Aircraft Electrical and Electronic Systems (Principles, Maintenance & Operation) PDF

Aircraft Electrical and Electronic Systems Principles, operation and maintenance Mike Tooley David Wyatt Brief Table of Contents Copyright Page Preface Acknowledgements Chapter 1. Electrical fundamentals Chapter 2. Electronic fundamentals...

Aircraft Electrical and Electronic Systems Principles, operation and maintenance Mike Tooley David Wyatt Brief Table of Contents Copyright Page Preface Acknowledgements Chapter 1. Electrical fundamentals Chapter 2. Electronic fundamentals Chapter 3. Digital fundamentals Chapter 4. Generators and motors Chapter 5. Batteries Chapter 6. Power supplies Chapter 7. Wiring and circuit protection Chapter 8. Distribution of power supplies Chapter 9. Controls and transducers Chapter 10. Engine systems Chapter 11. Fuel management Chapter 12. Lights Chapter 13. Cabin systems Chapter 14. Airframe monitoring, control and indicating systems Chapter 15. Warning and protection systems Chapter 16. Fire and overheat protection Chapter 17. Terrain awareness warning system (TAWS) Chapter 18. Flight data and cockpit voice recorders Chapter 19. Electrical and magnetic fields Chapter 20. Continuing airworthiness Index Table of Contents Copyright Page Preface Acknowledgements Chapter 1. Electrical fundamentals 1.1. Electron theory 1.2. Electrostatics and capacitors 1.2.1. Electric fields 1.3. Direct current 1.4. Current, voltage and resistance 1.5. Power and energy 1.6. Electromagnetism and inductors Example 1.16 1.6.1. Electromagnetic induction 1.6.2. Faraday’s and Lenz’s laws 1.6.3. Self-inductance and mutual inductance 1.6.4. Inductors 1.7. Alternating current and transformers 1.7.1. Frequency and periodic time 1.7.2. Average, peak, peak–peak, and r.m.s. values 1.7.3. Three-phase supplies 1.7.4. Reactance 1.7.5. Impedance 1.7.6. Resonance 1.7.7. Power factor  1.7.8. Transformers 1.8. Safety Other hazards 1.9. Multiple choice questions Chapter 2. Electronic fundamentals 2.1. Semiconductor theory 2.1.1. Temperature effects 2.2. Diodes 2.2.1. Diode characteristics 2.2.2. Zener diodes 2.2.3. Silicon-controlled rectifiers 2.2.4. Light-emitting diodes 2.2.5. Rectifiers 2.3. Transistors 2.3.1. Bias and current flow 2.3.2. Transistor characteristics 2.3.3. Transistor operating configurations 2.3.4. Current gain 2.4. Integrated circuits 2.5. Multiple choice questions Chapter 3. Digital fundamentals 3.1. Logic gates 3.1.1. Buffers  3.1.2. AND logic 3.1.3. OR logic 3.1.4. NAND logic 3.1.5. NOR logic 3.1.6. Exclusive-OR logic 3.1.7. Exclusive-NOR logic 3.1.8. Inverted inputs and outputs 3.2. Combinational logic systems 3.2.1. Landing gear warning logic 3.3. Monostable devices 3.3.1. APU starter logic 3.4. Bistable devices 3.5. Decoders 3.5.1. Gillham interface and Gillham code 3.6. Encoders 3.7. Multiplexers 3.8. Bus systems 3.8.1. Serial bus principles 3.8.2. ARINC 429 3.9. Computers 3.9.1. Memories and data storage 3.10. Multiple choice questions Chapter 4. Generators and motors Chapter 5. Batteries  5.1. Overview 5.2. Storage cells 5.3. Lead-acid batteries 5.3.1. Construction 5.3.2. Charging/discharging 5.3.3. Maintenance 5.3.4. Sealed batteries 5.4. Nickel-cadmium batteries 5.4.1. Construction 5.4.2. Charging 5.4.3. Discharging 5.4.4. Maintenance 5.5. Lithium batteries 5.6. Nickel-metal hydride batteries 5.7. Battery locations 5.8. Battery venting 5.9. Battery connections 5.10. Multiple choice questions Chapter 6. Power supplies 6.1. Regulators 6.1.1. Vibrating contact regulator 6.1.2. Carbon-pile regulator 6.1.3. Electronic voltage regulator 6.2. External power 6.2.1. Power conversion  6.3. Inverters 6.4. Transformer rectifier units 6.5. Transformers 6.6. Auxiliary power unit (APU) 6.7. Emergency power 6.8. Multiple choice questions Chapter 7. Wiring and circuit protection 7.1. Overview 7.1.1. Types of wire and cable 7.1.2. Operating environment 7.2. Construction and materials 7.3. Specifications 7.3.1. Wire size 7.3.2. Performance requirements 7.4. Shielding/screening 7.4.1. Crimps and splices 7.4.2. Coaxial cables 7.5. Circuit protection 7.5.1. Fuses 7.5.2. Circuit-breakers 7.5.3. Limiting resistors 7.6. Multiple choice questions Chapter 8. Distribution of power supplies 8.1. Single engine/general aviation aircraft  8.1.1. Reverse current relay 8.1.2. Current limiter 8.1.3. External power 8.1.4. Battery charging: single engine 8.2. Twin engine general aviation aircraft 8.3. Larger aircraft systems 8.4. Split bus system 8.5. Parallel bus system 8.6. Split/parallel bus system 8.7. Standby and essential power 8.8. Battery charging 8.9. Control and protection 8.9.1. Current transformers 8.9.2. Differential current protection 8.9.3. Phase protection (Merz Price circuit) 8.9.4. Breakers/contactors 8.10. Load-shedding 8.10.1. General aviation aircraft 8.10.2. Larger aircraft 8.10.3. Load-sharing of AC circuits 8.11. Multiple choice questions Chapter 9. Controls and transducers 9.1. Switches 9.1.1. Combined switch/light devices 9.1.2. Micro-switches 9.1.3. Proximity switch electronic unit  9.2. Relays and contactors 9.2.1. Relay configurations 9.2.2. Polarized relays 9.3. Variable resistors 9.4. Linear displacement transducers 9.4.1. Solenoids 9.4.2. LVDT 9.4.3. EI sensor 9.5. Fluid pressure transducers 9.5.1. Bourdon tube 9.5.2. Pressure capsule 9.6. Temperature transducers 9.6.1. Bi-metallic strip 9.6.2. Thermistors 9.6.3. Thermocouples 9.7. Strain transducers 9.8. Rotary position transducers 9.8.1. DC synchro 9.8.2. AC torque synchro 9.8.3. Magnesyn 9.9 Multiple choice questions Chapter 10. Engine systems 10.1. Starting and ignition 10.1.1. Piston engines  10.1.2. Twin-engine (piston) starting system 10.1.3. Turbine engine starting 10.1.4. Auxiliary power unit (APU) start and ignition 10.1.5. Main engine start 10.2. Indicating systems overview 10.3. Primary indicating systems 10.3.1. Engine speed 10.3.2. Engine temperature 10.3.3. Engine pressure ratio (EPR) 10.3.4. Fuel flow 10.3.5. Torque 10.4. Secondary indicating systems 10.4.1. Oil/fuel temperature 10.4.2. Vibration 10.4.3. Fluid pressure 10.4.4. Propeller synchronization 10.5. Electronic indicating systems 10.5.1. Eicas 10.5.2. Ecam 10.6. Multiple choice questions Chapter 11. Fuel management 11.1. Storage overview 11.2. Fuel quantity measurement and indication 11.2.1. Sight glass 11.2.2. Float gauge  11.2.3. Under-wing measurement 11.2.4. Capacitive fuel quantity system 11.3. Fuel feed and distribution 11.4. Fuel transfer 11.5. Refuelling and defuelling 11.6. Fuel jettison 11.7. Fuel tank venting 11.8. Fuel tank inerting 11.9. Multiple choice questions Chapter 12. Lights 12.1. Lighting technologies 12.2. Flight compartment lights 12.2.1. Instruments 12.2.2. Master warning 12.2.3. Emerging technology 12.3. Passenger cabin lights 12.4. Exterior lights 12.4.1. Logo lights 12.4.2. Landing lights 12.4.3. Wing illumination 12.4.4. Service lights 12.4.5. Navigation lights 12.5. Multiple choice questions Chapter 13. Cabin systems 13.1. Passenger address system  13.2. Galley equipment 13.3. In-flight entertainment (IFE) 13.3.1. Overview 13.3.2. Typical product specifications 13.3.3. IFE system safety and regulation 13.4. Satellite communications 13.4.1. Satellite communication network 13.4.2. Iridium ground network 13.5. Multiplexing 13.6. Fibre optics 13.6.1. Construction 13.6.2. Connectors 13.7. Air conditioning 13.7.1. Environmental control system 13.7.2. Ventilation 13.7.3. Equipment cooling 13.8. Pressurization 13.9. Airstairs 13.10. Multiple choice questions Chapter 14. Airframe monitoring, control and indicating systems 14.1. Landing gear 14.2. Trailing edge flaps 14.3. Control surfaces 14.4. Electronic indicating systems 14.5. Multiple choice questions Chapter 15. Warning and protection systems 15.1. Stall warning and protection 15.1.1. Reed sensor 15.1.2. Vane sensor 15.1.3. Pressure sensing sensor 15.1.4. Sensor vane 15.1.5. Stick shaker 15.1.6. Stall identification system 15.2. Airframe ice and rain protection 15.2.1. Ice detection 15.2.2. Ice protection 15.3. Windscreen ice and rain protection 15.3.1. Windscreen wiper 15.3.2. Rain repellent 15.4. Anti-skid 15.5. Configuration warning 15.6. Aural warnings 15.7. Multiple choice questions Chapter 16. Fire and overheat protection 16.1. Overview 16.2. Engine/APU fire detection 16.2.1. Thermal fire detection 16.2.2. Optical fire detection 16.3. Cargo bay/baggage area  16.3.1. Smoke detector principles 16.3.1.1. Ionization smoke detectors 16.4. Fire extinguishing 16.4.1. Overview 16.4.2. Cabin/flight compartment 16.4.3. Engine/APU and cargo bay 16.4.4. Fire extinguisher maintenance 16.5. Multiple choice questions Chapter 17. Terrain awareness warning system (TAWS) 17.1. System overview 17.2. System warnings and protection 17.3. External references 17.4. Ground proximity modes 17.4.1. Mode 1: excessive descent rate 17.4.2. Mode 2: excessive terrain closure rate 17.4.3. Mode 3: negative climb rate or altitude loss after take off or go around 17.4.4. Mode 4: flight into terrain when not in landing configuration 17.4.5. Mode 5: excessive downward deviation from an ILS glide slope 17.4.6. Mode 6 Altitude callouts 17.4.7. Mode 7 wind shear 17.5. Forward-looking terrain avoidance (FLTA) 17.6. Rotorcraft TAWS 17.7. Architecture and configurations 17.8. Future developments  17.9. Multiple choice questions Chapter 18. Flight data and cockpit voice recorders 18.1. Flight data recorder history 18.1.2. Magnetic recording 18.1.3. Solid state data recorders 18.2. Mandatory equipment requirements 18.3. Flight data recorder (FDR) specifications 18.3.1. Recording tape 18.3.2. Data acquisition 18.3.3. Digital data recording formats 18.4. Cockpit voice recorders 18.5. Health and usage monitoring system (HUMS) 18.6. Multiple choice questions Chapter 19. Electrical and magnetic fields 19.1. Electromagnetic Interference 19.1.1. Shielding 19.1.2. Electromagnet waves 19.1.3. Twisted pair 19.1.4. Bandwidth 19.1.5. Radiated EMI 19.1.6. EMI susceptibility 19.2. EMI reduction 19.3. High-intensity/energy radiated fields 19.3.1. HIRF environment 19.3.2. HIRF characteristics  19.4. Lightning 19.4.1. Faraday cage 19.4.2. Aircraft construction 19.4.3. Certification of aircraft for HIRF and lightning protection 19.4.4. Maintenance for HIRF/L protection 19.4.5. Aircraft wiring and cabling 19.5. Grounding and bonding 19.6. Electrostatic sensitive devices (ESSD) 19.6.1. Triboelectric effect 19.6.2. Working environment 19.7. Multiple choice questions Chapter 20. Continuing airworthiness 20.1. Wire and cable installation 20.1.1. Cable and wire looms 20.1.2. Wire terminations and connections 20.1.3. Connectors 20.1.4. Aluminium wires or cables 20.2. Bonding 20.2.1. Composite materials 20.2.2. Maintenance requirements 20.3. Static charges 20.4. Earth returns 20.5. Aircraft manuals 20.5.1. Maintenance manual 20.5.2. Wiring diagram manual  20.6. Circuit testing 20.6.1. Multimeters 20.6.2. Bonding meters 20.6.3. Oscilloscopes 20.7. Automatic test equipment 20.8. On-board diagnostic equipment 20.8.1. Built in test equipment 20.8.2. Centralized maintenance systems (CMS) 20.8.3. Aircraft communication addressing and reporting system 20.9. Multiple choice questions Index Copyright Page Linacre House, Jordan Hill, Oxford OX2 8DP, UK 30 Corporate Drive, Suite 400, Burlington, MA 01803, USA The right of Mike Tooley and David Wyatt to be identifi ed as the authors of this work has been asserted in accordance with the Copyright, Designs and Patents Act 1988 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 without the prior written permission of the publisher Permissions may be sought directly from Elsevier's Science & Technology Rights Department in Oxford, UK: phone (+44) (0) 1865 843830; fax (+44) (0) 1865 853333; email: [email protected]. Alternatively you can submit your request online