EASA PART 66 MODULE (3 ) PART (A)

MODULE (3)

PART (A)

Index

1 ATOMIC STRUCTURE 1-11.1 MATTER 1-1

1.1.1 States of Matter 1-11.1.2 Chemical classification of matter 1-11.1.3 Atomic classification of matter 1-1

1.2 MOLECULES 1-2

1.3 ATOMS 1-21.3.1 The Structure of an Atom 1-31.3.2 The Fundamental Particles 1-31.3.3 Particle function 1-41.3.4 ions 1-5

1.4 ELECTRICAL MATERIALS 1-51.4.1 Electron distribution 1-61.4.2 Ionisation 1-61.4.3 Energy levels 1-71.4.4 Conductors 1-71.4.5 Insulators 1-71.4.6 Semi-conductors 1-7

2 STATIC ELECTRICITY 2-12.1 ATTRACTION & REPULSION 2-3

2.2 UNIT OF CHARGE 2-32.3 STATIC ELECTRICITY & AIRCRAFT 2-3

3 ELECTRICAL TERMINOLOGY 3-13.1 VOLTAGE 3-1

3.1.1 Potential 3-13.1.2 Potential Difference 3-13.1.3 Electromotive Force - emf 3-2

3.2 CURRENT 3-23.2.1 Movement of charge 3-23.2.2 Conventional flow 3-33.2.3 Electron flow 3-3

3.3 RESISTANCE 3-33.3.1 Factors affecting resistance 3-43.3.2 Units of resistance 3-4

3.4 CONDUCTANCE AND CONDUCTIVITY 3-4

4 PRODUCTION OF ELECTRICITY 4-14.1 BY FRICTION 4-1

4.2 BY PRESSURE 4-1

4.3 BY MAGNETISM 4-2

Page Index 1

4.4 BY HEAT 4-2

4.5 BY LIGHT 4-3

4.6 BY CHEMICAL ACTION 4-3

5 CELLS & BATTERIES 5-15.1 PRINCIPLES 5-1

5.1.1 Cell & Battery symbols 5-15.1.2 Construction & chemical action 5-15.1.3 Primary & secondary cells 5-25.1.4 Cell emf 5-25.1.5 Cell capacity 5-35.1.6 Interconnection of cells 5-3

5.2 LEAD ACID BATTERIES 5-45.2.1 Conventional construction 5-45.2.2 Solid block type construction 5-55.2.3 Chemical action 5-65.2.4 Voltage & Specific Gravity characteristics 5-75.2.5 Common lead acid battery faults 5-7

5.3 NICKEL CADMIUM BATTERIES 5-85.3.1 Construction 5-85.3.2 Chemical action 5-95.3.3 Advantages & disadvantages 5-105.3.4 Thermal runaway 5-10

5.4 SMALL ALKALINE CELLS 5-11

6 OHM’S LAW 6-16.1 TRANSPOSITION OF OHM’S LAW 6-16.2 THE OHM’S LAW TRIANGLE 6-2

7 ELECTRICAL MEASURING INSTRUMENTS 7-17.1 CONNECTING METERS TO A CIRCUIT 7-1

7.1.1 Voltmeters 7-17.1.2 Ammeters 7-27.1.3 Ohmmeters 7-2

7.2 ANALOGUE MULTIMETERS 7-37.2.1 DC voltage measurements 7-47.2.2 DC current measurements 7-57.2.3 DC high-current measurement 7-67.2.4 AC voltage measurements 7-77.2.5 Resistance measurements 7-77.2.6 Continuity testing 7-97.2.7 Battery testing 7-107.2.8 DO's & DON'Ts of using an analogue multimeter .. 7-10

7.3 DIGITAL MULTIMETERS 7-127.3.1 DC voltage measurements 7-137.3.2 DC current measurements 7-137.3.3 High current measurements 7-14

Page Index 2

7.3.4 AC voltage measurements 7-147.3.5 Resistance measurements 7-157.3.6 Capacitor measurements 7-157.3.7 Continuity testing 7-167.3.8 DO's & DON'Ts of using a digital multimeter 7-16

8 RESISTANCE & RESISTORS 8-18.1 RESISTIVITY 8-1

8.2 CHANGES OF RESISTANCE WITH TEMPERATURE 8-1

8.3 TEMPERATURE CO-EFFICIENT OF RESISTANCE 8-2

8.4 RESISTORS 8-38.4.1 Fixed resistors 8-38.4.2 Colour codes 8-38.4.3 Preferred values and tolerances 8-58.4.4 Letter & digit codes 8-68.4.5 Power rating 8-68.4.6 Potentiometers 8-78.4.7 Rheostats 8-78.4.8 Voltage Dependent Resistors 8-7

8.5 THERMISTORS 8-7

9 RESISTORS IN DC CIRCUITS 9-19.1 RESISTORS IN SERIES 9-1

9.1.1 Kirchoff’s Second Law 9-29.1.2 Voltage division 9-29.1.3 The Potential Divider 9-39.1.4 Voltages relative to Earth 9-4

9.2 INTERNAL RESISTANCE 9-4

9.3 RESISTORS IN PARALLEL 9-69.3.1 Two resistors in parallel 9-79.3.2 Equal resistors connected in parallel 9-79.3.3 Effective value of resistors in parallel 9-89.3.4 Resistor size and current flow 9-89.3.5 Kirchoff’s First Law 9-8

9.4 RESISTORS IN SERIES / PARALLEL COMBINATIONS 9-99.4.1 Physical arrangement of resistors 9-99.4.2 Solution of resistor networks using Ohm’s Law 9-9

9.5 THE EFFECTS OF OPEN CIRCUITS 9-11

9.6 THE EFFECTS OF SHORT CIRCUITS 9-12

10 THE WHEATSTONE BRIDGE 10-110.1 CONSTRUCTION 10-1

10.2 CALCULATING UNKNOWN RESISTANCES 10-110.3 USES ON AIRCRAFT 10-2

11 ENERGY & POWER IN DC CIRCUITS 11-1

Page Index 3

11.1 ELECTRICAL WORK 11-1

11.2 ELECTRICAL ENERGY 11-1

11.3 ELECTRICAL POWER 11-2

11.4 POWER RATINGS 11-211.4.1 Power ratings of resistors 11-311.4.2 Size and power rating 11-311.4.3 The Kilowatt Hour 11-3

11.5 MAXIMUM POWER TRANSFER 11-4

12 CAPACITANCE & CAPACITORS 12-112.1 CHARGING A BODY 12-112.2 THE BASIC CAPACITOR 12-2

12.3 CAPACITANCE 12-2

12.4 FACTORS AFFECTING CAPACITANCE 12-2

12.5 ENERGY STORED IN A CAPACITOR 12-3

12.6 CAPACITOR CONSTRUCTION 12-412.6.1 Fixed capacitors 12-412.6.2 Variable capacitors 12-412.6.3 Electrolytic capacitors 12-412.6.4 Safe working voltage 12-4

12.7 CAPACITOR SYMBOLS 12-5

13 CAPACITORS IN DC CIRCUITS 13-113.1 CAPACITORS IN SERIES 13-1

13.2 CAPACITORS IN PARALLEL 13-2

13.3 CAPACITORS IN SERIES / PARALLEL COMBINATIONS 13-3

13.4 CHARGE & DISCHARGE CHARACTERISTICS 13-313.4.1 Charging a capacitor 13-313.4.2 Time Constant 13-413.4.3 Discharging a capacitor 13-513.4.4 A capacitor in a dc circuit 13-6

13.5 THE EFFECTS OF OPEN & SHORT CIRCUITS 13-613.6 SAFETY & TESTING 13-6

13.7 CIRCUITS INVOLVING CAPACITIVE DECAY 13-7

14 MAGNETISM 14-114.1 MAGNETIC THEORIES 14-1

14.1.1 Molecular Theory 14-114.1.2 Domain Theory 14-1

14.2 MAGNETIC PROPERTIES 14-214.2.1 Magnetic poles 14-214.2.2 Magnetic field 14-214.2.3 Lines of flux 14-2

14.3 THE EARTH’S FIELD 14-4

Page Index 4

14.4 MAGNETIC MATERIALS 14-414.4.1 Ferromagnetic materials 14-414.4.2 Paramagnetic materials 14-514.4.3 Diamagnetic materials 14-5

14.5 PRODUCTION OF A MAGNET 14-514.5.1 Stroke method 14-514.5.2 Induction 14-614.5.3 Use of electrical current 14-7

15 ELECTROMAGNETISM 15-115.1 PRODUCTION OF A BAR MAGNET 15-1

15.1.1 End Rule 15-215.1.2 Right Hand Gripping Rule 15-2

15.2 THE MAGNETIC CIRCUIT 15-215.2.1 Magnetomotive force (mmf) 15-215.2.2 Magnetising force 15-215.2.3 Flux & Flux density 15-315.2.4 Permeability 15-315.2.5 Reluctance 15-415.2.6 Composite paths and airgaps 15-4

15.3 BH CURVE 15-515.4 HYSTERESIS LOOP 15-5

15.5 COMPARISON OF ELECTRICAL & MAGNETIC CIRCUITS 15-7

15.6 MAGNETIC SCREENING 15-8

16 INDUCTION 16-116.1 ELECTRICITY FROM MAGNETISM 16-1

16.1.1 Factors affecting induced emf 16-116.1.2 Faradays Law 16-216.1.3 Lenz’s Law 16-216.1.4 Flemings Right Hand Rule 16-3

16.2 SELF INDUCTANCE 16-316.3 MUTUAL INDUCTANCE 16-4

16.4 COUPLING FACTOR 16-5

16.5 ENERGY STORED IN MAGNETIC FIELD 16-516.5.1 Spark suppression 16-5

17 INDUCTORS 17-117.1 CONSTRUCTION 17-1

17.2 INDUCTOR SYMBOLS 17-2

18 INDUCTORS IN DC CIRCUITS 18-118.1 INDUCTORS IN SERIES 18-1

18.2 INDUCTORS IN PARALLEL 18-118.3 INDUCTORS IN A DC CIRCUIT 18-2

18.3.1 When dc current is applied 18-2

Page Index 5

18.3.2 Time constant 18-318.3.3 The Effects of back emf on circuit current 18-418.3.4 When dc current is removed 18-518.3.5 Safety 18-6

19 CIRCUIT SYMBOLS 19-1

Page Index 6

1 ATOMIC STRUCTURE

1.1 MATTER

Matter is defined as anything that occupies space and may be classified in anumber of ways.

1.1.1 STATES OF MATTER

There are three normal states of matter:

Solid. A solid has definite mass, volume and shape.

Liquid. A liquid has definite mass and volume but takes the shape of itscontainer.

Gas. A gas has definite mass but takes the volume and shape of itscontainer.

1.1.2 CHEMICAL CLASSIFICATION OF MATTER

From a chemical view we again have three divisions:

Elements. An element is a substance which cannot by any known chemicalprocess be split into two or more chemically simpler substances.

Eg: Hydrogen; Oxygen; Copper; Iron; Aluminium; carbon.

Compounds. A compound is a substance which contains two or moreelements chemically joined together.

Eg: Water (Hydrogen and Oxygen); Salt (Sodium and Chlorine);Sulphuric Acid (Hydrogen, Oxygen and Sulphur).

Mixtures. A mixture consists of elements or compounds which are broughttogether by a physical process.

Eg: Salt and Sand; Earth and Sawdust; Carbon and Iron Filings.

1.1.3 ATOMIC CLASSIFICATION OF MATTER

Material may also be classified according to the particles it contains, this is theatomic view of matter. This view gives us a better understanding of electrical andelectronic phenomena and is the view we shall concentrate upon.

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1.2 MOLECULES

Let us take a piece of matter, for example, a drop of water and see whathappens when it is sub-divided into smaller and smaller portions.

