Introduction to Electric Circuits (eBook)

Ray Powell (Autor)

eBook Download: EPUB

1995 | 1. Auflage
264 Seiten
Elsevier Science (Verlag)
978-0-08-053509-8 (ISBN)

Infos

An Introduction to Electric Circuits is essential reading for first year students of electronics and electrical engineering who need to get to grips quickly with the basic theory. This text is a comprehensive introduction to the topic and, assuming virtually no knowledge, it keeps the mathematical content to a minimum.

As with other textbooks in the series, the format of this book enables the student to work at their own pace. It includes numerous worked examples throughout the text and graded exercises, with answers, at the end of each section.

Inhalt

Front Cover 1
Introduction to Electric Circuits 4
Copyright Page 5
Contents 8
Preface 12
Acknowledgements 14
Chapter 1. Units and dimensions 16
1.1 Introduction 16
1.2 The Systéme International d'Unités 16
1.3 Dimensional analysis 19
1.4 Multiples and submultiples of units 21
1.5 Self-assessment test 23
1.6 Problems 23
Chapter 2. Electric circuit elements 25
2.1 Electricity 25
2.2 Electric circuits 26
2.3 Circuit elements 26
2.4 Lumped parameters 49
2.5 Energy stored in circuit elements 50
2.6 Power dissipated in circuit elements 51
2.7 Self-assessment test 52
2.8 Problems 53
Chapter 3. DC circuit analysis 55
3.1 Introduction 55
3.2 Definition of terms 55
3.3 Kirchhoff's current law 57
3.4 Kirchhoff's voltage law 57
3.5 The Principle of Superposition 60
3.6 Thevenin's theorem 63
3.7 Norton's theorem 67
3.8 The Maximum Power Transfer Theorem 69
3.9 Delta-star transformation 71
3.10 Star-delta transformation 74
3.11 Self-assessment test 76
3.12 Problems 77
Chapter 4. Single-phase a.c. circuits 81
4.1 Alternating quantities 81
4.2 Single-phase a.c. circuits in the steady state 87
4.3 Series a.c. circuits 92
4.4 Complex notation 97
4.5 Parallel a.c. circuits 106
4.6 Series-parallel a.c. circuits 110
4.7 Power in single-phase a.c. circuits 112
4.8 Self-assessment test 118
4.9 Problems 120
Chapter 5. Three-phase a.c. circuits 122
5.1 Introduction 122
5.2 Generation of three-phase voltage 122
5.3 Phase sequence 123
5.4 Balanced three-phase systems 124
5.5 Power in balanced three-phase circuits 130
5.6 Self-assessment test 135
5.7 Problems 137
Chapter 6. Resonance 138
6.1 Series resonance 138
6.2 Parallel resonance 148
6.3 Self-assessment test 152
6.4 Problems 153
Chapter 7. Nodal and mesh analysis 156
7.1 Introduction 156
7.2 Matrices 156
7.3 Nodal voltage analysis 162
7.4 Mesh current analysis 173
7.5 Self-assessment test 183
7.6 Problems 183
Chapter 8 Transient analysis 187
8.1 Introduction 187
8.2 Circuits containing resistance and inductance 187
8.3 Circuits containing resistance and capacitance 196
8.4 The Laplace transform 207
8.5 Self-assessment test 216
8.6 Problems 217
Chapter 9. Two-port networks 220
9.1 Introduction 220
9.2 The impedance or z-parameters 220
9.3 The admittance or y-parameters 223
9.4 The hybrid or h-parameters 225
9.5 The inverse hybrid or g-parameters 226
9.6 The transmission or ABCD-parameters 228
9.7 The inverse transmission parameters 229
9.8 Cascaded two-port networks 234
9.9 Characteristic impedance (Z0) 240
9.10 Image impedances 241
9.11 Insertion loss 242
9.12 Propagation coefficient (.') 244
9.13 Self-assessment test 245
9.14 Problems 246
Chapter 10. Duals and analogues 248
10.1 Duals of circuit elements 248
10.2 Dual circuits 249
10.3 Analogues 253
10.4 Self-assessment test 256
Answers to self-assessment tests and problems 257
Index 261

Textauszug

1

Units and dimensions

1.1 INTRODUCTION

In electrical and electronic engineering, as in all branches of science and engineering, measurement is fundamentally important and two interconnected concepts are involved. First we need to know what it is that we wish to measure, and this is called a quantity. It may be a force or a current or a length (of a line say). The quantity must then be given a unit which indicates its magnitude, that is, it gives a measure of how strong the force is or how big the current is or how long the line is. In any system of units a certain number of physical quantities are arbitrarily chosen as the basic units and all other units are derived from these.

1.2 The SYSTÈME INTERNATIONAL D’UNITÉS

This system of units, abbreviated to ‘the SI’, is now in general use and in this system seven basic quantities, called dimensions, are selected. These are mass, length, time, electric current, thermodynamic temperature, luminous intensity and amount of substance, the first four of which are of particular importance to us in this book. In addition to these seven basic quantities there are two supplementary ones, namely plane angle and solid angle. All of these are shown, together with their unit names, in Table 1.1. These units are defined as follows:

Table 1.1

Quantity

Unit

Unit abbreviation

Mass

kilogram

kg

Length

metre

m

Time

second

s

Electric current

ampere

A

Thermodynamic temperature

Kelvin

K

Luminous intensity

candela

cd

Amount of substance

mole

mol

Plane angle

radian

rad

Solid angle

steradian

sr

kilogram (kg):

the mass of an actual piece of metal (platinum-iridium) kept under controlled conditions at the international bureau of weights and measures in Paris

metre (m):

the length equal to 1 650 763.73 wavelengths in vacuo of the radiation corresponding to the transition between the levels 2p10 and 5d5 of the krypton-86 atom

second (s):

the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom

ampere (A):

that constant current which, when maintained in each of two infinitely long parallel conductors of negligible cross-sectional area separated by a distance of 1 m in a vacuum, produces a mutual force between them of 2 × 10−7 N per metre length

kelvin (K):

the fraction 1/273.16 of the thermodynamic temperature of the triple point of water

candela (ed):

the luminous intensity, in the perpendicular direction, of a surface of area 1/600 000 m2 of a black body at the temperature of freezing platinum under a pressure of 101 325 Pa

mole (mol):

the amount of substance of a system which contains as many specified elementary particles (i.e. electrons, atoms, etc.) as there are atoms in 0.012 kg of carbon-12

radian (rad):

the plane angle between two radii of a circle which cut off on the circumference an arc equal to the radius

steradian (sr):

that solid angle which, having its vertex at the centre of a sphere, cuts off an area of the surface of the sphere equal to that of a square with sides equal to the radius.

The scale temperature (degree Celsius) is the thermodynamic temperature minus 273.16, so that 0 °C corresponds to 273.16 K and 0 K corresponds to −273.16 °C. Note that we write 0 K and 273 K, not 0 °K nor 273 °K.

As an example of how the other units may be derived from the basic units, velocity is length divided by time. It is usual to write these dimensional equations using square brackets, with the basic quantities being in capital letters and the derived quantities being in lower case letters. Thus for this example we can write [v] = [L]/[T], or

(1.1)

Example 1.1: Obtain the dimensions of (1) acceleration, (2) force, (3) torque.

Solution

1. Acceleration is the rate of change of velocity, so is velocity/time. Thus [a] = [v]/[T]. From Equation (1.1) we have that [v] = [LT−1], so

or

(1.2)

2. Force is mass times acceleration. Thus [f] = [M][a]. From Equation (1.2) we have that [a] = [LT−2], so

or

(1.3)

3. Torque is force times the length of the torque arm. Thus [t] = [f][L]. From Equation (1.3) we have that [f] = [MLT−2], so

or

(1.4)

Example 1.2: Determine the dimensions of (1) energy, (2) power.

Solution

1. Energy is work, which is force multiplied by distance. Thus [w] = [f][L]. From Equation (1.3) we have that [f] = [MLT−2], so

or

(1.5)

2. Power is energy divided by time. Thus [p] = [w]/[T]. From Equation (1.5) we have that [w] = [ML2T−2], so

or

(1.6)

Example 1.3: Find the dimensions of (1) electric charge, (2) electric potential difference.

Solution

1. Electric charge is electric current multiplied by time. Thus [q] = [A][T], so

(1.7)

2. When a charge of 1 coulomb is moved through a potential difference of 1 volt the work done is 1 joule of energy, so that electric potential difference is energy divided by electric charge. Thus [pd] = [w]/[q]. From Equation (1.5) we have that [w] = [ML2T−2], and from Equation (1.7) we see that [q] = [A T], so

or

(1.8)

Example 1.4: Obtain the dimensions of (1) resistance, (2) inductance, (3) capacitance.

Solution

1. Resistance is electric potential difference divided by electric current. From Equation (1.8) the dimensions of electric potential difference are [M L2 T−3 A−1]. Thus [r] = [M L2 T−3 A−1]/[A], so

(1.9)

2. The magnitude of the emf induced in a coil of inductance L when the current through it changes at the rate of I ampere in t seconds is given by e = LI/t, where e is measured in volts and is a potential difference. Thus the dimensions of L are given by [l] = [pd][T]/[A]. From Equation (1.8), [pd] = [ML2T−3A−1], so

(1.10)

3. Capacitance (C) is electric charge (Q) divided by electric potential difference (V). From Equation (1.7), [q] = [A T]. From Equation (1.8), [pd] = [M L2 T−3 A−1]. Thus [c] = [A T]/[M L2 T−3 A−1], so

(1.11)

1.3 DIMENSIONAL ANALYSIS

A necessary condition for the correctness of an equation is that it should be dimensionally balanced. It can be useful to perform a dimensional analysis on equations to check their correctness in this respect. This can be done by checking that the dimensions of each side of an equation are the same.

Example 1.5: The force between two charges q1 and q2 separated by a distance d in a vacuum is given by F = q1q2/4π∈0d2, where ∈0 is a constant whose dimensions are [M L−3 T4 A2]. Check the dimensional balance of this equation.

Solution

The left-hand side of the equation is simply the force F and from Example 1.1 (2) we see that its dimensions are [MLT−2].

The dimensions of the right-hand side are [q][q]/[4][π][∈0][d2]. From Example 1.3 (1) we see that the dimensions of electric charge [q] are [A T]. Numbers are dimensionless so that the figure 4 and the constant π have no dimensions. We are told in the question that the dimensions of ∈0 are [M−1 L−3 T4 A2]. The...

Produkt-Details

• Erscheint lt. Verlag: 17.9.1995
• Sprache: englisch
• Themenwelt: Kunst / Musik / Theater ► Design / Innenarchitektur / Mode
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Technik ► Elektrotechnik / Energietechnik
• ISBN-10: 0-08-053509-7 / 0080535097
• ISBN-13: 978-0-08-053509-8 / 9780080535098