by visiting the Elsevier web site at http://elsevier.com/locate/permissions , and selecting Obtaining permission to use Elsevier material NOTICE No responsibility is assumed by the publisher for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions or ideas contained in the material herein. Disclaimer This book draws on many sources. Some are facts, some hypotheses, some opinions. Most – including many of my own statements – are mixtures. Even 'facts' are unavoidably selective and can rarely be guaranteed. Despite careful checking, neither I nor my colleagues or publishers can accept responsibility for any errors, misinformation or unsuitable advice. This also applies to opinions – particularly on issues affecting health and safety. As any recommendations must balance complex, often opposing, factors, not everyone will reach the same conclusions. In this–as indeed in every issue this book touches on – every reader must make up her or his mind, for which they alone must be responsible. I offer the best advice I am capable of, but every circumstance is different. Anyone who acts on this advice must make their own evaluation, and adapt it to their particular circumstances. British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the Library of Congress ISBN: 978-0-75068695-2 For information on all Butterworth-Heinemann publicationsvisit our website at www.Elsevierdirect.com Printed and bound in Great Britain 09 10 11 12 13 10 9 8 7 6 5 4 3 2 1 Preface Aircraft Electrical and Electronic Systems continues the series of textbooks written for aircraft engineering students. This book addresses the electrical contents of the EASA Part 66 Modules 11 and 13; it also provides reference material for the avionic and aircraft electrical units of various BTEC National and Higher National, City and Guilds, NVQ and Foundation Degree modules. This book is designed to cover the essential knowledge base required by certifying mechanics, technicians and engineers engaged in engineering maintenance activities on commercial aircraft and in general aviation. In addition, this book should appeal to members of the armed forces and others attending training and educational establishments engaged in aircraft maintenance and related aeronautical engineering programmes. This book will also appeal to others within the aircraft industry who need an insight into electrical and electronic systems, e.g. pilots, engineering managers, etc. The book provides an introduction to the fundamentals of electrical, electronic and digital theory that underpins the principles of systems covered in the remainder of the book. For the reader that already has background knowledge of the fundamentals, the subsequent chapters can be read as individual subjects. For the reader that requires a deeper understanding of related fundamentals, additional material can be found in related books in the series: Aircraft Engineering Principles Aircraft Digital Electronic and Computer Systems Aircraft Communications and Navigation Systems. The books in this series have been designed for both independent and tutor- assisted studies. They are particularly useful to the ‘self-starter’ and to those wishing to update or upgrade their aircraft maintenance licence. The series also provides a useful source of reference for those taking ab initio training programmes in EASA Part 147 and FAR 147 approved organizations as well as those following related programmes in further and higher education institutions. The title of this book, Aircraft Electrical and Electronic Systems, has been specifically chosen to differentiate between other avionic systems such as communications, navigation, flight guidance and instruments. The term avionics (aviation electronics) was first used in the late 1940s to identify electrical and electronic equipment such as radar, radio navigation and communications, although the term was not in general use until the late 1960s. During the 1970s, integrated computer-based systems were being developed, e.g. ground proximity warning systems; these used a number of existing aircraft sensors that monitored parameters such as barometric altitude, vertical speed and radio altitude. The continued development and integration of electrical and electronic systems, together with the widespread use of integrated circuits, microprocessors, data communications and electronic displays, have given new meaning to the term avionics. Aircraft engineers will be exposed to in-service aircraft using older technology, together with the new aircraft entering service based on modern technology. Using trends from the last 40 years, there will be an ever-increasing dependence on avionic systems. The eventual outcome could be the all-electric aircraft, a concept where traditional mechanical linkages, hydraulics and pneumatics are totally replaced by electrical and electronic systems. This book establishes a reference point for engineering students; it does not attempt to address all system types for all aircraft types. It is also important to note that this book does not attempt to provide the level of detail found in the aircraft publications, including the maintenance and wiring diagram manuals. Although there are many examples quoted in the book that are based on specific aircraft types, this is only done to illustrate a specific point. Throughout the book, the principles and operation of systems are summarized by numerous ‘key points’. The reader will be invited at regular intervals to assess knowledge via ‘test your understanding’ questions. Finally, the principles and operation of systems are put into the context of aircraft maintenance engineering by numerous ‘key maintenance points’. Each chapter concludes with a number of multiple choice questions; the reader will then find revision papers in the appendices for additional assessment purposes. A summary of the book is as follows. Chapter 1 sets the scene by providing an explanation of electricity in terms of the motion of electric charge and basic electrical quantities such as current, voltage, resistance and power. The chapter provides an introduction to electrostatics and capacitors and also to electromagnetism and inductors. Here the emphasis is on the key concepts and fundamental laws that underpin the operation of the electrical systems found in aircraft. The chapter provides a detailed introduction to alternating current and transformer principles, and concludes with an essential section on safety. This chapter will be particularly useful if you have not previously studied electrical principles. It has also been designed to help fill any gaps in your knowledge and bring you quickly up to speed. Electronic fundamentals are introduced in Chapter 2. This chapter explains the principles, construction and basic application of a variety of common semiconductor devices including diodes, thyristors, transistors and integrated circuits. The chapter includes a detailed explanation of rectifier circuits, both half-wave and full-wave types, and the use of transistors as current amplifiers. The advent of digital techniques and integrated circuits has revolutionized the scope and applications for avionic systems. Chapter 3 provides readers with an introduction to digital techniques. The function and operation of logic gates are established before moving on to explore the use of combinational and sequential logic in several typical aircraft applications. The chapter also provides an overview of coding systems and the logic systems that are used to represent numerical data. An introduction to aircraft data bus systems is provided together with a brief overview of the architecture and principal constituents of simple computer systems. Generators and motors are widely used in modern aircraft. Chapter 4 explains the principles on which they operate as well as the theoretical and practical aspects of aircraft power generation and distribution. Three-phase systems and methods of connection are described in some detail. If you are in any doubt as to whether or not you should work through Chapters 1 to 4, you can always turn to the multiple choice questions at the end of each chapter to assess your knowledge. All electrical and electronic systems require a power source. Batteries are primary sources of electrical power found on most aircraft delivering direct current (DC). Chapter 5 reviews the battery types used on aircraft, typical applications and how they are installed and maintained. There are several types of battery used on aircraft, usually defined by the types of materials used in their construction; these include lead-acid and nickel-cadmium batteries. Other types of battery are being considered for primary power on aircraft; these include lithium and nickel-metal hydride. In Chapter 6, we review the other sources of electrical power used on aircraft and their typical applications. Electrical power can be derived from a variety of sources; these are categorized as either primary or secondary sources. Batteries and generators are primary sources of electrical power; inverters and transformer rectifier units (TRU) are secondary sources of power. This power is either in the form of direct or alternating current depending on system requirements. Generators can either supply direct or alternating current (AC); the outputs of generators need to be regulated. Inverters are used to convert DC (usually from the battery) into alternating (AC). Transformer rectifier units (TRU) convert AC into DC; these are often used to charge batteries from AC generators. In some installations, transformers (as described in Chapter 1) are used to convert AC into AC, typically for stepping down from 115 to 26 V AC. In addition to onboard equipment, most aircraft have the facility to be connected to an external power source during servicing or maintenance. An auxiliary power unit (APU) is normally used for starting the aircraft’s main engines via the air distribution system. While the aircraft is on the ground, the APU can also provide electrical power. In the event of generator failure(s), continuous power can be provided by a ram air turbine (RAT). The safe and economic operation of an aircraft is becoming ever more dependent on electrical and electronic systems. These systems are all interconnected with wires and cables; these take many forms. Chapter 7 describes the physical construction of wires and cables together with how they are protected from overload conditions before power is distributed to the various loads on the aircraft. Electrical wires and cables have to be treated as an integral part of the aircraft requiring careful installation; this is followed by direct ongoing inspection and maintenance requirements for continued airworthiness. Wire and cable installations cannot be considered (or treated) as ‘fit and forget’. System reliability will be seriously affected by wiring that has not been correctly installed or maintained. We need to distribute the sources of electrical power safely and efficiently and control its use on the aircraft. Once installed, the wires and cables must be protected from overload conditions that could lead to overheating, causing the release of toxic fumes, possibly leading to fire. Legislation is being proposed to introduce a new term: electrical wire interconnection system (EWIS); this will acknowledge the fact that wiring is just one of many components installed on the aircraft. EWIS relates to any wire, wiring device, or combination of these, including termination devices, installed in the aircraft for transmitting electrical energy between two or more termination points. Electrical power is supplied to the various loads in the aircraft via common points called busbars. In Chapter 8, we will focus on busbar configurations and how these are