The drop is first cut in half, each half drop-let halved and so on indefinitely. Theresulting smaller and smaller droplets will soon become invisible to the nakedeye, but it is known what happens if the process could be carried far enough; apoint would eventually be reached where the particles of water are of such a sizethat further sub-division would split them into the hydrogen and oxygen of whichthey are composed. These last minute particles of water are known as moleculesand are the smallest particles of water which can exist alone and still behavechemically as water.

Every material is built-up from molecules and there are as many differentmolecules as there are different substances in existence.

Molecules. The molecule of an element or compound is the smallest particle of itwhich can normally exist separately. It consists of one or more atoms, of thesame or different types joined together. The term ‘molecular structure’ is usedwhen compounds are discussed.

1.3 ATOMS

If a water molecule could be magnified sufficiently it would be seen to consist ofthree smaller particles closely bound together. These three particles are ATOMS,two of hydrogen and one of oxygen.

The water is a compound, the oxygen and hydrogen are elements. Everyelement has atoms of its own type. There are 92 naturally occurring elementsand therefore 92 types of naturally occurring atoms.

Every molecule consists of atoms. Molecules of elements contain atoms of thesame types, for example the hydrogen molecule consists of two atoms ofhydrogen joined together, the oxygen molecule consists of two atoms of oxygenjoined together, but the molecules of compound contain different atoms joinedtogether.

Most molecules contain more than one atom but some elements can exist assingle atoms. In such a case the atom is also the molecule. For example theHelium atom is also the Helium molecule.

An atom is the smallest indivisible particle of an element which can take part in achemical change. The term ‘atomic structure’ is use when talking aboutelements.

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1.3.1 THE STRUCTURE OF AN ATOM

The Nucleus and Electrons. Atoms themselves are also composed of evensmaller particles. Let us take an atom of hydrogen as an example. A hydrogenatom is very small indeed (about 10 -10 in diameter), but if it could be magnifiedsufficiently it would be ‘seen’ to consist of a core or nucleus with a particle calledan electron travelling around it in an elliptical orbit.

The nucleus has a positive charge of electricityand the electron an equal negative charge; thusthe whole atom is electrically neutral and theelectrical attraction keeps the electron circlingthe nucleus. Atoms of other elements havemore than one electron travelling around thenucleus, the nucleus containing sufficientpositive charges to balance the number ofelectrons.

Protons and Neutrons. The particles in the nucleus carrying a positive chargeare called protons. In addition to the protons the nucleus usually containselectrically neutral particles called neutrons. Neutrons have the same mass as

protons, whereas electrons are very much smaller - only

proton

1.3.2 THE FUNDAMENTAL PARTICLES

11836 of the mass of a

Although other atomic particles are known, the three fundamental ones are:

Protons. The proton has unit mass and carries a unit positive charge.

Neutron. The neutron has unit mass but no electrical charge.

Electron. The electron has only

negative charge.

11836 unit of mass but it carries a unit

Thus, although we have 92 types of naturally occurring atoms, they are all built-up from different numbers of these three fundamental particles.

Page 1-3

Thus our picture of the structure of matter is as shown below.

Material

MoleculesHundreds of different kinds

Atoms92 Natural types

Protons Neutrons Electrons

1.3.3 PARTICLE FUNCTION

1.3.3.1 Protons

The number of protons in an atom determines the kind of material:

Eg. Hydrogen 1 proton

Helium 2 protons

Lithium 3 protons

Beryllium 4 protons

etc

Copper 29 protons

etc

Uranium 92 protons

The number of protons is referred to a the atomic number, thus the atomicnumber of copper is 29.

1.3.3.2 Neutrons

The neutron simply adds to the weight of the nucleus and hence the atom. Thereis no simple rule for determining the number of neutrons in any atom. In factatoms of the same kind can contain different numbers of neutrons. For examplechlorine may contain 18 - 20 neutrons in its nucleus.

The atoms are chemically indistinguishable and are called isotopes. The weightof an atom is due to the protons and neutrons (the electrons are negligible inweight), thus the atomic weight is virtually equal to the sum of the protons and theneutrons.

Page 1-4

1.3.3.3 Electrons

The electron orbits define the size or volume occupied by the atom. Theelectrons travel in orbits which are many times the diameter of the nucleus and

hence the space occupied by an atom is virtually empty! The electrical propertiesof the atom are determined by how tightly the electrons are bound by electricalattraction to the nucleus.

1.3.4 IONS

A neutral atom contains an equal number of positive charges (protons) andnegative charges (electrons). It is possible for an atom to gain or loose anelectron.

An atom (or possibly a group of atoms) which loses an electron has lost one of itsnegative charges and is therefore left with an excess of one positive charge; it iscalled a positive ion. An atom that gains an electron has an excess of negativecharge and is called a negative ion.

1.4 ELECTRICAL MATERIALS

Materials which allow an electric current to flow easily are known as conductorsand those which prevent the flow of an appreciable current are known asinsulators. Conductors and insulators are used in electrical circuits to providepaths for and to control the flow of, electric current. Practically all normalmaterials are either good conductors or good insulators. There are, however, afew materials which fall between these two categories and these are calledsemiconductors. Semiconductors will be studied in detail when we begin theelectronics phase of the course.

The best electrical conductor is silver, but for most purposes its high cost isprohibitive so copper is the standard conductor material. Aluminium is an

alternative, but it is not such a good conductor. Brass, which is harder thancopper, is commonly used for terminals, switches etc. Tungsten and nickel areused in the construction of lamps and thermionic valves.

Page 1-5

1.4.1 ELECTRON DISTRIBUTION

The atoms of a solid have electrons rotating in orbits around the positive nucleus.This is true of gases and liquids as well. These orbiting electrons exist in energyshells or levels.

The potential energy (energy of position) increases with distance out from thenucleus. The outermost occupied energy level is called the valence shell. This isa higher energy level than the energy levels of electrons in the other shells sincethe electrons are rotating further from the nucleus.

The electrons in the valence shell can most easily pass from one atom to anotherand thus constitute an electric current. Furthermore, the valence electrons arethe ones that go into chemical reactions, or combinations, with other atoms.

When an outside influence such as an electric field or heat is applied, a valenceelectron may acquire sufficient energy to jump through a forbidden (energy) gapand on into the conductor band where it is free of any influence of the positivenucleus and becomes a carrier of electricity, ready to take the place of anotherelectron that has just left its own atom, in the same manner.

1.4.2 IONISATION

If the amount of external energy is large enough the valence electron can gainsufficient kinetic energy (energy of movement) to be removed completely from itsatomic orbit and may not be replaced by another accelerated electron. Thisprocess is known as ionisation, since an atom which now contains one moreproton than can be neutralised by the remaining electrons is a positive ion. Gas-filled devices such as Neon tubes make use of this process. In a solid whereatoms are close together, simple ionisation does not occur as with individualitems.

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1.4.3 ENERGY LEVELS

The energy levels, measured in electron volts (e.v.) in which orbiting electronsexist comply with a law of physics which states that energy can be given toelectrons only in discrete amounts (quanta) which means that there are energyvalues that an electron cannot acquire. From this it can be deducted that there isa forbidden energy gap between each of the allowed energy bands K to O.

The width of the forbidden energy gap between the top of the valence band andthe bottom of the conduction band determine the electrical conducting propertiesof materials.

1.4.4 CONDUCTORS

Elements with 1 or 2 electrons in their outer orbits readily transfer them from atomto atom, because there is an overlap between the valence and conduction bands.Silver and copper elements are good conductors.

1.4.5 INSULATORS

Elements with 6 to 8 valence electrons cannot have electrons-in the conductionbands because the forbidden gap is to large. Sulphur and rubber elements areinsulators.

1.4.6 SEMI-CONDUCTORS

The elements Germanium and Silicon have four electrons in their valence shells.In conductivity they lie between good conductors and good insulators, ie; they aresemi-conductors.

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2 STATIC ELECTRICITY

If electrons are removed from one material and placed on another, or if they aremoved from one region of a piece of material to another, we have a separation ofcharge. The material, or area, that receives the electrons becomes negativelycharged and the material or region that loses electrons becomes positivelycharged. If these accumulations of charge remain stationary after their transfer,they are referred to as static electricity.

Common examples of static electricity are the small shock you get when youtouch a door handle having walked across a carpet, or the crackling you hear

when you remove certain items of clothing. In both cases electrons have movedfrom one material to the other. This type of static charging between two or moredissimilar materials is known as triboelectric charging and is a very importantfactor in the design of aircraft and aircraft furnishings and equipment.

The nature and size of the charge produced depends on the materials, someloose or gain electrons more easily than others. The Triboelectric series on thenext page list materials in the order in which they gain or loose electrons. The listis arranged such that, if any two materials are selected and rubbed together theone higher up the list will obtain a positive charge and the one lower down the list,a negative charge. So if a glass rod is rubbed with fur, the rod will becomenegatively charged, but if it is rubbed with nylon it will become positively charged.

When an insulating material is charged by rubbing it with another material, theelectrons are not free to move through the material. The charge thereforeremains at the point of friction. If a conductor is charged through rubbing, theelectrons are free to move and the charge will dissipate unless the conductingmaterial is insulated from its surroundings.

If two statically charged items are brought into contact with one another, electronswill transfer from the more negative to the more positive one. This movement ofelectrons constitutes a current flow, which will cease once the charges are equal.

The region around the charged body may be detected and is called an electricfield, the electric field is analogous to a magnetic field, which will be studied laterin the course. The electric field is represented in magnitude and direction byelectric lines of force. The density or magnitude of the force may be representedby the number of lines, and the direction is indicated by arrows that point frompositive to negative.

Isolated positive andnegative charges

Page 2-1

Triboelectric Series

AirHuman SkinAsbestosRabbit FurGlass

MicaHuman HairNylon

WoolFur

LeadSilk

AluminiumPaperCottonSteelWoodAmber

Sealing WaxHard RubberNickel, CopperBrass, SilverGold, PlatinumSulphurAcetate RayonPolyester

CelluloidOrionSaran

PolyurethanePolyethylenePolypropylenePVC (vinyl)Kelf (ctfe)

SiliconTeflon

Increasingly Positive

Increasingly Negative

Page 2-2

2.1 ATTRACTION & REPULSION

It can be observed, that if two negatively charged bodies are brought together,there is a force of repulsion between them. Similarly if two positively chargedbodies are brought together there is a force of repulsion. However, if a positivelycharged body is brought close to a negatively charged body, they attract eachother. Hence:

Like Charges Repel, Unlike Charges Attract.

The force of attraction or repulsion is governed by an inverse square law

2.2 UNIT OF CHARGE

The charge on an electron is very small, therefore a more practical unit of chargecalled a Coulomb, has been chosen:

One Coulomb = 6.29 x 1018 electrons

2.3 STATIC ELECTRICITY & AIRCRAFT

As mentioned earlier, the effects of static electricity are of considerableimportance in the design of aircraft and aircraft equipment. An aircraft in flightpicks up static charges as it flies through rain, cloud, snow, dust and otherparticles in the atmosphere. This build-up of statics is referred to asprecipitation static.

The amount of charge that builds up in any particular part of the aircraft dependson the atmospheric conditions to which it is subjected, and the material of which itis made. If two adjacent pieces of material are able to build up charges atdifferent rates, a potential difference will exist between them. Eventually thepotential difference will be sufficient to break down the insulation and current willjump as a spark between the 2 materials. This spark creates numerousproblems; it damages the materials, it causes corrosion, it radiates radiofrequencies that interfere with radio and navigation equipment and it could ignitefuel or oil vapour. In order to prevent this happening, it is essential that all of theaircraft structure and equipment is interconnected or bonded. Bonding allowssmall currents to continuously flow between materials and equipment, therebypreventing the build up of large static charges.

