John Bird

Electrical circuit theory and technology

Preface Section 1 Basic Electrical Engineering Principles Units associated with basic electrical quantities An introduction to electric circuits Resistance variation Batteries and alternative sources of energy Series and parallel networks Capacitors and capacitance Magnetic circuits. Electromagnetism Electromagnetic induction Electrical measuring instruments and measurements Semiconductor diodes Transistors Main formulae for Part 1 Section 2 Electrical Principles and Technology D.c. circuit theory Alternating voltages and currents Single-phase series a.c. circuits Single-phase parallel a.c. circuits D.c. transients Operational amplifiers Three phase systems Transformers D.c. machines Three-phase induction motors Main formulae for Part 2 Part 3 Advanced Circuit Theory and Technology Revision of complex numbers Application of complex numbers to series a.c. circuits Application of complex numbers to parallel a.c. circuits Power in a.c. circuits A.c. bridges Series resonance and Q-factor Parallel resonance and Q-factor Introduction to network analysis Mesh-current and nodal analysis The superposition theorem Thevenins and Nortons theorems Delta-star and star-delta transformations Maximum power transfer theorems and impedance matching Complex waveforms A numerical method of harmonic analysis Magnetic materials Dielectrics and dielectric loss Field theory Attenuators Filter networks Magnetically coupled circuits Transmission lines Transients and Laplace transforms Main formulae for Part 3 Part 4 General reference Standard electrical quantities - their symbols and units Greek alphabet Common prefixes Resistor colour coding and ohmic values Index

Electrical measuring instruments and measurements

This chapter focuses on electrical measuring instruments and measurements. To detect electrical quantities, such as current, voltage, resistance or power, it is necessary to transform an electrical quantity or condition into a visible indication. This is done with the aid of instruments (or meters) that indicate the magnitude of quantities either by the position of a pointer moving over a graduated scale, known as an analog instrument, or in the form of a decimal number, known as a digital instrument. All analog electrical indicating instruments require three essential devices, namely, a deflecting or operating device, a controlling device, and a damping device. There is no difference between the basic instrument used to measure current and voltage as both uses a milli ammeter as their basic part. This is a sensitive instrument that gives FSD for currents of only a few milli amperes. When an ammeter is required to measure currents of larger magnitude, a proportion of the current is diverted through a low value resistance connected in parallel with the meter. Such a diverting resistance is called a shunt.

a.c. circuit analysis

This chapter presents the alternating circuit analysis. Circuit theory and analysis of alternating circuits is invariably achieved using complex numbers (otherwise known as symbolic or j ). The effect of multiplying a phasor by j is to rotate it in a positive direction on an Argand diagram through 90° without altering its length. There are a number of circuit theorems that have been developed for solving problems in alternating current electrical networks. These include: (1) the superposition theorem, (2) Thevenins theorem, (3) Nortons theorem, and (4) the maximum power transfer theorem. As a preliminary to using circuit theorems, star-delta and delta-star transformations may be used. Any network containing one or more current or voltage sources and linear impednaces can be reduced to a Thevenin equivalent circuit. When a load is connected to the terminals of this equivalent circuit, power is transferred from the circuit to the load. Sometimes networks are complicated and may be transformed using delta-star or star-delta transformations as a preliminary to using a circuit theorem.

Speed and velocity

This chapter explains the concept of speed and velocity. Speed is the rate of covering distance. The usual units for speed are meters per second, or kilometers per hour. The symbol for the SI unit of speed and velocity is written as m s −1 , called the index notation. One of the exceptions is when labeling the axes of graphs, when two oblique occur, and in this case the index notation is used. In general, the average speed of an object traveling between points M and N is given by the slope of line MN on the distance–time graph. One way of giving data on the motion of an object is graphically. A graph of distance traveled, against time is called a distance–time graph. The velocity of an object is the speed of the object in a specified direction. A graph of velocity against time is called a velocity–time graph.

10 – Transposition of formulae

In mathematics, engineering and science, formulae are used to relate physical quantities to each other. They provide rules so that if we know the values of certain quantities, we can calculate the values of others. In this unit we discuss how formulae can be transposed, or transformed, or rearranged. In order to master the techniques explained here it is vital that you undertake plenty of practice exercises so that they become second nature. After reading this text, and/or viewing the video tutorial on this topic, you should be able to: • transpose formulae in order to make other variables the subject of the formula

32 – The superposition theorem

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45 – Transients and Laplace transforms

At the end of this chapter you should be able to: ž determine the transient response of currents and voltages in R–L, R–C andL–R–C series circuits using differential equations ž define the Laplace transform of a function ž use a table of Laplace transforms of functions commonly met in electrical engineering for transient analysis of simple networks ž use partial fractions to deduce inverse Laplace transforms ž deduce expressions for component and circuit impedances in the s-plane given initial conditions ž use Laplace transform analysis directly from circuit diagrams in the s-plane ž deduce Kirchhoff law equations in the s-plane for determining the response of R–L, R–C andL–R–C networks, given initial conditions ž explain the conditions for which an L–R–C circuit response is over, critical, under or zero-damped and calculate circuit responses ž predict the circuit response of an L–R–C network, given non-zero initial conditions

Interference and diffraction

This chapter focuses on interference and diffraction in waves. At the point where two waves cross, the total displacement is the vector sum of the individual displacements because of each wave at that point. This is the principle of superposition. If the two waves are either both transverse or both longitudinal, interference effects may be observed. Interference takes place between the two waves and a standing or stationary wave is produced. Standing waves may be set up in a string, for example, when a wave is reflected at the end of the string and is super imposed on the incoming wave. Under these circumstances, standing waves are produced only for certain frequencies. Moreover, the nodes may not be perfect because the reflected wave can have slightly reduced amplitude. Diffraction is a phenomenon where waves can spread round obstacles into regions that would be in shadow if the energy travelled exactly in straight lines.

Scalar and vector quantities

This chapter discusses the quantities used in engineering and science, and can be divided into two groups. Scalar quantities have a size or magnitude only and need no other information to specify them. Thus, 10 cm, 50 s, 7 l, and 3 kg are all examples of scalar quantities. Vector quantities have both a size or magnitude and a direction, called the line of action of the quantity. Thus, a velocity of 50 km/h due east, on acceleration of 9.8 m/s 2 vertically downward, and a force of 15 N at an angle of 30° are all examples of vector quantities.

21 – d.c. machines

Publisher Summary This chapter provides an overview on direct current (d.c.). When the input to an electrical machine is electrical energy and the output is mechanical energy, the machine is called an electric motor. Thus, an electric motor converts electrical energy into mechanical energy. The efficiency of an electrical machine is the ratio of the output power to the input power and is usually expressed as a percentage. There are many conductors on the rotating partof a d.c. machine, and these are attached to many commutator segments. The basic parts of any d.c.machine area stationary part called the stator and a rotating part called the armature mounted in bearings housed in the stator. Furthermore, the two principal generator characteristics are the generated voltage/field current characteristic, called the open-circuit characteristic and the terminal voltage/load current characteristic, called the load characteristic.