arranged for the protection and management of the various power supply sources available on the aircraft. The electrical power distribution system is based on one or more busbar(s); these provide pre-determined routes to circuits and components throughout the aircraft. The nature and complexity of the distribution system depend on the size and role of the aircraft, ranging from single-engine general aviation through to multi-engine passenger transport aircraft. The word ‘bus’ (as used in electrical systems) is derived from the Latin word omnibus meaning ‘for all’. The busbar can be supplied from one or more of the power sources previously described (generator, inverter, transformer rectifier unit or battery). Protection devices, whether fuses or circuit breakers, are connected in series with a specific system; they will remove the power from that system if an overload condition arises. There also needs to be a means of protecting the power source and feeder lines to the busbar, i.e. before the individual circuit protection devices. There are many systems on an aircraft that need to be controlled and/or monitored, either manually by the crew, or automatically. Chapter 9 describes generic controls and transducer devices used on aircraft. A switch provides the simplest form of circuit control and monitoring. Switches can be operated manually by a person, activated by sensing movement, or controlled remotely. Many other aircraft parameters need to be measured; this is achieved by a variety of transducers; these are devices used to convert the desired parameter, e.g. pressure, temperature, displacement, etc. into electrical energy. The aircraft engine is installed with many systems requiring electrical power. Chapter 10 describes engine starting, ignition and indicating system for both piston and gas turbine engines. The predominant electrical requirement (in terms of current consumption) is for the engine starting system. General aviation aircraft use electrical starter motors for both piston and gas turbine engines; larger transport aircraft use an air-start system (controlled electrically) derived from ground support equipment or by air cross-fed from another engine. Electrical starting systems on piston and gas turbine engines are very different. The trend towards the all-electric aircraft will see more aircraft types using electrical starting methods. The engine also requires electrical power for the ignition system; once again, the needs of piston and gas turbine engines are quite different. Although starting and ignition systems are described in this chapter as separate systems, they are both required on a co-ordinated basis, i.e. a means to rotate the engine and ignite the air/fuel mixture. Electrical and electronic requirements for engines also include the variety of indicating systems required to operate and manage the engine. These indicating systems include (but are not limited to) the measurement and indication of: rotational speed, thrust, torque, temperature, fuel flow and oil pressure. Indications can be provided by individual indicators or by electronic displays. The management of fuel is essential for the safe and economic operation of the aircraft. The scope of fuel management depends on the size and type of aircraft; fuel is delivered to the engines using a variety of methods. Chapter 11 provides an overview of fuel management on a range of aircraft types. The system typically comprises fuel quantity indication, distribution, refuelling, defuelling and fuel jettison. In the first instance, we need to measure the quantity of fuel on board. Various technologies and methods are used to measure fuel quantity: this depends mainly on the type and size of aircraft. Technologies range from sight gauges through to electronic sensors. On larger aircraft, fuel is fed to the engines by electrically driven pumps. On smaller aircraft, an engine-driven pump is used with electrical pumps used as back-up devices. Solenoid or motorized valves are used to isolate the fuel supply to engines under abnormal conditions. On larger aircrafts, the fuel can be transferred between tanks; this is controlled manually by the crew, or automatically by a fuel control computer. Lighting is installed on aircraft for a number of reasons including: safety, operational needs, servicing and for the convenience of passengers. Chapter 12 reviews a number of lighting technologies and the type of equipment used in specific aircraft applications. The applications of aircraft lights can be broadly grouped into four areas: flight compartment (cockpit), passenger cabin, exterior and servicing (cargo and equipment bays). Lights are controlled by on/off switches, variable resistors or by automatic control circuits. Passenger transport and business aircraft are fitted with a range of cabin electronic equipment for passenger safety, convenience and entertainment. Typical applications for this equipment includes lighting, audio and visual systems. Chapter 13 describes the many types of systems and equipment used for passenger safety, convenience and entertainment. Audio systems include the passenger address system used by the flight or cabin crew to give out safety announcements and other flight information. These announcements are made from hand-held microphones and are heard over loudspeakers in the cabin and passenger headsets. The same system can be used to play automatic sound tracks; this is often used for announcements in foreign languages, or to play background music during boarding and disembarkation. A range of galley equipment is installed on business and passenger aircraft. The nature of this equipment depends on the size and role of the aircraft. Air conditioning is provided in passenger aircraft for the comfort of passengers; pressurization is required for flying at high altitudes. Airstairs allow passengers, flight crew and ground personnel to board or depart the aircraft without the need for a mobile staircase or access to a terminal. All of these systems have electrical/electronic interfaces and control functions. Chapter 14 reviews airframe systems such as landing gear control and indication, control surface position and indicating systems. Various sensors are needed for the monitoring and control of airframe systems. Broadly speaking, the sensors can be considered as detecting one of two states (or ‘conditions’), or a variable position. Two-state conditions include: landing gear (up or down) or cabin doors (open or closed). Variable positions include: control surfaces and flap position. Micro-switches or proximity sensors detect two-state positions; variable position devices are detected by a variety of devices including synchros and variable resistors. Chapter 15 describes a variety of systems installed on aircraft to protect them from a variety of hazards including: stalling, ice, rain, unsafe take-off configuration and skidding. Stall protection systems provide the crew with a clear and distinctive warning before an unsafe condition is reached. Flying in ice and/or rain conditions poses a number of threats to the safe operation of the aircraft; ice formation can affect the aerodynamics and/or trim of the aircraft. The configuration warning system (also known as a take-off warning system) provides a warning if the pilot attempts to take off with specific controls not selected in the correct position, i.e. an unsafe configuration. The anti-skid system (also called an anti-lock braking system: ABS) is designed to prevent the main landing gear wheels from locking up during landing, particularly on wet or icy runway surfaces. Fire on board an aircraft is a very serious hazard; all precautions must be taken to minimize the risk of a fire starting. In the event that a fire does occur, there must be adequate fire protection on the aircraft. Chapter 16 focuses on the equipment and systems used to detect fire and smoke together with the means of delivering the fire-extinguishing agent. The subject of fire protection theory is a branch of engineering in its own right. Basic fire protection theory is covered in this chapter to provide the reader with sufficient information to understand how this theory is applied through aircraft electrical systems. During the 1970s, studies were carried out by accident investigators and regulatory authorities to examine one of the most significant causes of aircraft accidents of the time: controlled flight into terrain (CFIT). This can be defined as an accident where a serviceable aircraft, under the control of a qualified pilot, inadvertently flies into terrain, an obstacle or water. Chapter 17 describes the generic name given to this type of protection: terrain awareness warning system (TAWS). CFIT accidents usually occur during poor visual conditions, often influenced by other factors, e.g. flight crew distraction, malfunctioning equipment or air traffic control (ATC) miscommunication. With CFIT, the pilots are generally unaware of this situation until it is too late. Ground proximity warning system (GPWS) were developed in 1967 to alert pilots that their aircraft was in immediate danger of CFIT. This system was further developed into the enhanced ground proximity warning system (EGPWS) by adding a forward- looking terrain avoidance (FLTA) feature, made possible via global positioning system technology. One of the fundamental electrical/electronic systems associated with the aircraft industry is the crash survivable flight data recorder (FDR). This is often referred to in the press as the ‘black box’, even though the item is actually bright orange! Flight data recorders used for accident investigation are mandatory items of equipment in commercial transport aircraft. Efforts to introduce crash-survivable flight data recorders can be traced back to the 1940s; the FDR has now been supplemented with the cockpit voice recorder (CVR). Chapter 18 reviews the range of FDR/CVR technologies that are employed for both accident investigation and trend monitoring. Recorders are used after an incident or accident as an integral part of the investigators’ efforts to establish the cause(s). Data recorders can also be used to indicate trends in aircraft and engine performance. Algorithms are established for healthy and normal conditions during the aircraft’s flight-testing programme and the early period of service. These algorithms include engine parameters such as engine exhaust temperature, oil pressure and shaft vibration for given speeds and altitudes. These parameters are then monitored during the aircraft’s life; any deviations from the norm are analysed to determine if the engine requires inspection, maintenance or removal. One of the consequences of operating electrical and electronic equipment is the possibility of disturbing, or interfering with, nearby items of electronic equipment. Chapter 19 looks at some of the implications of interference from electrical and magnetic fields. The term given to this type of disturbance is electromagnetic interference (EMI). Electrical or electronic products will both radiate and be susceptible to the effects of EMI. This is a paradox since many principles of electrical engineering are based on electromagnetic waves coupling with conductors to produce electrical energy and vice versa (generators and motors). Furthermore, systems are specifically designed to transmit and receive electromagnetic energy, i.e. radio equipment. In complex avionic systems, the consequences of EMI can cause serious, if not hard-to-find–problems. The ability of an item of equipment to operate alongside other items of equipment without causing EMI is electromagnetic compatibility (EMC). Modern digital equipment operates at very high speed and relatively low power levels. In addition to EMI, high-intensity radiated