Page 2-3

An aircraft often accumulates very high electric charges, not only fromprecipitation but also from the high velocity gases exiting the engine exhausts.When the charge is sufficiently large, it will start to dissipate into the surroundingatmosphere from any sharp or pointed parts of the aircraft, such as the trailingedges of aerofoil sections. The point at which this occurs is called the coronathreshold. The corona discharge produces severe radio interference and needsto be controlled. This is achieved using special devices called wicks, that allowthe charge to dissipate in a controlled manner from specific points on the aircraftso that it causes minimum interference.

The subject of static electricity can be considered amusing or annoying when onesuffers from its effects. However, it must be taken very seriously by aircraftmaintenance engineers. The following are a few points to consider.

It essential to maintain the integrity of bonding when carrying out anymaintenance work on aircraft.

You can build up a charge on yourself as you move and work around theaircraft. Much of the equipment in modern aircraft is electronic, and caneasily be destroyed by you discharging static through it.

When an aircraft is refuelled, is the refuel vehicle at the same potential as theaircraft. If it isn’t, then it could be possible for a spark to ignite fuel vapour asthe fuel nozzle comes into close proximity with the aircraft. It is essential thatthe two vehicles are interconnected electrically before any hoses or fillers areopened.

An aircraft in flight can have a potential several thousand volts higher than theground. This charge is dissipated through the tyres or special straps on theundercarriage when the aircraft lands.

When an aircraft is inside a hangar for maintenance it should be correctlygrounded.

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3 ELECTRICAL TERMINOLOGY

3.1 VOLTAGE

Voltage is the electrical equivalent of mechanical potential. If a person drops arock from the first storey of a building, the velocity it will reach when dropped willbe fairly small. However, if the rock is dropped from the twentieth floor, it willhave reached a much greater velocity on reaching the ground. On the twentiethfloor the rock had much more potential energy.

The potential energy of an electrical supply is given by its voltage. The greaterthe voltage of a supply source, the greater its potential to produce a current flow.Thus, a 115 volt supply has 115 times the potential to produce a current flow thana 1 volt supply.

3.1.1 POTENTIAL

If one coulomb of electrons is added to a body and one joule of work has beendone, then the body will acquire of potential of - 1 volt. If the electrons had beenremoved, then the body would have acquired a potential of +1 volt. The unit ofpotential is the volt.

3.1.2 POTENTIAL DIFFERENCE

When charges move from one point to another, it is not the actual values ofpotential at those points which are Important, but the potential different (pd)

through which the charge has travelled. Just as lifting weight in the gymnasium,the height above sea level is not important, but the distance between the gymfloor and the height of one’s body. In cases where an actual level of potential isrequired, the zero of potential is taken as Earth and whenever the potential at apoint is given, it means the difference in potential between the point and theearth’s surface.

If one coulomb of electricity requires one joule of work to move it between twopoints, then there is a potential difference of 1 volt between them. It is sometimeshelpful to think of potential difference as a difference of ‘electrical pressure’forcing a current through a load.

If a current flows round a circuit, then a potential difference must exist betweenany two points in that circuit and each point in the circuit must be at a differentpotential. However because there is very little opposition to current flow inconducting wires, very little potential difference is required to push the currentalong the wires and it is normally assumed to be zero. Whenever the oppositionto current flow is not negligible, then a potential different exists across thatcomponent to push the electrons through the device.

The converse is also true, if no current is flowing, then no potential differenceexists. The larger the potential difference the larger the current.

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3.1.3 ELECTROMOTIVE FORCE - EMF

To make use of electricity by provision of an electric current, the potentialdifferent must be maintained. That is, the positive and negative charge must becontinuously replenished. A cell (or battery) uses chemical energy to maintainthe potential difference.

Another device used for this purpose is the generator, which uses electro-mechanical energy to maintain the potential difference. The potential differenceacross the terminals of the source (cell, battery or generator) when it is notsupplying current, is called Electromotive Force (emf), since this is a measure ofthe force available to push electrons around the circuit. In a circuit with a currentflowing, the potential difference across the terminals of the source is always lessthan the emf and is referred to as the terminal voltage.

3.2 CURRENT

The SI unit of current is the ampere (A). Although it is known that electric currentis a flow of electrons, this flow cannot be measured directly.

3.2.1 MOVEMENT OF CHARGE

Although electric current is referred to as the flow of electrons through aconductor, it should be noted that more exactly, any movement of electric chargeconstitutes an electric current. Thus, passage of electricity may occur through a:

conductor such as metal, due to the movement of the loosely held outerelectrons of the atoms.

vacuum or gas, due to the movement of electrons.

gas, due to the movement of the ionised gas molecules.

liquid, due to the ionisation of certain molecules, particularly those of acidsand salts in solution (e.g. Electrolytes).

The ampere may be defined in terms of the mechanical units of force and length,a more helpful picture is that of moving electrons. When a current of one ampereis flowing in a conductor, one coulomb of charge passes any point in theconductor every second.

The ampere is thus a measure if the rate of flow of electrons.

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The Coulomb and the Ampere

Since one coulomb = 6.29 x 1018 electrons, one ampere equals a flow rate of

6.29 x 1018 electrons per second,

Ampere =Coulomb

Secondsor I

Q

T

3.2.2 CONVENTIONAL FLOW

An applied emf causes directional flow. Using conventional flow the charge

carriers are considered to be positive, that is they leave the positive terminal of a

supply and return to the negative terminal.

This form of flow was decided upon before anybody knew exactly what ‘current

flow’ was, however it is still widely used in Britain and will be assumed throughout

the course, unless stated otherwise.

3.2.3 ELECTRON FLOW

It is now known that current flow is a movement of negatively charged particles.

I.e., electrons. Electrons flow from the negative terminal to the positive terminal.

This form of flow is referred to as electron flow and is used extensively in the

United States.

3.3 RESISTANCE

An electric current is a flow of free electrons through a conductor. The size of

current flowing through a conductor for a given applied voltage depends on:

The number of free electrons.

The opposition to free movement of the electrons caused by the structure of

the material.

These two factors taken together give an effective opposition to current flow

which is called resistance. To simplify matters it is usual to ignore the second

factor and equate good conductors to a large number of free electrons and poor

conductors to fewer free electrons. Hence, a good conductor is a material which

has low resistance, i.e. a large number of free electrons, and allows a large

current to flow. Conversely a poor conductor has a high resistance, i.e. few free

electrons and allows only a small current to flow for the same applied voltage.

Because the value of the current flowing is determined by the resistance in the

circuit, current flow can be controlled by varying the resistance.

Even the best conductors have resistance.

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3.3.1 FACTORS AFFECTING RESISTANCE

The four factors that affect the resistance of a wire conductor are:

Material. Some materials conduct better than others.

Length (). Resistance is directly proportional to length, thus if the length isdoubled (other factors remaining constant), resistance is doubled.

Cross Sectional Area (A). Resistance is inversely proportional to A. Thus ifthe cross sectional area is doubled, resistance is halved.

Temperature. Temperature affects the number of free electrons and henceresistance.

3.3.2 UNITS OF RESISTANCE

Resistance is measured in ohms, symbol (omega). The resistance of a pieceof material is one ohm if a potential difference of one volt applied across it causesa current of one ampere to flow.

3.4 CONDUCTANCE AND CONDUCTIVITY

The conductance, G of a material is the reciprocal of its resistance and is;

G 1

R

1

/a

a

The conductivity of a material is the reciprocal of its resistivity. It is given the

Greek symbol (sigma) and has the units siemens per metre (s/m).

Thus at 0C copper has a conductivity of;

1

1-815510

6645210 s/m

Conductance and conductivity are rarely used in the course, but a mention isrequired.

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4 PRODUCTION OF ELECTRICITY

Very large amounts of electrical energy lie dormant in the atoms of every speck ofmaterial in the universe. Whilst the atoms remain electrically balanced however,this electricity cannot be put to any practical use. What is needed is some form ofexternal energy that will separate the electrons from their nuclei. In this way, theexternal energy that is applied will give rise to electrical energy.

There are six sources of external energy that are capable of separating theelectrons from their nuclei, these are friction, pressure, magnetism, heat, light andchemical action.

4.1 BY FRICTION

Static electricity, that is the separation and build-up of charge is an everydayphenomenon that is often caused by friction - the physical stripping of electronsfrom one body and depositing on another. Early examples in science were therubbing of a glass rod (which loses electrons and gains a positive charge) with asilk stocking!(gains electrons, receives negative charge) and the rubbing of anebonite rod (receives negative charge) with cats fur (becomes positivelycharged). Everyday examples are:

Combing the hair (dry). The comb attracts the individual hairs and the hairsrepel each other and stand on end.

Removing a shirt (especially nylon). The shirt crackles and sparks may beseen, the shirt is also attracted to the body.

The receiving of ‘electric shock’ from cars (also aircraft) when touching themon the outside. Here the charge has been produced by the friction of airpassing around the vehicle.

The rapid collection of dust by records. The dust is attracted by the chargebuilt up on the record produced by friction of handling and playing.

Lightning flash is a result of the build up of static electricity in clouds.

Although not used to produce electricity for any aircraft systems, staticelectricity is generated by friction as the aircraft moves through the air andwill therefore be considered at various points throughout the course.

4.2 BY PRESSURE

Certain crystals and semiconductors produce an emf between two opposite faceswhen the mechanical pressure on them is either increased or decreased (thepolarity of the emf is reversed when the pressure changes from an increase to adecrease). This emf is known as the piezoelectric emf.

Page 4-1

This effect is used in a number of devices including semi-conductor strain gaugesand vibration sensors. As the mechanical pressure on the crystal is altered, avarying voltage which is related to the pressure is produced by the crystal. Thevoltage can be as small as a fraction of a volt or as large as several thousandvolts depending on the crystal material and the pressure. Aircraft systemsemploying the piezoelectric effect generally only produce very small emf’s, thevery high voltages produced by materials such as lead zirconate titanate are usedin ignition systems for gas ovens and gas fires.

4.3 BY MAGNETISM

Magnetism itself is not used as the direct source of external energy. In a mannerwhich will be studied in great detail later in the course, large amounts of electricalenergy are produced by machines called generators. Energy is used to drive thegenerator, which when it turns, makes use of the properties of magnetism toproduce the external energy necessary to break the electrons away from theirnuclei and so make it possible for electric current to flow.

4.4 BY HEAT

The Seebeck effect - the thermocouple. When two different metals arebrought into contact with one another, it is found that electrons can leave one ofthe metals more easily than they can leave the other metal. This is because ofthe difference in what is known as the work function of the two metals. Sinceelectrons leave one metal and are gained by the other, a potential differenceexists between the two metals; thus the emf is known as the contact potential orcontact emf.

If two metals, say copper and iron, are joined at two points as shown in thediagram above, and both junctions are at the same temperature, the contact

potentials cancel each other out and no current flows in the loop of wire.However, Thomas Johann Seebeck (1770 -1831) discovered that if the two

junctions are kept at different temperatures, there is a drift of electrons around thecircuit, that is to say, current flows.

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The magnitude of the voltage produced by this method is small - only a fewmillivolts per degree centigrade - but it is sufficient to be measured. The currentflow is a measure of the difference in temperature between the ‘hot’ junction andthe ‘cold’ junction.

Each junction is known as a thermocouple and if a number of thermocouples areconnected in series so that alternate junctions are ‘hot’ and the other junctionsare ‘cold’, the total emf is increased; this arrangement is known as a thermopile.

On aircraft, thermocouples are used for temperature measurement and will beexamined in more detail at a later date.

4.5 BY LIGHT

The Photovoltaic Cell or Solar Cell. A photovoltaic cell generates an emf whenlight falls onto it. Several forms of photovoltaic cell exist, one of the earliest typesbeing the selenium photovoltaic cell in which a layer of selenium is deposited oniron and any light falling on the selenium produces an emf between the seleniumand the iron.

