6 DC and AC Signals
Until now, we have considered the time concept in circuits for studying energy (which needs to be defined in time intervals) and power (which may depend on time). In fact, the time dependence of the power of a component corresponds to the time dependence of its voltage and/or current. This brings us to the definition of direct current (DC) and alternating current (AC), which are important terms in describing and categorizing circuits and their components.
DC means a unidirectional flow of electric charges, leading to a current only in a single direction. However, the term ‘DC signal’ is commonly used to describe voltages and other quantities that do not change polarity. DC signals are produced by DC sources, whose voltages or currents are assumed to be fixed in terms of direction and amplitude. Examples of DC sources are batteries and dynamos. Voltage and current values of these sources may have very slight variations with respect to time, which are often neglected in circuit analysis.