fields (HIRF) are received from the external environment, e.g. from radio and radar transmitters, power lines and lightning. The high energy created by these radiated fields disrupts electronic components and systems in the aircraft. (This effect is also referred to as high-energy radiated fields – HERF.) The electromagnetic energy induces large currents to flow, causing direct damage to electronic components together with the secondary effects of EMI. Advances in electronic technology bring many new features and benefits, e.g. faster processors, higher-density memory and highly efficient displays. These advances are primarily due to the reduction in the physical size of semiconductor junctions; this leads to higher-density components in given size of integrated circuit. One significant problem associated with certain types of semiconductor devices is that the smaller junctions are susceptible to damage from electrostatic voltages. This is a problem that can potentially affect a wide range of electronic equipment fitted in an aircraft. Effects range from weakening of semiconductor junctions through total failure of the equipment; both these effects can occur without any visible signs of damage to the naked eye! Electrostatic sensitive devices (ESSD) are electronic components that are prone to damage from stray electrical charge produced primarily from human operators. This problem is particularly prevalent with high-density memory devices and electronic displays. Weakening and damage to static-sensitive devices can result from mishandling and inappropriate methods of storage; the practical issues for handling ESSD are addressed in Chapter 19. Many processes are required throughout the aircraft’s operating life to ensure that it complies with the applicable airworthiness requirements and can be safely operated. The generic term for this range of processes is continuing airworthiness. Chapter 20 reviews some practical installation requirements, documentation and test equipment required by the avionics engineer to ensure the continued airworthiness of aircraft electrical and electronic systems. The term ‘maintenance’ is used for any combination of overhaul, repair, inspection, replacement, modification or defect rectification of an aircraft or component, with the exception of the pre-flight inspection. Particular emphasis is given to wire and cable installations since these cannot be considered (or treated) as ‘fit and forget’. System reliability will be seriously affected by wiring that has not been correctly installed or maintained. Persons responsible for the release of an aircraft or a component after maintenance are the certifying staff. Maintenance of an aircraft and its associated systems requires a variety of test equipment and documentation; these are required by certifying staff to fulfil their obligations in ensuring continued airworthiness. Supporting material for the book series (including interactive questions, media files, etc.) is available online at www.66web.co.uk or www.key2study.com and then follow the links for aircraft engineering. Acknowledgements The authors would like to express their thanks to the following persons for ideas, support and contributions to the book. We thank Lloyd Dingle, who had the original idea for the aircraft engineering series, and Alex Hollingsworth for commissioning this book. Thanks also to Lucy Potter and Holly Bathie, editorial assistants at Elsevier Science & Technology Books. Thanks also to the following organizations for permission to reproduce their information: Advanced Technological Systems International Limited (new generation aircraft batteries) Aero Quality (battery maintenance details) Flight Display Systems (in-flight entertainment systems) Iridium Satellite LLC (satellite communication systems) Lees Avionics, Helicopter Services and Wycombe Air Centre (photo images taken at their premises) Specialist Electronic Services Ltd (flight data recorders). Chapter 1. Electrical fundamentals This chapter will provide you with an introduction to the essential electrical theory that underpins the rest of this book. It has been designed to help fill any gaps in your knowledge and bring you quickly up to speed. You will find this chapter particularly useful if you have not previously studied electrical principles. However, if you are in any doubt as to whether or not you should work through this chapter you can always turn to Section 1.9 on page 33 and see how you get on with the multiple choice questions at the end of this chapter. 1.1. Electron theory All matter is made up of atoms or groups of atoms (molecules) bonded together in a particular way. In order to understand something about the nature of electrical charge we need to consider a simple model of the atom. This model, known as the Bohr model (see Fig. 1.1), shows a single atom consisting of a central nucleus with orbiting electrons. Figure 1.1. The Bohr model of the atom Within the nucleus there are protons which are positively charged and neutrons which, as their name implies, are electrical neutral and have no charge. Orbiting the nucleus are electrons that have a negative charge, equal in magnitude (size) to the charge on the proton. These electrons are approximately two thousand times lighter than the protons and neutrons in the nucleus. In a stable atom the number of protons and electrons are equal, so that overall, the atom is neutral and has no charge. However, if we rub two particular materials together, electrons may be transferred from one to another. This alters the stability of the atom, leaving it with a net positive or negative charge. When an atom within a material loses electrons it becomes positively charged and is known as a positive ion, when an atom gains an electron it has a surplus negative charge and so is referred to as a negative ion. These differences in charge can cause electrostatic effects. For example, combing your hair with a nylon comb may result in a difference in charge between your hair and the rest of your body, resulting in your hair standing on end when your hand or some other differently charged body is brought close to it. The number of electrons occupying a given orbit within an atom is predictable and is based on the position of the element within the periodic table. The electrons in all atoms sit in a particular orbit, or shell, dependent on their energy level. Each of these shells within the atom is filled by electrons from the nucleus outwards, as shown in Fig. 1.2). The first, innermost, of these shells can have up to two electrons, the second shell can have up to eight and the third up to 18. Figure 1.2. A material with a loosely bound electron in its outer shell All electrons and protons carry an electrostatic charge but its value is so small that a more convenient unit of charge is needed for practical use which we call the coulomb. One coulomb (C) is the total amount of the charge carried by 6.21 × 1018 electrons. Thus a single electron has a charge of a mere 1.61 × 10−19 C! A material which has many free electrons available to act as charge carriers, and thus allows current to flow freely, is known as a conductor. Examples of good conductors include aluminium, copper, gold and iron. Figure 1.2 shows a material with one outer electron that can become easily detached from the parent atom. A small amount of external energy is required to overcome the attraction of the nucleus. Sources of such energy may include heat, light or electrostatic fields. The atom once detached from the atom is able to move freely around the structure of the material and is called a free electron. It is these free electrons that become the charge carriers within a material. Materials that have large numbers of free electrons make good conductors of electrical energy and heat. In a material containing free electrons their direction of motion is random, as shown in Fig. 1.3(a), but if an external force is applied that causes the free electrons to move in a uniform manner (Fig. 1.3(b)) an electric current is said to flow. Figure 1.3. Free electrons and the application of an external force Metals are the best conductors, since they have a very large number of free electrons available to act as charge carriers. Materials that do not conduct charge are called insulators; their electrons are tightly bound to the nuclei of their atoms. Examples of insulators include plastics, glass, rubber and ceramic materials. The effects of electric current flow can be detected by the presence of one or more of the following effects: light, heat, magnetism, chemical, pressure andfriction. For example, heat is produced when an electric current is passed through a resistive heating element. Light is produced when an electric current flows through the thin filament wire in the evacuated bulb of an electric lamp. Key point Electrons each carry a tiny amount of negative electrical charge.  Key point Metals such as copper and silver are good conductors of electricity and they readily support the flow of electric current. Plastics, rubber and ceramic materials on the other hand are insulators and do not support the flow of electric current. Test your understanding 1.1 1. Explain the following terms: electron ion charge conductor insulator. 2. State, with reasons, whether an insulator or conductor is required in each of the following applications: the body of a fuse the outer protective sheath of a power cable the fuselage covering of a transport aircraft the radiating element of an antenna. 1.2. Electrostatics and capacitors Electric charge is all around us. Indeed, many of the everyday items that we use in the home and at work rely for their operation on the existence of electric charge and the ability to make that charge do something useful. Electric charge is also present in the natural world and anyone who has experienced an electrical storm cannot fail to have been awed by its effects. In this section we begin by explaining what electric charge is and how it can be used to produce conduction in solids, liquids and gases. We have already found that, if a conductor has a deficit of electrons, it will exhibit a net positive charge. If, on the other hand, it has a surplus of electrons, it will exhibit a net positive charge. An imbalance in charge can be produced by friction (removing or depositing electrons using materials such as silk and fur, respectively) or induction (by attracting or repelling electrons using a second body which is respectively positively or negatively charged). If two bodies have charges with the same polarity (i.e. either both positively or both negatively charged) the two bodies will move apart, indicating that a force of repulsion exists between them. If, on the other hand, the charges on the two bodies are unlike (i.e. one positively charged and one negatively charged) the two bodies will move together, indicating that a force of attraction exists between them. From this we can conclude that like charges repel and unlike charges attract. Static charges can be produced by friction. In this case, electrons and protons in an insulator are separated from each other by rubbing two materials together in order to produce opposite charges. These charges will remain separated for some time until they eventually leak away due to losses in the insulating dielectric material or in the air surrounding the materials. Note that more charge will be lost in a given time if the air is damp. Static electricity is something that can cause particular problems in an aircraft and special measures are taken to ensure that excessive charges do not build up on the aircraft’s structure. The aim is that of equalizing the potential of all points on the aircraft’s external surfaces. The static charge that builds up during normal flight