Modern theory shows that the junction at the interface between the two forms,what is known as a semi-conductor p-n junction in which one of the materials is p-type and the other is n-type. The most efficient photovoltaic cells incorporatesemi-conductor p-n junctions in which one of the regions is a very thin layer(about 1m thick) through which light can pass without significant loss of energy.When the light reaches the junction of the two regions it causes electrons andholes to be released, to give the electrovoltaic potential between the two regions.

A better understanding of this action will be obtained later in the course whensemi-conductor materials and devices are studied.

4.6 BY CHEMICAL ACTION

The final method of producing electricity is by chemical action. It is the particularkind of chemical action that takes place in ‘electric cells’ and ‘batteries’ which isput to practical use in the production of electricity.

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Page 4-4

5 CELLS & BATTERIES

To study electrical principles further we require a source of emf. Although an emfcan be produced by any of the six methods discussed above, large amounts ofuseable power can only be produced chemically or by generation. Generationrequires a more in depth study of magnetism and therefore cells and batteries willbe studied first.

On an aircraft, the battery may be used for engine starting, but far moreimportantly, the battery is the source of emergency power when the generatorfails. Although aircraft battery systems and servicing will be studied at a laterdate, battery principles and battery construction will be studied now and will notbe repeated.

5.1 PRINCIPLES

A Cell is a portable device which converts chemical energy into electrical energy.A group of interconnected cells is known as a battery. Cells operate on aprinciple of the exchange of charges between dissimilar metals.

5.1.1 CELL & BATTERY SYMBOLS

The circuit symbols for cells and batteries are shown below. To identify thepolarity of the terminals, a long thin line is used to represent the positive terminaland a short thick line the negative terminal. Sometimes the terminal voltage isindicated.

5.1.2 CONSTRUCTION & CHEMICAL ACTION

In cells, an electrolyte separates two charge collecting materials calledelectrodes, to which external connections are made. The electrolyte pushes

electrons onto one of the plates and takes them off the other. This action resultsin an excess of electrons, or a negative charge, on one plate and a loss ofelectrons, or a positive charge, on the other plate.

Electrolytes are chemical solutions manufactured to allow the generation and freemovement of both types of ions, and are normally acid or alkaline pastes orliquids.

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The action of the electrolyte in carrying electrons fromone plate to the other is actually a chemical reactionbetween the electrolyte and the two plates. This actionchanges chemical energy into electrical charges onthe cell plates and terminals.

With nothing connected to the cell terminals, theelectrons would be pushed onto the negative plateuntil there was no more room. At the same time theelectrolyte would take electrons from the positive plateto make up for those it had pushed onto the negativeplate. Both plates would then be fully charged and themovement of electrons would cease.

If a wire were connected between the negative and positive terminals of the cell,electrons on the negative terminal would leave the terminal and travel through thewire to the positive terminal. The electrolyte would carry more electrons acrossfrom the positive plate to the negative plate. Whilst the electrolyte is carryingelectrons you would see the negative plate being used up and you would seebubbles of gas at the positive plate.

5.1.3 PRIMARY & SECONDARY CELLS

In a primary cell, current will continue to flow until chemical action had dissolvedthe negative plate into the electrolyte, at which point the cell would be exhaustedand of no further use.

In a secondary cell, the chemical action that takes place whilst the cell isproducing a current flow is reversible, enabling the cell to be re-used. The

process of reversing the chemical action is referred to as charging and entailspassing a current through the cell in the opposite direction to the dischargecurrent.

5.1.4 CELL EMF

The size of a cell has no bearing on the emf that it will produce, the generatedemf being determined solely by the materials used in its construction. Anotherpoint to note is that the potential difference, or voltage measured across theterminals of a cell, is not the same as the emf generated by the cell. The terminalvoltage of a cell depends on the:

internal resistance of the cell.

size of the discharge current.

charge state of the cell.

The size of the discharge current. As a general rule, whenever a cell isproviding current, the terminal voltage will be less than the cell emf. The

larger the discharge current, the greater the difference between the cell emfand its terminal voltage.

Page 5-2

The internal voltage of the cell. All sources of electricity have internalresistance which affects the terminal voltage, this will be examined in moredetail later in the notes.

5.1.5 CELL CAPACITY

The amount of electrical energy that a cell can provide from new to the end of itsuseful voltage on load is called the cell capacity and is quoted in Ampere-hours(A-h).

Capacity varies with the amount of current drawn from the cell, the greater thecurrent the lower the capacity, therefore capacity is normally quoted at a standardrate. The 1hr rate is the internationally accepted standard for Nickel Cadmiumcells, with 10 hr or 20 hr rates being used for Lead Acid cells.

A cell quoted at 40A-h at the 10 hr rate will provide 4 Amps continuously for 10hours.

A battery quoted at 40A-h at the 1 hr rate will provide 40 Amps continuously for 1hour.

A 40 A-h cell will only be able to provide a discharge current of 80 amps forapproximately 20 minutes, not 30 minutes as may be expected by calculation.Similarly, it will be able to supply a discharge current of 20 amps for longer thanthe expected 2 hrs.

The capacity of a cell is also affected by its age, the older a cell, the lower itscapacity, therefore the only way of determining actual capacity is to measure it.

5.1.6 INTERCONNECTION OF CELLS

Cells may be connected in series, parallel or any combination of the two in orderto form a battery. When cells are connected to form a battery they should be ofsimilar construction, and have the same terminal voltage, internal resistance andcapacity.

Series connection. When connected in series:

The battery voltage is the total of the individual cell voltages.

The battery resistance is equal to the total of the individual cell resistances.

The battery capacity is the same as the capacity of a single cell.

Page 5-3

Parallel connection. When connected in parallel:

The battery voltage is the same as the voltage of a single cell.

The battery resistance is equal to the parallel total of the cell resistances.

The battery capacity is equal to the total of the individual cell capacities.

These rules can also be applied when connecting batteries together in series,parallel or any combination of the two.

5.2 LEAD ACID BATTERIES

Lead acid cells have a nominal voltage of 2 Volts, therefore a typical 24V aircraftbattery would consist of 12 cells connected in series. The active material in thepositive plates is Lead Peroxide (Pb02) the negative plates, Spongy Lead (Pb).The electrolyte is dilute sulphuric acid (2H2SO4).

5.2.1 CONVENTIONAL CONSTRUCTION

There are two forms of Lead Acid battery construction, conventional and solidblock, often referred to as a Varley type battery.

In the conventional battery the plates consist of lead grids into which the activematerials are pressed. The positive and negative plates are then interleaved andconnected to a lug that forms both a mechanical support and the terminal.

Cells are generally constructed with an additional negative plate, making bothoutside plates negative. This ensures that chemical action takes place on bothsides of each positive plate. When chemical action only takes place on one sideof a positive plate it tends to buckle.

The plate arrangement is then inserted into a composite material container whichis fitted with a lid. The inside of the container is ribbed to provide additionalsupport for the plates, which are raised clear of the bottom of the container toprevent shorting by any sediment that forms.

Page 5-4

To provide further support for the plates and to ensure they cannot touch,separators are fitted, these were originally cedar wood but modern batteries usemicro-porous plastic materials.

Each cell is fitted with a special non spill valve that allows gasses to escape, butprevents the spillage of electrolyte, this valve can be removed for checking andadjusting the electrolyte level.

The electrolyte used is sulphuric acid diluted with pure distilled water, the specificgravity of the electrolyte used is determined by the manufacturer, however, it isgenerally lower than 1300.

5.2.2 SOLID BLOCK TYPE CONSTRUCTION

In the solid block type battery the electrolyte is completely absorbed into acompressed block consisting of porous plates and separators.

The plates are completely supported and therefore a more porous active materialpaste can be used, this gives better absorption and an enhanced electrochemicalactivity.

The support given to the plates means practically no distortion and no shedding,therefore no sludge gap is required, all the space inside the cells being used forthe plates.

All of these advantage result in a battery that is stronger, less susceptible tovibration damage and has a higher capacity to weight ratio than its conventionalcounterpart.

Page 5-5

5.2.3 CHEMICAL ACTION

When the lead acid battery is delivering current, the sulphuric acid breaks up intoHydrogen ions (H2) carrying a positive charge and Sulphate ions (SO4) carrying anegative charge. The SO4 ions combine with the lead plate (Pb) and form leadsulphate (PbSO4). At the same time they give up their negative charge, thuscreating an excess of electrons on the negative plate.

The H2 ions go to the positive plate and combine with the oxygen of the leadperoxide (PbO2) forming water (H2O), during the process they take electrons fromthe positive plate. The lead of the lead peroxide combines with some of the SO4

ions to form lead sulphate on the positive plate.

The result of this action is a deficiency of electrons on the positive plate and anexcess of electrons on the negative plate.

When a circuit is connected to the battery, electrons flow from the negative plateto the positive plate. This process will continue until both plates are coated withlead sulphate. The lead sulphate is highly resistive, and it is mainly the formationof the lead sulphate which gradually lowers the battery capacity until it isdischarged.

During charging, current is passed through the battery in a reverse direction. TheSO4 ions are driven back into solution in the electrolyte, where they combine withthe H2 ions of the water, thus forming sulphuric acid. The plates are thus returnedto their original compositions.

The sulphuric acid is effectively used up as the battery is discharged, andreturned to the electrolyte as it is charged, a test of the specific gravity of theelectrolyte will give a good indication of the state of charge of the battery.

Page 5-6

5.2.3.1A simple overview of the charge and discharge characteristics

During discharge the plates are converted into lead sulphate, the water content ofthe electrolyte increases, the internal resistance of the cell increases and theterminal voltage decreases.

By passing a current through the battery in the opposite direction these effectsare reversed. The plates are converted back to their original form, the watercontent of the electrolyte decreases, the internal resistance decreases and theterminal voltage increases. The process of recharging takes approximately 8 to

10 hours.

During most of the charge and discharge cycle the battery terminal voltageremains constant at 1.95V, it therefore gives no indication as to the battery’s stateof charge.

The specific gravity of the electrolyte however changes at a regular rate as thebattery is charged, or discharged and can therefore be used to determine thebattery’s state of charge.

5.2.4 VOLTAGE & SPECIFIC GRAVITY CHARACTERISTICS

The voltage and specific gravity figures for a lead acid battery are:

Fully charged and still connected to the charging board charge:

2.5 to 2.7 Volts 1270 to 1280 SG

Fully charged and off charge:

2.2 to 2.5 Volts 1270 to 1280

SG

Fully Discharged:1.8 Volts 1150 SG

The battery will be damaged if allowed to go below the above discharged values.

5.2.5 COMMON LEAD ACID BATTERY FAULTS

Careful treatment of lead acid batteries prevents damage and early failure,however, some common faults associated with lead acid batteries are:

Sulphation is the formation of hard, permanent lead sulphate on the plates andappears as random greyish white patches. Sulphation causes an increase in theinternal resistance of the battery, leading to possible overheating and buckling ofthe plates.

Sulphation is caused by continually undercharging the battery or by dischargingbelow 1.8 Volts or 1150 SG and is severe there is no cure, however if mild it cansometimes be cured by giving the battery a long low charge.

Buckling is twisting and bending of the plates. Because the active material issqueezed out of the plates the capacity of the battery may be reduced, if severe itcan lead to internal shorting of the battery.

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Buckling is caused by excessive charge and discharge currents being imposedon the battery and by the effects of sulphation.

There is no cure for buckling only prevention.

Sedimentation is the collection of discarded active material from the plates at thebottom of the cell.

Sedimentation may result in shorting of the plates and complete loss of capacity,slight shedding is normal in a well maintained battery.

5.3 NICKEL CADMIUM BATTERIES

5.3.1 CONSTRUCTION

The plates of a nickel cadmium battery are made by sintering a nickel plated steelscreen with nickel carbonyl powder. The resultant plaques are then impregnatedwith the active materials, Nickel salts on the positive, cadmium salts on thenegative. The plaques are then placed in electrolyte and subjected to a smallcurrent to convert them to their final form.

After washing and drying the plaques are cut into plates, each one having anickel tab welded to it. The plates are then stacked alternately to produce a cell.

Whilst producing the stack a continuous separator is wound between the plates to

prevent them shorting.

Terminals are then welded to the plates and the stack-up is inserted into itscontainer, which is sealed and pressure tested.

The separator used is normally a triple layer type, one layer of cellophane, two ofwoven nylon cloth. Cellophane is used because it has a low resistance and is agood barrier material, it prevents metal particles from shorting the plates whilstallowing current to flow. The cellophane also acts as a gas barrier, preventingoxygen given off by the positive plate during overcharge, from passing to thenegative plates. At the negative plates the oxygen combines with the cadmium,reducing the cell voltage and producing heat.

Page 5-8

The electrolyte, a solution of potassium hydroxide and distilled water, with a SGof between 1240 and 1300, is then injected into the cell under a vacuum. Fitted tothe top of each cell is a special vent that allows the escape of gas but preventselectrolyte spillage.

In a typical Ni-Cad battery the cells are mounted in a metal case that incorporates2 venting outlets, carrying handles, a quick release connector and a lid. Each cellis separated from its neighbour by its moulded plastic case and electricallyconnected by nickel plated steel links between the terminals.

5.3.2 CHEMICAL ACTION

As the battery discharges, hydroxide ions (OH) from the electrolyte combine withthe cadmium in the negative plates and release electrons to the plate. Thecadmium is converted to cadmium hydroxide during the process. At the sametime, hydroxide ions from the nickel hydroxide positive plates go into theelectrolyte carrying extra electrons with them. Thus electrons are removed fromthe positive plate and delivered to the negative plate during discharge.

The composition of the electrolyte remains a solution of potassium hydroxidebecause hydroxide ions are added to the electrolyte as quickly as they are

removed. For this reason the specific gravity of the electrolyte remains essentiallyconstant at any state of charge. It is therefore impossible to use the specificgravity as an indication of the charge state of the battery.

When the battery is charged, the hydroxide ions are caused to leave the negativeplate and enter the electrolyte. Thus the cadmium hydroxide of the negative plateis converted back to metallic cadmium. Hydroxide ions from the electrolyterecombine with the nickel hydroxide of the positive plates, and the active materialis brought to a higher state of oxidation. This process continues until all the activematerial of the plates have been converted. If charging is continued, the batterywill be in overcharge, and the water in the electrolyte will be decomposed byelectrolysis. Hydrogen will be released at the negative plates and oxygen at thepositive plates. This combination of gases is highly explosive.

Page 5-9

5.3.2.1A simple overview of the charge and discharge characteristics

During charging and discharging the electrolyte acts only as an ionisedconductor, transporting electrons from one plate to the other, its specific gravityremaining constant.

On discharge the terminal voltage initially falls rapidly and then remains constantfor most of the discharge cycle, dropping rapidly again when the battery is nearlyfully discharged.

When charged, the terminal voltage initially rises rapidly and then settles to agradual increase. A second rapid rise takes place as the battery reaches the fullycharged condition, at this time gassing takes place, hydrogen being released atthe negative plates, oxygen at the positive plates, this combination of gases isexplosive. Prolonged gassing should be avoided as it reduces the water contentof the electrolyte and causes overheating of the battery, a slight amount ofgassing, however, is necessary to ensure charging is complete.

The terminal voltage remains constant for most of the batteries life and thespecific gravity of the electrolyte remains unchanged, the only way of determiningthe state of charge of the battery therefore, is to carry out a full charge followedby a capacity test.

During discharge the plates absorb electrolyte to such an extent that the levelmay disappear from view. As the battery is charged, the electrolyte is forced backout of the plates, a point to note when topping up the cells.

5.3.3 ADVANTAGES & DISADVANTAGES

A Nickel Cadmium battery has the following advantages over a Lead Acid battery:

They have a longer life

The terminal voltage remains almost constant during the discharge cycle

They can be charged and discharged at much higher currents withoutcausing cell damage

They can be discharged to a very low voltage without causing cell

damage

But have the following disadvantages: They are far more expensive to buy and maintain

Each cell has a lower voltage, therefore more cell are required to produce abattery.

They are more susceptible to thermal runaway.

5.3.4 THERMAL RUNAWAY

The battery looses heat by conduction and radiation. Provided the rate of heatloss is greater than the rate at which heat is generated there is no problem.

Page 5-10

Should the battery not be able to loose heat so quickly it will start to get hot. As itstemperature goes up the internal resistance decreases and the current increases.This increase in current leads to an increase in chemical activity within thebattery, this generates more heat and the cycle repeats.

Nickel Cadmium batteries are very susceptible to thermal runaway which canresult in the battery boiling, or even being totally destroyed.

5.4 SMALL ALKALINE CELLS

Hermetically sealed Ni-Cad cells are produced in the same size and shape astheir primary counterparts. They are small, portable and maintenance free, buthave the added advantage of being rechargeable.

The plates are constructed in a similar manner to the larger Ni-Cad cells, theseparator being a thin porous material. The electrolyte is fully absorbed by theplates and separator in a similar manner to the Varley type cell. With steel orplastic being used for the case.

Special vents are fitted to each cell, these allow the escape of gas but prevent theentry of oxygen and electrolyte leakage.

The nominal voltage of a fully charged cell is 125 volts and these can then beinterconnected to form batteries.

A 10 hour rate capacity is generally used with an end of life voltage of 1.1 volts, itis possible to discharge the cells further but damage will occur if allowed to gobelow 1 volt.

Charging should be carried out using a constant current at the 10 hour rate, totalcharge taking approximately 14 hrs, the end of charge “on charge” voltage being145 volts. Overcharging should be avoided, it produces heat and shortens thelong term life of the cell.

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Page 5-12

6 OHM’S LAW

So far you have been introduced to the concepts of electric current (as a

movement of free electrons through a conducting material), voltage (or potential)

and potential difference and to the resistance to current flow by any conducting

material. The relationship which exists between these quantities was discovered

by a physicist called Ohm and is now referred to as Ohm’s Law. This is the most

fundamental law in all electric’s and electronics.

Ohm’s law states: For a fixed metal conductor, with temperature and other

conditions remaining constant, the current through it is proportional to the

potential difference between its ends.

Mathematically this is expressed as:

I V

Thus the ratioV

IConstant

and this ratio is called the resistance of the conductor.

Hence we may write V = R where V is in voltsI I is in amperes

R is in ohms

6.1 TRANSPOSITION OF OHM’S LAW

By transposition it is seen that Ohm’s law may be written in three forms:

R = V

I

I = V

R

V = IR

thus resistance may be calculated if V and I are known.

thus current may be calculated if V and R are known.

thus voltage may be calculated if I and R are known.

Page 6-1

6.2 THE OHM’S LAW TRIANGLE

One simple way of memorising Ohm’s law is the Ohm’s law triangle - see below.

V

I R

By covering up the unknown quantity, the relationship between the remaining twois directly observed. You may check this against the equations in the above sub-chapter. This is not necessary if you are able to remember one form of theequation and derive the other two directly by transposition.

Page 6-2

7 ELECTRICAL MEASURING INSTRUMENTS

Quantities of electrical current, voltage and resistance are measured usinginstruments called meters. Until the advent of electronic displays andsemiconductor components, meters comprised a movement, working on themotor principle, driving a needle across a scale. These types of meters werecalled 'moving coil meters' or 'analogue meters'. Moving coil meters will bestudied in some depth later in the course, because the principle behind theiroperation is the same as the principle employed in many aircraft instruments.

Modern meters are referred to as a 'digital meters' or 'digital voltmeters', morecommonly abbreviated to DVM's, although they measure far more than justvoltage. Digital meters are cheaper, more reliable, more robust and generallyconsidered more accurate than their analogue counterparts, although somewould argue that, used correctly, an analogue instrument is just as accurate.

It is essential that you are confident in the use of both types of meter. There areinstances where a digital meter cannot be used, leaving no choice but to revert toan analogue meter.

7.1 CONNECTING METERS TO A CIRCUIT

Irrespective of whether the meter is digital or analogue, the way that it isconnected to the circuit under test is the same.

7.1.1 VOLTMETERS

Voltmeters are used to measure emf's and more commonly potential differences.The two probes of the meter are therefore connected to the two points betweenwhich the potential difference is required.

If the potential at A with respect to B is required, the red lead is connected topoint A, the black lead point B.

If the potential at B with respect to A is required, the red lead is connected topoint B, the black lead point A.

If the potential between a point and Earth or ground is required. The red lead isconnected to the point and the black lead is connected to ground or Earth.

Page 7-1

7.1.2 AMMETERS

Ammeters are used to measure current flow, as such they need to be inserted inseries with the circuit under test so that the current to be measured flows throughthe meter. This means the circuit must be broken.

To connect an ammeter, the power must be switched off. The circuit isbroken at the point where the current is to be measured. The meter is then

inserted into the circuit in such a way that, 'conventional current' flows into the redlead and out of the black lead. Once the meter is connected, circuit power isrestored and the measurement taken.

To disconnect the meter, the circuit power must again be switched off.Once the meter is removed from the circuit, the circuit must be reconnected.

7.1.3 OHMMETERS

The use of ohmmeters is somewhat more involved. Most importantly whenmeasuring resistance the circuit power must be switched off, power is

derived from within the instrument. Secondly, great care must be taken to ensurethere are no parallel paths that would affect the measurement. This is generallybest confirmed by removing the component or device, or by disconnecting oneend of it from the circuit concerned. Thirdly, it is essential that an analoguemeter is zeroed before it is used.

To measure resistance, the meter is simply connected across the component ordevice to be measured. The polarity of the leads is not important unlesssemiconductor type devices are present. (this will be discussed in a latermodule).

When making resistance measurement, care must be taken to ensure the correctrange is used. It is easy to mistake a low resistance value for a zero reading orshort circuit.

Page 7-2

7.2 ANALOGUE MULTIMETERS

Even the most basic analogue multimeter can prove to be invaluable when in thehands of an experienced user. Simple measurements of voltage, current andresistance can provide useful information on the state of almost any circuit. Whatmatters, of course, is the interpretation put on the readings obtained. To get thebest from such a simple instruments it is not only necessary to select anappropriate measurement function and range, but also to be aware of thelimitation of the instrument and the effect that it might, or might not, have on thecircuit under investigation.

The diagram below shows the controls and display provided by a simpleanalogue multimeter.

The range selector allows you to select from a total of twenty ranges and sixmeasurement functions. These functions are:

DC voltage (DC, V) DC current (DC, mA)

AC voltage (AC, V) Resistance (OHM)

Continuity test (BUZZ) Battery check (BAT)

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7.2.1 DC VOLTAGE MEASUREMENTS

Examples of how to make DC voltage measurements are show in the twodiagrams below. In both cases, the red and black test leads are connected to the'+' and '-' sockets respectively.

In the first diagram, the range selector is set to DC, V, 50V. The pointer isreading just less than 45 on the range that has 50 as its full-scale indication (notethat there are three calibrated voltage scales with maximum indications of 10V,50V and 250V respectively). The reading indicated is thus 45V, approximately.

Page 7-4

In the second diagram, the range selector is set to DC, V, 250V. The pointer ispositioned midway between the 50 and 100 scale markings and this indicates avoltage reading of 75V.

7.2.2 DC CURRENT MEASUREMENTS

An example of how to make a DC current measurement is shown in the diagrambelow. Once again, the red and black test leads connected to the '+' and '-'sockets respectively. The range selector is set to DC, 50mA. The pointer isreading just less than midway between 45 and 50 on the range that has 50 as itsfull-scale indication. The actual reading indicated is thus slightly less than

47.5mA, or approximately 47mA.