can be dissipated into the atmosphere surrounding the aircraft by means of small conductive rods connected to the aircraft’s trailing surfaces. These are known as static dischargers or static wicks – see Fig. 1.4. Key point Charged bodies with the same polarity repel one another whilst charges with opposite polarity will attract one another. Key point A significant amount of charge can build up between conducting surfaces when they are insulated from one another. Where this might be a problem steps are taken to dissipate the charge instead of allowing it to accumulate  uncontrolled. Key maintenance point Stray static charges can very easily damage static-sensitive devices such as semiconductors, memory devices and other integrated circuits. Damage can be prevented by adopting the appropriate electrostatic sensitive device (ESD) precautions (described in the aircraft maintenance manual) when handling such devices. Precautions usually involve using wrist straps and grounding leads as well as using static-dissipative packaging materials. Figure 1.4. Static discharging devices 1.2.1. Electric fields The force exerted on a charged particle is a manifestation of the existence of an electric field. The electric field defines the direction and magnitude of a force on a charged object. The field itself is invisible to the human eye but can be drawn by constructing lines which indicate the motion of a free positive charge within the field; the number of field lines in a particular region being used to indicate the relative strength of the field at the point in question. Figures 1.5 and 1.6 show the electric fields between isolated unlike and like charges whilst Fig. 1.7 shows the field that exists between two charged parallel metal plates which forms a charge storage device known as a capacitor. Figure 1.5. Electric field between isolated unlike charges Figure 1.6. Electric field between isolated like charges Figure 1.7. Electric field between the two charged parallel metal plates of a capacitor The strength of an electric field (E) is proportional to the applied potential difference and inversely proportional to the distance between the two conducting surfaces (see Fig. 1.8). The electric field strength is given by: where E is the electric field strength (in V/m), V is the applied potential difference (in V) and d is the distance (in m). Figure 1.8. Electric field strength between two charged conducting surfaces The amount of charge that can be stored by a capacitor is given by the relationship: where Q is the charge in coulomb, C is the capacitance in farads, F, and V is the voltage in volts, V. This relationship can be re-arranged to make C or V the subject as follows: Example 1.1 Two parallel conductors are separated by a distance of 25 mm. Determine the electric field strength if they are fed from a 600 V DC supply. The electric field strength will be given by: where V=600 V and d=25 mm=0.025 m. Thus: Example 1.2 The field strength between two parallel plates in a cathode ray tube is 18 kV/m. If the plates are separated by a distance of 21 mm determine the potential difference that exists between the plates. The electric field strength will be given by: Re-arranging this formula to make V the subject gives: Now E=16 kV/m=18,000 V/m and d=21 mm=0.021 m, thus: Example 1.3 A potential difference of 150 V appears across the plates of a 2 μF capacitor. What charge is present? The charge can be calculated from: where C=2 μF and V=150 V, thus: Example 1.4 A 68 μF capacitor is required to store a charge of 170 μC. What voltage should be applied to the capacitor? The voltage can be calculated from: where Q=170 μC and C=68 μF; thus: Key maintenance point When replacing a capacitor it is essential to ensure that the replacement component is correctly rated in terms of type, value, working voltage and temperature. Capacitors are prone to failure if their maximum working voltage is exceeded and they should be derated when operated at a relatively high ambient temperature according to manufacturers’ specifications. It is also essential to observe the correct polarity when replacing an electrolytic (polarized) component. This is usually clearly marked on the external casing. Key maintenance point When working with high-voltage capacitors it is essential to ensure that the capacitor is fully discharged before attempting to replace the component. In most cases, any accumulated charge will safely drain away within a few seconds after removal of power. However, this should not be relied upon and a safe discharge path through a high-value resistor (say 1 MΩ) fitted with appropriate probes will ensure that capacitor is safe to work on. Figure 1.9. A selection of capacitors with values ranging from 12 pF to 1000 μF and working voltages ranging from 25 V to 450 V Test your understanding 1.2 1. The two plates of a parallel plate capacitor are separated by a distance of 15 mm. If the potential difference between the plates  is 300 V what will the electric field strength be? 2. The electric field between two conducting surfaces is 500 V/m. If the plates are separated by a distance of 2.5 mm, determine the potential difference between the plates. 1.3. Direct current Direct current (DC) is current that flows in one direction only. DC circuits are found in every aircraft. An understanding of how and why these circuits work is an essential prerequisite to understanding more complex circuits. Because of their negative charge, electrons will flow from a point of negative potential to a point with more positive potential (recall that like charges attract and unlike charges repel). However, when we indicate the direction of current in a circuit we show it as moving from a point that has the greatest positive potential to a point that has the most negative potential. We call this conventional current and, although it may seem odd, you just need to remember that it flows in the opposite direction to that of the motion of electrons! The most commonly used method of generating direct current is the electrochemical cell. A cell is a device that produces a charge when a chemical reaction takes place. When several cells are connected together they form a battery. Figure 1.10. A typical aircraft battery There are two types of cell: primary and secondary. Primary cells produce electrical energy at the expense of the chemicals from which they are made and once these chemicals are used up, no more electricity can be obtained from the cell. In secondary cells, the chemical action is reversible. This means that the chemical energy is converted into electrical energy when the cell is discharged whereas electrical energy is converted into chemical energy when the cell is being charged. You will find more information on aircraft batteries in Chapter 5. Key point Conventional current flows from positive to negative whilst electrons travel in the opposite direction, from negative to positive. Key point In a primary cell the conversion of chemical energy to electrical energy is irreversible and so these cells cannot be recharged. In secondary cells, the conversion of chemical energy to electrical energy is reversible. Thus these cells can be recharged and reused many times. Key maintenance point When removing and replacing batteries, it is essential to observe the guidance given in the aircraft maintenance manual (AMM) when removing, charging or replacing aircraft batteries. The AMM will describe the correct procedures for isolating the battery from the aircraft’s electrical system prior to its physical removal. Test your understanding 1.3 1. Explain the difference between a primary and a secondary cell. 2. Explain the difference between electron flow and conventional current. 1.4. Current, voltage and resistance Current, I, is defined as the rate of flow of charge and its unit is the ampere, A. One ampere is equal to one coulomb C per second, or: Where t=time in seconds So, for example: if a steady current of 3 A flows for two minutes, then the amount of charge transferred will be: Example 1.5 A current of 45 mA flows from one point in a circuit to another. What charge is transferred between the two points in 10 minutes? Here we will use Q=It where I=45 mA=0.045 A and t=10 minutes=10 × 60=600 s. Thus: Example 1.6 A charge of 1.5 C is transferred to a capacitor in 30 seconds. What current is flowing in the capacitor? Here we will use where Q=1.5C and t=30 s. Thus: Key point Current is the rate of flow of charge. Thus, if more charge moves in a given time, more current will be flowing. If no charge moves then no current is  flowing. 1.4.1. Potential difference (voltage) The force that creates the flow of current (or rate of flow of charge carriers) in a circuit is known as the electromotive force (or e.m.f.) and it is measured in volts (V). The potential difference (or p.d.) is the voltage difference, or voltage drop between two points. One volt is the potential difference between two points if one Joule of energy is required to move one coulomb of charge between them. Hence: where W=energy and Q=charge, as before. Energy is defined later in Section 1.6. Test your understanding 1.4 1. How much charge will be transferred when a current of 6A flows for two minutes? 2. How long will it take for a charge of 0.2C to be transferred using a current of 0.5A? 3. If 0.4 J of energy is used to transfer 0.05C of charge between two points what is the potential difference between the two points? 1.4.2. Resistance All materials at normal temperatures oppose the movement of electric charge through them; this opposition to the flow of the charge carriers is known as the resistance, R, of the material. This resistance is due to collisions between the charge carriers (electrons) and the atoms of the material. The unit of resistance is the ohm, with symbol Ω. Note that 1 V is the electromotive force (e.m.f.) required to move 6.21 × 1018 electrons (1C) through a resistance of 1 Ω in 1 second. Hence: where Q=charge, t=time, and R=resistance. Re-arranging this equation to make R the subject gives: Example 1.7 A 28 V DC aircraft supply delivers a charge of 5C to a window heater every second. What is the resistance of the heater? Here we will use where V=28 V, Q=5C and t=1s. Thus: Key point Metals such as copper and silver are good conductors of electricity. Good conductors have low resistance whilst poor conductors have high resistance. 1.4.3. Ohm’s law The most basic DC circuit uses only two components; a cell (or battery) acting as a source of e.m.f., and a resistor (or load) through which a current is passing. These two components are connected together with wire conductors in order to form a completely closed circuit as shown in Fig. 1.11. Figure 1.11. A simple DC circuit consisting of a battery (source) and resistor (load) For any conductor, the current flowing is directly proportional to the e.m.f. applied. The current flowing will also be dependent on the physical dimensions (length and cross-sectional area) and material of which the conductor is composed. The amount of current that will flow in a conductor when a given e.m.f. is applied is inversely proportional to its resistance. Resistance, therefore, may be thought of as an ‘opposition to current flow’; the higher the resistance the lower the current that will flow (assuming that the applied e.m.f. remains constant). Provided that temperature does not vary, the ratio of p.d. across the ends of a conductor to the current flowing in the conductor is a constant. This relationship is known as Ohm’s law and it leads to the relationship: where V is the potential difference (or voltage drop) in volts (V), I is the current in amps (A), and R is the resistance in ohms (Ω). This important formula may be arranged to make V, I or R the subject, as follows: The triangle shown in Fig. 1.12 should help you remember these three important relationships. It is important to note that, when performing calculations of currents, voltages and resistances in practical circuits, it is seldom necessary to work with an accuracy of better than ±1% simply because component tolerances are invariably somewhat greater than this. Furthermore, in calculations involving Ohm’s law, it is sometimes convenient to work in units of kΩ and mA (or MΩ and μA), in which case potential differences will be expressed directly in V. Figure 1.12. Relationship between V, I and R Example 1.8 A current of 0.1A flows in a 220 Ω resistor. What voltage drop (potential difference) will be developed across the resistor? Here we must use V=I×R and ensure that we work in units of volts (V), amps (A), and ohms (Ω). Hence a p.d. of 22 V will be developed across the resistor. Example 1.9 An 18 Ω resistor is connected to a 12 V battery. What current will flow in the resistor? Figure 1.13. A selection of resistors with values ranging from 0.1 Ω to 10 MΩ and power ratings from 0.1 W to 15 W Here we must use (where V=12 V and R=18 Ω): Hence a current of 2.4 A will flow in the resistor. Example 1.10 A voltage drop of 15 V appears across a resistor in which a current of 1 mA flows. What is the value of the resistance? Here we must use (where V=15 V and I=1 mA=0.001 A) Note that it is sometimes more convenient to work in units of mA and V, which will produce an answer directly in kΩ, i.e. Test your understanding 1.5 1. An aircraft cable has a resistance of 0.02 Ω per foot. If a 20 foot length of this cable carries a current of 0.5A what voltage will be dropped  across the ends of the cable? 2. A relay has a coil resistance of 400 Ω. What current is required to operate the relay from a 24 V supply? 3. A current of 125 μA flows when an insulation tester delivers 500 V to a circuit. What is the resistance of the circuit? Key maintenance point When replacing a resistor it is essential to ensure that the replacement component is correctly rated in terms of type, value, power and temperature. Resistors are prone to failure if their maximum power is exceeded and they should be derated when operated at a relatively high ambient temperature according to manufacturers’ specifications. 1.4.4. Kirchhoff’s laws Used on its own, Ohm’s law is insufficient to determine the magnitude of the voltages and currents present in complex circuits. For these circuits we need to make use of two further laws; Kirchhoff’s current law and Kirchhoff’s voltage law. Kirchhoff’s current law states that the algebraic sum of the currents present at a junction (or node) in a circuit is zero – see Fig. 1.14. Kirchhoff’s voltage law states that the algebraic sum of the potential drops present in a closed network (or mesh) is zero – see Fig. 1.15. Figure 1.14. Kirchhoff’s current law Figure 1.15. Kirchhoff’s voltage law 1.4.5. Series and parallel circuits Ohm’s law and Kirchhoff’s laws can be combined to solve more complex series–parallel circuits. Before we show you how this is done, however, it’s important to understand what we mean by ‘series’ and ‘parallel’ circuit! Figure 1.16 shows three circuits, each containing three resistors, R1, R2 and R3:  In Fig. 1.16(a), the three resistors are connected one after another. We refer to this as a series circuit. In other words the resistors are said to be connected in series. It’s important to note that, in this arrangement, the same current flows through each resistor. In Fig. 1.16(b), the three resistors are all connected across one another. We refer to this as a parallel circuit. In other words the resistors are said to be connected in parallel. It’s important to note that, in this arrangement, the same voltage appears across each resistor. In Fig. 1.16(c), we have shown a mixture of these two types of connection. Here we can say that R1 is connected in series with the parallel combination of R2 and R3. In other words, R2 and R3 are connected in parallel and R2 is connected in series with the parallel combination. Figure 1.16. Series and parallel circuits Example 1.11 Figure 1.17 shows a simple battery test circuit which is designed to draw a current of 2A from a 24 V DC supply. The two test points, A and B, are designed for connecting a meter. Determine: the voltage that appears between terminals A and B (without the meter connected); the value of resistor, R. Figure 1.17. Battery test circuit – see Example 1.11 We need to solve this problem in several small stages. Since we know that the circuit draws 2A from the 24 V supply we know that this current must flow both through the 9 Ω resistor and through R (we hope that you have spotted that these two components are connected in series!). We can determine the voltage drop across the 9 Ω resistor by applying Ohm’s law: Figure 1.18. Using Ohm’s law to find the voltage dropped across the 9 Ω resistor – see Example 1.11 Next we can apply Kirchhoff’s voltage law in order to determine the voltage drop, V, that appears across R (i.e. the potential drop between terminals A and B): Figure 1.19. Using Kirchhoff’s law to find the voltage that appears between terminals A and B – see Example 1.11 From which: Figure 1.20 Figure 1.20. Using Ohm’s law to find the value of R – see Example 1.11 Finally, since we now know the voltage, V, and current, I, that flows in R, we can apply Ohm’s law again in order to determine the value of R: Key point Circuits with multiple branches can be solved using a combination of Kirchhoff’s laws and Ohm’s law. Test your understanding 1.6  Determine the current and voltage present in each branch of the circuit shown in Fig. 1.21. Figure 1.21. See Test your understanding 1.6 1.5. Power and energy Power, P, is the rate at which energy is converted from one form to another and it is measured in watts (W). The larger the amount of power the greater the amount of energy that is converted in a given period of time. or thus: Like all other forms of energy, electrical energy is the capacity to do work. Energy can be converted from one form to another. An electric fire, for example, converts electrical energy into heat. A filament lamp converts electrical energy into light, and so on. Energy can only be transferred when a difference in energy levels exists. The unit of energy is the joule (J). Then, from the definition of power, hence: thus Thus joules are measured in watt-seconds. If the power was to be measured in kilowatts and the time in hours, then the unit of electrical energy would be the kilowatt-hour (kWh) (commonly knows as a unit of electricity). The electricity meter in your home records the amount of energy that you have used expressed in kilowatt-hours. The power in an electrical circuit is equivalent to the product of voltage and current. Hence: where P is the power in watts (W), I is the current in amps (A), and V is the voltage in volts (V). The formula may be arranged to make P, I or V the subject, as follows: The triangle shown in Fig. 1.22 should help you remember these three important relationships. It is important to note that, when performing calculations of power, current and voltages in practical circuits it is seldom necessary to work with an accuracy of better than ±1% simply because component tolerances are invariably somewhat greater than this. Figure 1.22. Relationship between P, I and V Finally, we can combine the Ohm’s law relationship that we met earlier with the formulae for power to arrive at two further useful relationships: Key point  Power is the rate of using energy and a power of one watt corresponds to energy being used at the rate of one joule per second. Example 1.12 An auxiliary power unit (APU) provides an output of 1.5 kW for 20 minutes. How much energy has it supplied to the aircraft? Here we will use W=Pt where P=1.5 kW=1500 W and t=20 minutes=20 × 60=1200 s. Thus: Example 1.13 The reservoir capacitor in a power supply is required to store 20 J of energy. How much power is required to store this energy in a time interval of 0.5s? Re-arranging W=Pt to make P the subject gives: We can now find P when W=20 J and t=0.5s. Thus Example 1.14 A main aircraft battery is used to start an engine. If the starter demands a current of 1000 A for 30 s and the battery voltage remains at 12 V during this period, determine the amount of electrical energy required to start the engine. We need to solve this problem in two stages. First we need to find the power delivered to the starter from: where I=1000 A and V=12 V. Thus Next we need to find the energy from: where P=12 kW and t=30 s. Thus Example 1.15 A 24V bench power unit is to be tested at its rated load current of 3A. What value of load resistor is required and what should its minimum power rating be? The value of load resistance required can be calculated using Ohm’s law, as follows: The minimum power rating for the resistor will be given by: Key point Power is the rate at which energy is converted from one form to another. A power of one watt is equivalent to one joule of energy being converted every second. Test your understanding 1.7 1. A window heater is rated at 150 W. How much energy is required to operate the heater for one hour? 2. A resistor is rated at 11 Ω, 2 W. What is the maximum current that should be allowed to flow in it? 3. An emergency locator transmitter is fitted with a lithium battery having a rated energy content of 18 kJ. How long can the unit be expected to operate if the transmitter consumes an input power of 2 W? 1.6. Electromagnetism and inductors Magnetism is an effect created by moving the elementary atomic particles in certain materials such as iron, nickel and cobalt. Iron has outstanding magnetic properties, and materials that behave magnetically, in a similar manner to iron, are known as ferromagnetic materials. These materials experience forces that act on them when placed near a magnet. A magnetic field of flux is the region in which the forces created by the magnet have influence. This field surrounds a magnet in all directions, being strongest at the end extremities of the magnet, known as the poles. Magnetic fields are mapped by an arrangement of lines that give an indication of strength and direction of the flux as illustrated in Fig. 1.23. Figure 1.23. Field and flux directions for a bar magnet Whenever an electric current flows in a conductor a magnetic field is set up around the conductor in the form of concentric circles, as shown in Fig. 1.24. The field is present along the whole length of the conductor and is strongest nearest to the conductor. Now like permanent magnets, this field also has direction. The direction of the magnetic field is dependent on the direction of the current passing through the conductor. Figure 1.24. Field around a current-carrying conductor If we place a current-carrying conductor in a magnetic field , the conductor has a force exerted on it. Consider the arrangement shown in Fig. 1.25, in which a current-carrying conductor is placed between two magnetic poles. The direction of the current passing through it is into the page going away from us. Then by the right-hand screw rule, the direction of the magnetic field, created by the current in the conductor, is clockwise, as shown. We also know that the flux lines from the permanent magnet exit at a north pole and enter at a south pole; in other words, they travel from north to south, as indicated by the direction arrows. The net effect of the coming together of these two magnetic force fields is that at position A, they both travel in the same direction and reinforce one another. While at position B, they travel in the opposite direction and tend to cancel one another. So with a stronger force field at position A and a weaker force at position B the conductor is forced upwards out