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7.2.3 DC HIGH-CURRENT MEASUREMENT

In common with many simple multimeters, both analogue and digital, the highcurrent range (e.g. 10A) is not only selected using the range selector switch but aseparate input connection must also be made. The reason for this is simply thatthe range switch and associated wiring is not designed to carry a high current.Instead, the high-current shunt is terminated separately at its own '10A' socket.

The connections and range selector settings to permit high-current DCmeasurement are shown below. The range selector is set to DC, 10A and the

red and black test leads are connected to '10A' and '-' respectively. The pointer isreading midway between 8 and 10 on the range that has 10 as its full-scaleindication. The actual reading indicated is thus 9A.

Page 7-6

7.2.4 AC VOLTAGE MEASUREMENTS

An example of how to make AC voltage measurements is shown in the diagrambelow. Once again, the red and black test leads are connected to the '+' and '-'sockets respectively. The range selector is set to AC, 10V. The pointer isreading midway between 0 and 2 and the indicated reading is 1V, approximately.

7.2.5 RESISTANCE MEASUREMENTS

Examples of how to make resistance measurements are shown in the diagramsbelow. In all three cases, the red and black test leads are connected to the '+'and '-' sockets respectively. Before making any measurements it is absolutelyessential to zero the meter. This is achieved by shorting the test leads togetherand adjusting the 'zero adj' control until the meters reads full-scale (i.e., zero onthe ohms scale).

Page 7-7

In the first diagram, the range selector is set to OHM, 1. The pointer is readingmidway between 0 and 10 and the resistance indicated is approximately 5.

In the second diagram, the range is set to OHM, 10. The pointer is readingexactly 30 and the resistance indicated is 30 10 or 300.

Page 7-8

In the third diagram, the range selector is set to OHM, 1k. The pointer isreading exactly 5k and the resistance indicated is 5k 1k or 5M.

7.2.6 CONTINUITY TESTING

An example of how to make continuity tests is shown below. The red and blacktest leads are connected to the '+' and '-' terminals respectively. The rangeselector is set to BUZZ. When there is a low-resistance path between the twotest probes, an audible buzz will be produced. No meter indication is producedon the continuity range.

Page 7-9

7.2.7 BATTERY TESTING

Several analogue multimeters provide a battery testing facility. The diagrambelow shows how to carry out a battery test on a 9V battery (e.g., PP3, PP9, etc).It is important to note that a battery test should not merely be a measurement ofthe battery terminal voltage and ideally such a measurement should be carriedout with the battery on-load (i.e. supplying current to a load resistance within themeter). The range selector is set to BAT, 9V. The indication on the meter showsthat the battery is 'good' (but will need replacing in the near future).

7.2.8 DO'S & DON'TS OF USING AN ANALOGUE MULTIMETER

Do ensure that you have selected the correct range and measuring functionbefore attempting to connect the meter into a circuit.

Do ensure that the correct polarity of the probes, where appropriate , isobserved before connecting the meter into the circuit.

Do select a higher range than expected and then progressively increase thesensitivity as necessary to obtain a meaningful indication.

Do remember to zero on the ohms range before measuring resistance.

Do switch the meter to the 'off' position (if one is available) before attemptingto transport the meter.

Do check and, if necessary, replace the internal batteries regularly.

Do use properly insulated test leads and prods.

Don't attempt to measure resistance in a circuit that has the power applied toit.

Page 7-10

Don't rely on voltage readings made on high-impedance circuits (the meter'sown internal resistance may have a significant effect on the voltages).

Don't rely on voltage and current readings made on circuits where highfrequency signals may be present (an analogue meter may produce readingsthat are wildly inaccurate or misleading in such circumstances.

Don't subject the instrument to excessive mechanical shock or vibration (thiscan damage the sensitive meter movement).

Page 7-11

7.3 DIGITAL MULTIMETERS

Digital multimeters offer a number of significant advantages when compared withtheir more humble analogue counterparts. The display fitted to a digitalmultimeter usually consists of a 3½ digit seven-segment display - the '½' simplyindicates that the first digit is either blank (zero) or 1. Consequently, themaximum indication on the 2V range will be 1.999V and this shows that theinstrument is capable of offering a resolution of 1mV on the 2V range. Theresolution obtained from a comparable analogue meter would be of the order of50mV, or so, and thus the digital instrument provides a resolution which is manytimes greater than its analogue counterpart.

The controls and display provided by a simple digital multimeter are shown in thediagram below. The mode switch and range selector allows you to select froma total of twenty ranges and eight measurement functions. These functions are:

DC voltage (DC, V) DC current (DC, A)

AC voltage (AC, V) AC current (AC, A)

Resistance (OHM) Capacitance (CAP)

Continuity test (buzzer) Transistor current gain (hFE)

Page 7-12

7.3.1 DC VOLTAGE MEASUREMENTS

An example of how tomake DC voltagemeasurements isshown to the left.The red and blacktest leads are

connected to the 'V-' and 'COM' socketsrespectively. Themode switch andrange selector is setto DC, 200V and thedisplay indicates areading of 124.5V.

7.3.2 DC CURRENTMEASUREMENTS

An example of how tomake a DC currentmeasurement isshown to the right.Here, the red andblack test leads areconnected to the 'mA'and 'COM' socketsrespectively. Themode switch and

range selectors are setto DC, 200mA, and thedisplay indicates areading of 85.9mA.

Page 7-13

7.3.3 HIGH CURRENT MEASUREMENTS

In common with simpleanalogue multimeters, themeter used a shunt which isdirectly connected to aseparate 10A terminal. Thediagram shows theconnections, mode switch

and range selector settings topermit high-current DCmeasurements. The modeswitch and range selectorsare set to DC, 2000mA (2A),and the red and black testleads are connected to '10A'and 'COM' respectively. Thedisplay indicates a reading of

2.99A.

7.3.4 AC VOLTAGE MEASUREMENTS

An example of how tomake a AC voltagemeasurement isshown to the left.Once again, the redand black test leadsare connected to the'V-' and 'COM'sockets respectively.The mode switch andrange selectors areset to AC, 2V, and thedisplay indicates areading of 1.736V.

Page 7-14

7.3.5 RESISTANCE MEASUREMENTS

The diagram shows anexample of how to makeresistance measurements.As before, the red and blacktest leads are connected tothe 'V-' and 'COM' socketsrespectively. The modeswitch and range selectorsare set to OHM,200, andthe meter indicated a readingof 55.8. Note that it is notnecessary to 'zero' the meterby shorting the test probestogether before taking anymeasurements (as would bethe case with an analogueinstrument).

7.3.6 CAPACITOR MEASUREMENTS

Many modern digitalmultimeters incorporate a

capacitance measuring facilityalthough this may be limited tojust one or two ranges. Thediagram below shows how tocarry out a capacitancemeasurement. The capacitoron test is inserted into the two-way connector marked 'CAP'whilst the mode switch andrange selector controls are setto DC, 200pF. The displayindication shown correspondsto a capacitance of 329pF.

Page 7-15

7.3.7 CONTINUITY TESTING

An example of how to make continuity (buzzer) tests is shown in the diagrambelow. The mode switch and range selectors are set to DC, buzzer (note that thisis indicated by means of an icon on the front panel of the instrument) and the redand black test leads are connected to the 'V-' and 'COM' sockets as usual.When there is a low-resistance path between the two test probes, an audiblebuzz will be produced. No meter indication is produced (instead, the meterdisplays an 'over-range' indication with the leading digit illuminated).

7.3.8 DO'S & DON'TS OF USING A DIGITAL MULTIMETER

Do ensure that you have selected the correct range and measuring functionbefore attempting to connect the meter into a circuit.

Do ensure that the correct polarity of the probes, where appropriate, isobserved before connecting the meter into the circuit.

Do select a higher range than expected and then progressively increase thesensitivity as necessary to obtain a meaningful indication.

Do switch the meter to the 'off' position in order to conserve battery life whenthe instrument is not being used.

Do check and, if necessary, replace the internal battery (often a PP3)regularly.

Do use properly insulated test leads and probes.

Do check that a suitably rated fuse is used in conjunction with the currentranges.

Page 7-16

Don't attempt to measure resistance in a circuit that has the power applied toit.

Don't rely on voltage and current readings made on circuits where highfrequency signals may be present (as with analogue instruments, digital

meters may produce readings that are wildly inaccurate or misleading in suchcircumstances).

Don't rely on measurements made when voltage/current is changing or whena significant amount of AC may be present superimposed on a DC level.

Page 7-17

Blank Page

Page 7-18

8 RESISTANCE & RESISTORS

8.1 RESISTIVITY

The factors affecting the resistance of a conductor of a given material at constant

temperature are related by the expression:

R(length)

A (crosssectionalarea)

R Constant A

R

AOhms

The constant depends on whether the material itself is a good or a poor

conductor; this constant is called ‘resistivity’ of the material. Resistivity has the

symbol (Rho) and is measured in ohm meters (check this from RA

) and

is defined as ‘the resistance between the ends of a piece of material one metre

long which has a cross sectional area of one square metres (i.e. between the

faces of a one metre cube).

Typical values of at 0C are:

Silver 1.5 x 10-8 - m

Copper 1.6 x 10-8 - m

Manganin 41 x 10-8 - m

Carbon 7000 x 10-8 - m

8.2 CHANGES OF RESISTANCE WITH TEMPERATURE

The resistance of all materials changes with changes in temperature. The

resistance of all pure metal increases with temperature. The resistance of

electrolytes, insulators, carbon and semi-conductors decreases with increasing

temperatures.

If it is assumed that the resistance change is in proportion to the temperature

change, then the ratio provides an indication of the material behaviour. It is

necessary however, to relate the change of resistance to its initial value. A large

value resistor will change its value more than a small value resistor for the same

temperature change.

Page 8-1

Suppose the resistance of a material at 0ºC (to) is Ro

and at some other temperature (t) the resistance is Rt

the change of resistance is Rt - Ro.

But the change of resistance is per unit value of the original resistance is givenby;

R = Rt - RoRo

this resistance change has been brought about by a temperature change t equalto t -to (to being 0º).

Hence the change in resistance, caused by a 1ºC change in temperature is;

R Rt - Ro

T = Ro (t - to) = Rt - Ro because t = 1 and to = 0Rot

This ratio is called the temperature co-efficient of resistance.

8.3 TEMPERATURE CO-EFFICIENT OF RESISTANCE

The temperature co-efficient of resistance is defined as;

The Fractional change in resistance from 0ºC, per degree temperaturechange.

and may be represented graphically as shown below.

The graph is reasonably linear for manymaterials over a moderate temperaturerange (0º - 200ºC).

The units are ºC because the ohms cancelout in the calculation.

Materials whose resistance increases withincreasing temperature have a positivetemperature co-efficient of resistance.

Materials whose resistance decreases withincreasing temperature have a negativetemperature co-efficient of resistance.

Some materials have very small temperature co-efficients of resistance and areused where it is important that the resistance does not change with temperature.Examples are Manganin and Eureka.

Page 8-2

8.4 RESISTORS

The electrical component used to introduce resistance into a circuit is called aresistor. Resistors can be fixed or variable. Symbols used in circuit diagrams areshown below:

Resistor Type Old Symbol New Symbol

Fixed resistor

Fixed resistorwith fixedtapping point

Variable resistor

Resistor withpre-set

adjustment

Voltage divider(potentiometer)

Pre-setpotentiometer

The physical size of a resistor does not give any clue to the resistance value ofthe component. This value must be marked on individual components. Twocodes are currently used to indicate resistor values: a Colour Code and a Letterand Digit Code.

8.4.1 FIXED RESISTORS

Fixed resistors may be:

Wire wound. Special resistance wire is wound onto a former. The wirewound resistor can dissipate heat easily and is therefore used when largercurrents are expected (the larger the current the greater the heat produced).These resistors are usually larger than other types. The student shouldnote that size does not indicate resistance value, but depends upon the heatto be dissipated.

Carbon Composition, Metal Oxide and Metal Film. Resistors made fromcarbon composition or from metal films and oxides are usually small. Theyare therefore used where the currents are kept small.

8.4.2 COLOUR CODES

The current method of colour code marking of resistors is the Band System.

Page 8-3

Close to one end of the resistor are fourcoloured bands (there may appear to be onlythree, in this case the forth band is ‘no colour’

- see diagram below). They are known asbands 1 - 4. Bands 1 and 2 give the first twonumbers of the resistor value, band 3 givesthe multiplication factor, i.e. the number ofzeros, the fourth band gives the tolerance,which indicates how close the actual valuemay be to the stated value.

Colour First band Second Third band Fourth(or body) band (or spot) bandFirst figure (or tip) Multiply by Tolerance

Secondfigure

Black 0 0 1 -

Brown 1 1 10 +1%

Red 2 2 100 + 2%

Orange 3 3 1000 -

Yellow 4 4 10,000 -

Green 5 5 100,000 + 0.5%

Blue 6 6 1,000,000 + 0.25%

Violet 7 7 10,000,000 + 0.1%

Grey 8 8 - -

White 9 9 - -

Gold - - 0.1 + 5%

Silver - - 0.01 + 10%

No colour - - - + 20%

Certain resistors remain very close to their stated value, despite temperaturechanges. These are called ‘high stability’ resistors and this is shown by a fifthband coloured ‘pink’.

High value resistors. High value resistors may have three significant figures. Ifthe colour code is used here, the first three bands represent figures, the fourthband is the multiplier and the fifth band is the tolerance. For example, a resistorof value 249,000 + 1% would be coded as shown below:

Page 8-4

First band Red is 2

Second band Yellowis 4

Third band White is 9

Fourth band Orange is 3 zeros

Fifth band Brown Tolerance + 1%

Note: To avoid possible confusion, the fifth band is 1.5 times to 2 times widerthan the other bands.

8.4.3 PREFERRED VALUES AND TOLERANCES

In practical electrical circuits the precise value for a resistor is not usually critical.It is more economic to produce large tolerance resistors than low tolerance ones.The number of resistor values required to cover a given range of resistancedepends on the tolerance of the resistors being used. An example of resistorPreferred Values for 10% is given in the table below.

1 10 100

1.2 12 120

1.5 15 150

1.8 18 180

2.2 22 220

2.7 27 270

3.3 33 330

3.9 39 390

4.7 47 470

5.6 56 560

6.8 68 680

8.2 82 820

Note that the upper and lower tolerance resistance limits of each preferred valuecover the complete range;

eg. 2.2K + 10% = 1.98K to 2.42K

2.7K + 10% = 2.43K to 2.97K

Page 8-5

8.4.4 LETTER & DIGIT CODES

In this code the numbers are printed on the body of the resistor to indicate its

value. In addition, letters are used to indicate the multiplying factor (eg, M) and

the tolerance as shown below.

Multiplying Factor Tolerance %

X1 R 0.1 B 5 J

(resistor)

X103 K K 0.25 C 10 K

X106 M M 0.5 D 20 M

X109 G G 1.0 F 30 N

X101 T T 2 G2

The position of the multiplying letter is also used to indicate the decimal pointposition.

eg. 470R is 470

4K7 is 4·7K

R47 is 0·47

4R7 is 4·7

The tolerance letter is added on the end.

eg. 1M5 B is 1·5M + 0.1%

2K2 N is 2·2K + 30%

Other markings may also be used in the code to represent date of manufacture.They are placed after the value and tolerance markings.

8.4.5 POWER RATING

Resistors are rated according to their resistance value and also to the rate atwhich they can dissipate heat. Rate of heat dissipation is measured in watts.

(The watt will be discussed later in the course). The higher the wattage rating themore current it can carry.

Page 8-6

8.4.6 POTENTIOMETERS

A variable resistor arranged so as to control voltage ina circuit is called a ‘Potentiometer’ and controls thepotential difference between two points in a circuit. It isused to ‘tap off’ part of the supply or signal voltage forconnection to a load. See diagram.

8.4.7 RHEOSTATS

Variable resistors can be made to vary either currentor voltage. A variable resistor arranged to controlcurrent is called a ‘Rheostat’ and controls the currentby varying the resistance in the circuit. See diagram.

8.4.8 VOLTAGE DEPENDENT RESISTORS

Some components do not obey Ohm’s law, that is the current flow through themdoes not vary linearly as the applied voltage is varied. These elements areknown as non-linear resistors or non-linear conductors. Transistors, diodes andvoltage dependent resistors all fall into this group.

The current through a voltage dependent resistor increases at a progressivelyrapid rate as the voltage across it increases, such a device is used for protectingcircuits against voltage surges or as a voltage stabiliser.

8.5 THERMISTORS

Insulators and semi-conductors behave in a different way when the temperatureincreases, because their resistivity decreases. That is: the resistance of aninsulator and of a semi-conductor decreases with temperature increase, (theirresistance-temperature coefficient is negative!). This feature can be used toadvantage as the following example shows.

One example of this effect occurs in a thermistor, which is a thermally sensitiveresistor whose resistance alters with temperature; a negative temperaturecoefficient (n.t.c.) thermistor is one whose resistance reduces with increase intemperature. A thermistor is used in the cooling-water temperature-measuringcircuit of a car or lorry; it is inserted in the cooling water and connected in serieswith the battery and temperature gauge. As the water temperature rises, theresistance of the n.t.c. thermistor falls and allows more current to flow through thetemperature gauge; this causes the gauge to indicate variations in watertemperature.

Page 8-7

9 RESISTORS IN DC CIRCUITS

9.1 RESISTORS IN SERIES

Components are said to be in series when they are connected end-to-endproviding only one path for the current. Thus the same current passes through allthe components (including the power supply). See diagram below.

When a current flows through a resistor (or a component having resistance) thereis a potential difference between its ends. Thus where two or more resistors areconnected in series the potential difference between the extreme ends is the sumof the individual potential differences.

Hence E = V1 + V2 + V3

But from Ohm’s Law V = IR

Therefore E = IRTOTAL

So V1 = IR1 V2 = IR2 V3 = IR3

Thus IRTOTAL = IR1 + IR2 + IR3

= I (R1 + R2 + R3)

So RTOTAL = R1 + R2 + R3

Page 9-1

9.1.1 KIRCHOFF’S SECOND LAW

This law states that in any closed circuit the sum of all the potential differences(voltage drops) is equal to the total applied voltage in that circuit.

Thus the potential difference across R2 is given by: VR2 = 9 - 7 = 2V

9.1.1.1 Example of kirchoff’s second law

There are four possible routes around thecircuit shown and whichever one is taken,Kirchoff’s law is true:

Note that Q is at a higher potential than R.Also a potential drop is positive and a potentialrise is negative.

Route MPQSNM 3 + 7 - 10 = 0

Route MPRSNM 4 + 6 - 10 = 0

Route MPQRSNM 3 + 1 + 6 -10 = 0

Route MPRQSNM 4 - 1 + 7 -10 = 0

It should also be noted that within the resistor network;

Route PRQP 4 - 1 - 3 = 0 Route PQRP 3 + 1 - 4 = 0

Route RSQR 6 - 7 + 1 =0 Route RQSR -1 + 7 - 6 = 0

9.1.2 VOLTAGE DIVISION

In a series circuit Ohm’s law applies for each component. However, since thecurrent is common to all components we have:

Page 9-2

V1 = IR1, V2 = IR2, V3 = IR3

Therefore V1 R1, V2 R2, V3 R3

i.e. Vn Rn

Hence the voltage drops across each resistor can be calculated from the ratio ofthe resistance values.

It should also be noted, that for any given appliedvoltage we may derive any smaller voltages we wish byinserting resistors of the appropriate values in series.The following example shows how voltages of 8V, 4Vand 24V can be derived from a 36V supply.

RTOTAL = 12 + 6 + 36 = 54

54 36V and 1 36/54V

12 = 36/54 12 = 8V across AB

and 6 = 36/54 6 = 4V across BC

and 36 = 36/54 36 = 24V across CD

9.1.3 THE POTENTIAL DIVIDER

A device which employs voltage division and which iscommonly used in electrical and electronic circuits isthe potential divider. Here two or more resistors areused to divide a given input voltage to achieve aspecified output voltage. See diagram.

The potential divider is also known as a voltage divideror scaling circuit.

Note that if current is drawn from the output then the effective resistance of thecircuit changes and the output voltage vOUT changes.

Page 9-3

9.1.4 VOLTAGES RELATIVE TO EARTH

It is very common in electrical circuits to have an earth connection. This earthconnection has no effect on potential differences across components, however itdoes affect the values of the potentials or voltages at points in the circuit.

The earth is a reference point and considered to be at zero volts. Potentialdifferences between earth and the negative terminal of the supply result innegative voltages and potential differences between earth and the positive

terminal result in positive voltages. It should be noted that due to static build upon the airframe, the earth connection (airframe) of an airborne aircraft is unlikelyto be at zero potential with respect to the ground

You should also note that earth connections, for example to the chassis of anequipment or the airframe of an aircraft, are often used as the current return leadin an electrical circuit.

9.2 INTERNAL RESISTANCE

As mentioned earlier in the section on batteries, every source of electricity, suchas a cell or generator has resistance to current flow called internal resistance.

Cells (and batteries): The internal resistance is mainly due to theresistance of the electrolyte. This varies considerably with temperature andconcentration of the electrolyte.

Generators. Internal resistance is mainly the resistance of the wires whichform the internal windings.

Page 9-4

Electronic Power Supplies. Here the internal resistance is due to theresistance of components within the power supply.

When the source forces electrons around a closed circuit they must passthrough the internal resistance of the source, thus causing a drop in voltagewithin the source itself, i.e. the source has to do work to push currentthrough itself. This loss of potential or ‘voltage drop’ may be referred to aslost volts, since they are not available in the external circuit, thus theterminal voltage is less than the emf by the value of the lost volts whencurrent is drawn from the supply.

CLOSED CIRCUIT TERMINAL VOLTAGE = EMF - LOST VOLTS

Loss of potential only occurs when current flows from the source. If therefore theexternal circuit is open, no current flows and the terminal voltage is equal to theemf.

OPEN CIRCUIT TERMINAL VOLTAGE = EMF

The Size of the ‘lost voltage’ is determined by the internal resistance and thecurrent flowing (Ir). For a given emf the larger the external resistance, the smallerthe current and the smaller the ‘lost volts’. Thus if the internal resistance is muchsmaller than the external resistance the ‘lost volts’ is very small and the terminalvoltage is almost equal to the source emf.

Page 9-5

9.3 RESISTORS IN PARALLEL

Components are said to be in parallel when they are

connected in such a way as to provide alternative

paths for current flow.

The characteristics of such a parallel combination

are:

The voltage across each component is the same.

The current through each component is determined by the resistance of that

component

Ohm’s law applies to each component connected in parallel.

In the diagram below.

and

From Ohm’s law I

V

V1 = V2 = V3 = V

I = I1 + I2 + I3 (by Kirchoff’s first law)

V

R

V1 V2 V3 V V VThereforeRTOTAL

and 1 1

R1

1

R2

1

R3

R1

R2

R3

RTOTAL

R1

R2

R3

Hence the three resistors shown above may be replaced by a single resistor of

value RTOTAL which may be computed using the above equation. Note that the

most usual error which occurs when using this equation is to forget that the

calculation on the right hand side of the equation gives the reciprocal of theequivalent resistance 1 and therefore needs inverting to find RTOTAL.

RTOTAL

Page 9-6

To avoid this possible error the equation may be remembered in the form:

RTOTAL1

R1

1

R2

1

1

R3

1

R n

Having found RTOTAL it is now possible to use Ohm’s law to calculate either V or I,

providing one of the two is known. Knowing V (= V1 = V2 = V3 etc) it is now

possible to find the current values through the branches I1, I2, I3 etc (provided of

course that R1, R2, R3 etc are known).