of the magnetic field. If the direction of the current was reversed, i.e. if it was to travel towards us out of the page, then the direction of the magnetic field in the current-carrying conductor would be reversed and therefore so would the direction of motion of the conductor. Key point A magnetic field of flux is the region in which the forces created by the magnet have influence. This field surrounds a magnet in all directions and is concentrated at the north and south poles of the magnet. Key point Whenever an electric current flows in a conductor a magnetic field is set up in the space surrounding the conductor. The field spreads out around the conductor in concentric circles with the greatest density of magnetic flux nearest to the conductor. Figure 1.25. A current-carrying conductor in a magnetic field The magnitude of the force acting on the conductor depends on the current flowing in the conductor, the length of the conductor in the field, and the strength of the magnetic flux (expressed in terms of its flux density). The size of the force will be given by the expression: where F is the force in newtons (N), B is the flux density in tesla (T), I is the current (A) and l is the length (m). Flux density is a term that merits a little more explanation. The total flux present in a magnetic field is a measure of the total magnetic intensity present in the field and it is measured in webers (Wb) and represented by the Greek symbol, Φ. The flux density, B, is simply the total flux, Φ, divided by the area over which the flux acts, A. Hence: where B is the flux density (T), Φ is the total flux present (Wb), and A is the area (m2). In order to increase the strength of the field, a conductor may be shaped into a loop (Fig. 1.26) or coiled to form a solenoid (Fig. 1.27). Figure 1.26. Magnetic field around a single turn loop Figure 1.27. Magnetic field around a coil or solenoid Example 1.16 A flux density of 0.25 T is developed in free space over an area of 20 cm2. Determine the total flux. Re-arranging the formula to make Φ the subject gives: thus: Key point If we place a current-carrying conductor in a magnetic field, the conductor has a force exerted on it. If the conductor is free to move this force will produce motion. Key point Flux density is found by dividing the total flux present by the area over which the flux acts. 1.6.1. Electromagnetic induction The way in which electricity is generated in a conductor may be viewed as being the exact opposite to that which produces the motor force. In order to generate electricity we require movement in to get electricity out. In fact we need the same components to generate electricity as those needed for the electric motor, namely a closed conductor, a magnetic field and movement. Whenever relative motion occurs between a magnetic field and a conductor acting at right angles to the field, an e.m.f. is induced, or generated in the conductor. The manner in which this e.m.f. is generated is based on the principle of electromagnetic induction. Consider Fig. 1.28, which shows relative movement between a magnet and a closed coil of wire. An e.m.f. will be induced in the coil whenever the magnet is moved in or out of the coil (or the magnet is held stationary and the coil moved). The magnitude of the induced e.m.f., e, depends on the number of turns, N, and the rate at which the flux changes in thecoil,. Note that this last expression is simply amathematical way of expressing the rate of change of flux with respect to time. Figure 1.28. Demonstration of electromagnetic induction The e.m.f., e, is given by the relationship: where N is the number of turns and is the rateof change of flux. The minus sign indicates that the polarity of the  generated e.m.f. opposes the change. Now the number of turns N is directly related to the length of the conductor, l, moving through a magnetic field with flux density, B. Also, the velocity with which the conductor moves through the field determines the rate at which the flux changes in the coil as it cuts the flux field. Thus the magnitude of the induced (generated) e.m.f., e, is proportional to the flux density, length of conductor and relative velocity between the field and the conductor. The magnitude of the induced e.m.f. also depends on: the length of the conductor l in m the strength of the magnetic field, B, in tesla (T) the velocity of the conductor, v, in m/s. Hence: where B is the strength of the magnetic field (T), l is the length of the conductor in the field (m), and v is the velocity of the conductor (m/s). Now you are probably wondering why the above relationship has the proportionality sign. In order to generator an e.m.f. the conductor must cut the lines of magnetic flux. If the conductor cuts the lines of flux at right angles (Fig. 1.29(a)) then the maximum e.m.f. is generated; cutting them at any other angle θ (Fig. 1.29(b)), reduces this value until θ=0°, at which point the lines of flux are not being cut at all and no e.m.f. is induced or generated in the conductor. So the magnitude of the induced e.m.f. is also dependent on sin θ. So we may write: Figure 1.29. Cutting lines of flux and the e.m.f. generated: (a) cutting lines of flux at 90°, e=Blv; (b) cutting lines of flux at θ, e=Blv sin θ 1.6.2. Faraday’s and Lenz’s laws When a magnetic flux through a coil is made to vary, an e.m.f. is induced. The magnitude of this e.m.f. is proportional to the rate of change of magnetic flux. What this law is saying in effect is that relative movement between the magnetic flux and the conductor is essential to generate an e.m.f. The voltmeter shown in Fig. 1.29 indicates the induced (generated) e.m.f. and if the direction of motion changes the polarity of the induced e.m.f. in the conductor changes. Faraday’s law also tells us that the magnitude of the induced e.m.f. is dependent on the relative velocity with which the conductor cuts the lines of magnetic flux. Lenz’s law states that the current induced in a conductor opposes the changing field that produces it. It is therefore important to remember that the induced current always acts in such a direction so as to oppose the change in flux. This is the reason for the minus sign in the formula that we met earlier: Key point The induced e.m.f. tends to oppose any change of current and because of this we often refer to it as a back e.m.f. Example 1.17 A closed conductor of length 15 cm cuts the magnetic flux field of 1.25 T with a velocity of 25 m/s. Determine the induced e.m.f. when:  the angle between the conductor and field lines is 60° the angle between the conductor and field lines is 90°. The induced e.m.f. is found using e=Blv sinθ, hence: The maximum induced e.m.f. occurs when the lines of flux are cut at 90°. In this case e=Blv sin θ=Blv (recall that sin 90°=1), hence: 1.6.3. Self-inductance and mutual inductance We have already shown how an induced e.m.f. (i.e. a back e.m.f.) is produced by a flux change in an inductor. The back e.m.f. is proportional to the rate of change of current (from Lenz’s law), as illustrated in Fig. 1.30. Figure 1.30. Self-inductance This effect is called self-inductance (or just inductance) which has the symbol L. Self-inductance is measured in henries (H) and is calculated from: where L is the self-inductance, is the rate ofchange of current and the minus sign indicates that the polarity of the generated e.m.f. opposes the change (you might like to compare this relationship with the one shown earlier for electromagnetic induction). The unit of inductance is the henry (H) and a coil is said to have an inductance of 1 H if a voltage of 1 V is induced across it when a current changing at the rate of 1 A/s is flowing in it. Example 1.18 A coil has a self-inductance of 15 mH and is subject to a current that changes at a rate of 450 A/s. What e.m.f. is produced? Now and hence: Note the minus sign. This reminds us that a back e.m.f. of 6.75 V is induced. Example 1.19 A current increases at a uniform rate from 2A to 6A in a time of 250 ms. If this current is applied to an inductor determine the value of inductance if a back e.m.f. of 15 V is produced across its terminals. Now and hence Thus Finally, when two inductors are placed close to one another, the flux generated when a changing current flows in the first inductor will cut through the other inductor (see Fig. 1.31). This changing flux will, in turn, induce a current in the second inductor. This effect is known as mutual inductance and it occurs whenever two inductors are inductively coupled. This is the principle of a very useful component, the transformer, which we shall meet later. Figure 1.31. Mutual inductance 1.6.4. Inductors Inductors provide us with a means of storing electrical energy in the form of a magnetic field. Typical applications include chokes, filters, and frequency selective circuits. The electrical characteristics of an inductor are determined by a number of factors including the material of the core (if any), the number of turns, and the physical dimensions of the coil. In practice every coil comprises both inductance and resistance and the circuit of Fig. 1.32 shows these as two discrete components. In reality the inductance, L, and resistance, R, are both distributed throughout the component but it is convenient to treat the inductance and resistance as separate components in the analysis of the circuit. Key point An e.m.f. is produced when the magnetic flux passing through an inductor changes. Figure 1.33. A selection of inductors with values ranging from 100 nH to 4 H and current ratings ranging from 0.1 A to 10 A  Key point The current induced in a conductor always opposes the change that produces it. Test your understanding 1.8 1. A 1.5 m length of wire moves perpendicular to a magnetic flux field of 0.75 T. Determine the e.m.f. that will be induced across the ends of the wire if it moves at 10 m/s. 2. An e.m.f. of 30 V is developed across the terminals of an inductor when the current flowing in it changes from zero to 10 A in half a second. What is the value of inductance? Figure 1.32. A real inductor has resistance as well as inductance 1.7. Alternating current and transformers Direct currents are currents which, even though their magnitude may vary, essentially flow only in one direction. In other words, direct currents are unidirectional. Alternating currents, on the other hand, are bi-directional and continuously reversing their direction of flow, as shown in Fig. 1.34. Figure 1.34. Comparison of direct and alternating current A graph showing the variation of voltage or current present in a circuit is known as a waveform. There are many common types of waveform encountered in electrical circuits including sine (or sinusoidal), square, triangle, ramp or sawtooth (which may be either positive or negative), and pulse. Complex waveforms like speech or music usually comprise many components at different frequencies. Pulse waveforms found in digital circuits are often categorized as either repetitive or non-repetitive (the former comprises a pattern of pulses which regularly repeats whilst the latter comprises pulses which constitute a unique event). Several of the most common waveform types are shown in Fig. 1.35. Figure 1.35. Various waveforms 1.7.1. Frequency and periodic time The frequency of a repetitive waveform is the number of cycles of the waveform that occur in unit time. Frequency is expressed in hertz (Hz). A frequency of 1 Hz is equivalent to one cycle per second. Hence, if an aircraft supply has a frequency of 400 Hz, 400 cycles of the supply will occur in every second (Fig. 1.36). Figure 1.36. Waveforms with different frequencies The periodic time (or period) of a waveform is the time taken for one complete cycle of the wave (see Fig. 1.37). The relationship between periodic time and frequency is thus: Figure 1.37. Periodic time where t is the periodic time (in seconds) and f is the frequency (in Hz). Example 1.20 An aircraft generator operates at a frequency of 400 Hz. What is the periodic time of the voltage generated? Now Hence the voltage will have a periodic time of 2.5 ms. Example 1.21 A bench AC supply has a periodic time of 20 ms. What is the frequency of the supply? Now Hence the supply has a frequency of 50 Hz. 1.7.2. Average, peak, peak–peak, and r.m.s. values The average value of an alternating current which swings symmetrically above and below zero will obviously be zero when measured over a long period of time. Hence average values of currents and voltages are invariably taken over one complete half cycle (either positive or negative) rather than over on complete full cycle (which would result in an average value of zero). The peak value (or maximum value or amplitude) of a waveform is a measure of the extent of its voltage or current excursion from the resting value (usually zero). The peak-to-peak value for a wave which is symmetrical about its resting value is twice its peak value. The root mean square (r.m.s.) or effective value of an alternating voltage or current is the value which would produce the same heat energy in a resistor as a direct voltage or current of the same magnitude. Since the r.m.s. value of a waveform is very much dependent upon its shape, values are only meaningful when dealing with a waveform of known shape. Where the shape of a waveform is not specified, r.m.s. values are normally assumed to refer to sinusoidal conditions. For a given waveform, a set of fixed relationships exist between average, peak, peak–peak, and r.m.s. values. The required multiplying factors for sinusoidal voltages and currents are summarized in the table shown below. Table Wanted quantity average peak peak–peak r.m.s. Given quantity average 1 1.57 3.14 1.11 peak 0.636 1 2 0.707 peak–peak 0.318 0.5 1 0.353 r.m.s. 0.9 1.414 2.828 1 From the table we can conclude that, for example: Similar relationships apply to the corresponding alternating currents, thus: Example 1.22 A generator produces an r.m.s. sine wave output 110 V. What is the peak value of the voltage? Now Hence the voltage has a peak value of 311 V. Example 1.23 A sinusoidal current of 40A peak–peak flows in a circuit. What is the r.m.s. value of the current? Now Hence the current has an r.m.s. value of 14.12 A. Key point The root mean square (r.m.s.) value of an alternating voltage will produce the same amount of heat in a resistor as a direct voltage of the same magnitude. Figure 1.38. Average, r.m.s., peak and peak–peak values of a sine wave 1.7.3. Three-phase supplies The most simple method of distributing an AC supply is a system that uses two wires. In fact, this is how AC is distributed in your home (the third wire present is simply an earth connection for any appliances that may require it for safety reasons). In many practical applications, including aircraft, it can be advantageous to use a multiphase supply rather than a single-phase supply (here the word phase simply refers to an AC voltage source that may not be rising and falling at the same time as other voltage sources that may be present). Figure 1.39. Waveforms for a three-phase AC supply The most common system uses three separate voltage sources (and three wires) and is known as three-phase. The voltages produced by the three sources are spaced equally in time such that the angle between them is 120° (or 360°/3). The waveforms for a three-phase supply are shown in Fig. 1.37 (note that each is a sine wave and all three sine waves have the same frequency and periodic time). We shall be returning to this topic in greater detail in Chapter 4 when we introduce three-phase power generation. 1.7.4. Reactance In an AC circuit, reactance, like resistance, is simply the ratio of applied voltage to the current flowing. Thus: where X is the reactance in ohms (Ω), V is the alternating potential difference in volts (V) and I is the alternating current in amps (A). In the case of capacitive reactance (i.e. the reactance of a capacitor) we use the suffix, C, so that the reactance equation becomes: Similarly, in the case of inductive reactance (i.e. the reactance of an inductor) we use the suffix, L, so that the reactance equation becomes: The voltage and current in a circuit containing pure reactance (either capacitive or inductive) will be out of phase by 90°. In the case of a circuit containing pure capacitance the current will lead the voltage by 90° (alternatively we can say that the voltage lags the current by 90°). This relationship is illustrated by the waveforms shown in Fig. 1.40. Figure 1.40. Voltage and current waveforms for a pure capacitor (the current leads the voltage by 90°) In the case of a circuit containing pure inductance the voltage will lead the current by 90° (alternatively we can also say that the current lags the voltage by 90°). This relationship is illustrated by the waveforms shown in Fig. 1.41. Key point A good way of remembering leading and lagging phase relationships is to recall the word CIVIL, as shown in Fig. 1.42. Note that, in the case of a circuit containing pure capacitance (C) the current (I) will lead the voltage (V) by 90° whilst in the case of a circuit containing pure inductance (L) the voltage (V) will lead the current (I) by 90°. Figure 1.42. Using CIVIL to determine phase relationships in circuits containing capacitance and inductance Figure 1.41. Voltage and current waveforms for a pure capacitor (the voltage leads the current by 90°) The reactance of an inductor (inductive reactance) is directly proportional to the frequency of the applied alternating current and can be determined from the following formula: where XL is the reactance in Ω, f is the frequency in Hz, and L is the inductance in H. Since inductive reactance is directly proportional to frequency (XL∝f), the graph of inductive reactance plotted against frequency takes the form of a straight line (see Fig. 1.43). Figure 1.43. Variation of inductive reactance, XL, with frequency, f Example 1.24 Determine the reactance of a 0.1 H inductor at (a) 100 Hz and (b) 10 kHz. At 100 Hz, XL=2π× 100 × 0.1=62.8 Ω At 10 kHz, XL=2π× 10,000 × 0.1=6280 Ω=6.28 kΩ. The reactance of a capacitor (capacitive reactance) is inversely proportional to the frequency of the applied alternating current and can be determined from the following formula: where XC is the reactance in Ω, f is the frequency in Hz, and C is the capacitance in F. Since capacitive reactance is inversely proportional to frequency (XL∝ 1/f), the graph of inductive reactance plotted against frequency takes the form of a rectangular hyperbola (see Fig. 1.44). Figure 1.44. Variation of capacitive reactance, XC, with frequency, f Example 1.25 Determine the reactance of a 1 μF capacitor at (a) 100 Hz and (b) 10 kHz. Key point When alternating voltages are applied to capacitors or inductors the magnitude of the current flowing will depend upon the value of capacitance  or inductance and on the frequency of the voltage. In effect, capacitors and inductors oppose the flow of current in much the same way as a resistor. The important difference being that the effective resistance (or reactance) of the component varies with frequency (unlike the case of a conventional resistor where the magnitude of the current does not change with frequency). At 100 Hz, At 10 kHz, 1.7.5. Impedance Circuits that contain a mixture of both resistance and reactance (either capacitive reactance or inductive reactance or both) are said to exhibit impedance. Impedance, like resistance and reactance, is simply the ratio of applied voltage to the current flowing. Thus: where Z is the impedance in ohms (Ω), V is the alternating potential difference in volts (V) and I is the alternating current in amps (A). Because the voltage and current in a pure reactance are at 90° to one another (we say that they are in quadrature) we can’t simply add up the resistance and reactance present in a circuit in order to find its impedance. Instead, we can use the impedance triangle shown in Fig. 1.45. The impedance triangle takes into account the 90° phase angle and from it we can infer that the impedance of a series circuit (R in series with X) is given by: where Z is the impedance (in Ω), X is the reactance, either capacitive or inductive (expressed in Ω), and R is the resistance (also in Ω). Figure 1.45. The impedance triangle We shall be explaining the significance of the phase angle, φ, later on. For now you simply need to be aware that φ is the angle between the impedance, Z, and the resistance, R. Later on we shall obtain some useful information from the fact that: and Key point Resistance and reactance combine together to make impedance. In other words, impedance is the resultant of combining resistance and reactance in the impedance triangle. Because of the quadrature relationship between voltage and current in a pure capacitor or inductor, the angle between resistance and reactance in the impedance triangle is always 90°. Example 1.26 A resistor of 30 Ω is connected in series with a capacitive reactance of 40 Ω. Determine the impedance of the circuit and the current flowing when the circuit is connected to a 115 V supply. First we must find the impedance of the C–R series circuit: The current taken from the supply can now be found: Example 1.27 A coil is connected to a 50 V AC supply at 400 Hz. If the current supplied to the coil is 200 mA and the coil has a resistance of 60 Ω, determine the value of inductance. Like most practical forms of inductor, the coil in this example has both resistance and reactance (see Fig. 1.31). We can find the impedance of the coil from: Since , from which: Thus Now since XL=2πfL, Hence 1.7.6. Resonance It is important to note that a special case occurs when XC=XL in which case the two equal but opposite reactances effectively cancel each other out. The result of this is that the circuit behaves as if only resistance, R, is present (in other words, the impedance of the circuit, Z=R). In this condition the circuit is said to be resonant. The frequency at which resonance occurs is given by: thus from which and thus where f is the resonant frequency (in Hz), L is the inductance (in H) and C is the capacitance (in F). Example 1.28 A series circuit comprises an inductor of 10 mH, a resistor of 50 Ω and a capacitor of 40 nF. Determine the frequency at which this circuit is resonant and the current that will flow in it when it is connected to a 20 V AC supply at the resonant frequency. Using: where L=10 × 10−3 H and C=40 × 10−9F gives: At the resonant frequency the circuit will behave as a pure resistance (recall that the two reactances will be equal but opposite) and thus the supply current at resonance can be determined from: 1.7.7. Power factor The power factor in an AC circuit containing resistance and reactance is simply the ratio of true power to apparent power. Hence: The true power in an AC circuit is the power that is actually dissipated as heat in the resistive component. Thus: where I is r.m.s. current and R is the resistance. True power is measured in watts (W). The apparent power in an AC circuit is the power that is apparently consumed by the circuit and is the product of the supply current and supply voltage (which may not be in phase). Note that, unless the voltage and current are in phase (i.e. φ=0°), the apparent power will not be the same as the power which is actually dissipated as heat. Hence: where I is r.m.s. current and V is the supply voltage. To distinguish apparent power from true power, apparent power is measured in volt- amperes (VA). Now since V=IZ we can re-arrange the apparent power equation as follows: Now returning to our