As a check, the total resistance of any parallel combination of resistors

should always be less than the value of the lowest resistor in the network.

9.3.1 TWO RESISTORS IN PARALLEL

When we have only two resistors in parallel then the general equation may still be

used. However a simpler formula can be derived.

Using the general equation we obtain:

1

RTOTAL

1

R1

1

R2

R2R1

R1R2

Therefore RTOTALR1R2

R1R2

Product

Sum

9.3.2 EQUAL RESISTORS CONNECTED IN PARALLEL

Where we have two or more resistors of equal value connected in parallel then :

1

RTOTAL

1 1 1 1 4 R R R R R

Therefore RTOTAL = R4

Generally, when any number of equal value resistors are connected in parallel,

the effective resistance (RTOTAL) is equal to the value of one resistor divided by

the number of resistors.

RT OT AL R

The totalnumber of resistorsconnected in parallel

Page 9-7

9.3.3 EFFECTIVE VALUE OF RESISTORS IN PARALLEL

If a second resistor is connected in parallel with a first, the voltage across thesecond is equal to the voltage across the first. The first resistor still draws thesame current and the second now also draws current. Thus the total currentdrawn from the supply has increased and therefore the effective resistance(RTOTAL) has decreased. Since the supply of current is now greater than eitherindividually would draw, the effective resistance of the two is less than theresistance of either individually. This is generally true and for any number ofparallel resistors the effective resistor (RTOTAL) is less than the value of any singleresistor in the parallel combination. An important point to note here is that thesupply current has increased and unless the supply wiring can cope with it, it maybe damaged (e.g. begin to melt).

9.3.4 RESISTOR SIZE AND CURRENT FLOW

Ohm’s law states that the current flowing is inversely proportional to resistanceprovided that the voltage remains constant. In a parallel network the voltageacross each component is the same, therefore the current through eachcomponent is inversely proportional to its resistance. Simply stated, this meansthat the largest current always flows through the smallest resistor and vice-versa.This is a simple check that may often be useful in numerical calculation.

9.3.5 KIRCHOFF’S FIRST LAW

Kirchoff’s first law states that at any circuit junction, the sum of the currentsflowing towards the junction is equal to the sum of the currents flowing away fromit.

10A

9A

8A

2A

7A

Current flowing towards junction = 2 + 7 + 9 = 18A

Current flowing away from junction = 10 + 8 = 18A

Page 9-8

9.4 RESISTORS IN SERIES / PARALLEL COMBINATIONS

In the previous units we have used Ohm’s law to solve combinations of resistorsin series or in parallel. It is possible to solve combinations of resistors in bothserial and parallel by Ohm’s law provided sufficient information is given. Howeverin some cases solution is not possible without the use of Kirchoff’s laws.

9.4.1 PHYSICAL ARRANGEMENT OF RESISTORS

Before we look at some problems it is necessary to warn you that physicalappearances can be deceptive. When components are mounted they are usuallydone so in a manner as to reduce the space they occupy to a minimum. Caremust be taken to decide whether they are mounted in series or parallel or in acombination of both.

Thus on the Tag Board above, the resistors may appear to be in parallel,however, only R3 and R4 are in parallel.

9.4.2 SOLUTION OF RESISTOR NETWORKS USING OHM’S LAW

Many problems may be solved by combining series and parallel groups ofresistors and applying Ohm’s law. Remember that Ohm’s law involves three

quantities - I, V and R, thus to find any one quantity the other two must be knownor be capable of determination. Where resistors appear in both series andparallel they may be reduced to a single effective resistance using a step-by-stepsequence as follows.

Combine any simple series groupings within branches ( R = R1 + R2 + --- ).

Page 9-9

Replace any simple parallel groups by single equivalent resistors

1

R

1

R

1

R----

1 2

Combine any simple series groupings ( R = R1 + R2 + --- ).

Replace any simple parallel groups.

Page 9-10

Determine the single equivalent resistance.

At this point the total circuit current (Is) may be found if Vs is given, or Vs found if Isis given. Having determined Vs or Is, as appropriate, the current in any branchand the voltage drop across any resistor can be found by working backwardsthrough the sequence in the first paragraph of this section, applying Ohm’s law ateach stage.

9.5 THE EFFECTS OF OPEN CIRCUITS

An open circuit is essentially a break in the circuit. An open circuit in a seriescircuit will prevent the flow of current through the circuit. With no current flowing inthe circuit there can be no voltage drop across any resistors, and therefore thesupply potential will be measured at all points between the positive terminal andthe break.

Page 9-11

In a circuit with parallel paths, an open circuit path will cause an increase in thecircuit resistance and a reduction in the circuit current. The change in current flowwill cause the voltages measured around the circuit to change.

9.6 THE EFFECTS OF SHORT CIRCUITS

A short circuit is a path for current where a path should not exist, the path isgenerally considered to have a low resistance. If a short circuit is placed across aresistor, the current will flow through the short circuit rather than through theresistor.

Short circuits across series or parallel connected resistors will result in adecrease in the circuit resistance and an increase in the current drawn from thesupply. Short circuits may result in the fuse blowing, the circuit breaker tripping orthe circuit burning out if no protection devices are fitted.

If the definition of a short circuit is taken to be 'an unwanted current path', thenhigh resistance short circuits are also possible.

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10 THE WHEATSTONE BRIDGE

You have already solved resistor networks using Ohm’s law and Kirchoff’s laws.In this unit we are going to look at a special arrangement of series and parallelresistors called a Wheatstone Bridge.

10.1 CONSTRUCTION

The Wheatstone Bridge circuit and other similar variants were widely used in testequipment to determine the value of an unknown resistor by comparison withother resistors whose values are accurately known.

The normal arrangement in a Wheatstone bridge used for resistancemeasurement is for two resistors, usually R1 and R2, to be fixed and of knownvalue and R4 to be an accurate variable resistor adjusted by means of acalibrated dial. The resistor R3 is then the unknown whose value is to bemeasured.

10.2 CALCULATING UNKNOWN RESISTANCES

The current through the galvanometer (G) - a very sensitive ammeter, is reducedto zero by adjusting R4. The bridge is then said to be balanced. When the bridgeis balanced, the voltage at A is equal to the voltage at B and no current flowsbetween A and B.

Hence VR1 = VR2

therefore I1 R1 = I2 R2 ------------- (1) (by Ohm’s law)

Also VR3 = VR4

therefore I1 R3 = I2 R4 ------------- (2)

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R R1 2

R RDividing (1) by (2) R 2

1R

4

3

Therefore the unknown resistor R3 = R1 x R4 (all known values)R2

In calculations it is possible for any of the four resistors to be unknown. However,provided that the bridge is balanced, the theory remains the same and all that isrequired is to transpose the equation to find the unknown. Thus, for example:

10.3 USES ON AIRCRAFT

Whilst the Wheatstone bridge may be used to determine the value of an unknownresistor, it is far easier to use an Ohmmeter. The Wheatstone bridge is howeverextremely useful for measuring and displaying remote indications.

On aircraft, Wheatstone bridge circuits are used for the measurement anddisplay of temperatures, pressures, positions and quantities. In each case, the

item being measured varies the value of resistor R3, causing a voltage imbalancethat produces a current flow through the galvanometer. The amount of currentthrough the galvanometer, and the amount of pointer deflection depend upon thepotential difference across the bridge, which in turn depends upon the change inresistance of R3. The galvanometer can therefore be calibrated to give theappropriate indication.

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11 ENERGY & POWER IN DC CIRCUITS

11.1 ELECTRICAL WORK

Electrical work is done if a quantity of charge (coulombs) is moved between twopoints which are at different electrical potentials.

The SI unit of work is the ‘joule’. One joule of work is done when a chargeof one coulomb moves through a potential difference of one volt.

Electrical Work (joule) = Charge (coulomb) Potential Difference (volt)

Work = Q V joules

Since one coulomb is one ampere second

Q = I t

then Work = V It joules

11.2 ELECTRICAL ENERGY

Electrical energy is the ability of an electrical system to do work.

Energy is expended when work is done and the amount of energy used is equalto the work done. The units of energy and work are the same, that is joules andthe same equation is used for both.

Energy = Work = VIt joules

The energy a body contains may be determined by calculating the electrical workdone on the body to give it that energy. Conversely, the work that a body coulddo if it used up all its energy may be determined by calculating how much energyit contains.

This assumes that no energy is lost in the conversion. In practice energy is often‘lost’ in the form of heat.

However no energy is actually destroyed, it is simply converted into some otherform. This is stated in the Law of Conservation of Energy - energy can neitherbe created nor destroyed but merely changed into other forms.

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11.3 ELECTRICAL POWER

Electrical power (symbol P) is the rate at which work is done or the rate ofconversion of energy by an electrical system.

Power (watts) = Work done (joules) = VIt

Time taken (seconds) t

The SI unit of power is the watt which is a rate of work of 1 joule per second.

Therefore P = V I

That is watts = volts amps

By substituting V = IR in the above formula, two other expressions for electrical

power are obtained:

P = VI = I2R = V2 wattsR

11.4 POWER RATINGS

Electrical equipment can only stand a certain amount of heat production withoutdamage and the safe power which a piece of equipment can consume withoutdamage is its ‘power rating’ or ‘wattage rating’. Each component is given awattage rating and if this is exceeded the component will overheat.

The more power consumed by a device the more heat or light it produces in agiven time; a 100w lamp gives more light than a 60w lamp. The rating 6V 12Won a lamp means that if is connected to a 6V supply, its resistance is such that itdevelops 12W of power and that it is intended to work at this rating.

Note that:

The above bulb consumes 12W only at the correct voltage. If the voltage isincreased more power is developed and the component may be damaged.

A fluorescent tube of 12W rating produces more light than a 12W filamentbulb because the tube produces much less heat and is therefore moreefficient.

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11.4.1 POWER RATINGS OF RESISTORS

This power rating has a different meaning from that of a bulb. In this case wemust always keep below the stated value.

To keep below the stated power value, there are maximum permissible values ofvoltage and current, which may be calculated as follows:

Maximum Current P = I2R

Therefore IP

Rand this is the maximum current to avoid damage tothe resistor.Maximum Voltage P = V2

R

Therefore V = P R and this is the maximum voltage to avoid damage to theresistor.

11.4.2 SIZE AND POWER RATING

The surface area and therefore the size of a component determines the rate atwhich heat is dissipated from the component to its surroundings. Generallytherefore the larger a component, the higher its power rating.

Carbon resistors of the same resistance value are commonly available in ratingsbetween ¼W and 2W. When higher wattage is required wire-wound resistorsmay be used, the normal range here is 1W to 200W.

11.4.3 THE KILOWATT HOUR

The unit of electrical energy is the joule which may be expressed in terms ofpower as a Watt second.

The joule however is a very small unit and it is therefore often more convenient tomeasure energy used in kilowatt hours where:

1kWh = 1000 watt hours

= 1000 3600 watt seconds or joules

= 3 600 000 J or 3.6 MJ

Page 11-3

11.5 MAXIMUM POWER TRANSFER

Every source of EMF has internal resistance. If it is required to develop themaximum possible amount of power in an external load, then the load resistancemust be equal in value to the internal resistance of the source.

This may be shown by calculating the power developed in RLoad for differentvalues of RLoad.

This illustrates that maximum power is developed in the load when RLoad equalsRInternal.

Matching is very important in electronic circuits which usually have a fairly highsource resistance. A typical example is the ‘matching’ of a loudspeaker to anaudio amplifier. Note however that:

For a power source with variable internal resistance and given load (RL), thesmaller the internal resistance, the higher the power transfer to the load.The highest power transfer is achieved here when the internal resistance iszero.

Batteries, generators and other power supply systems are not operatedunder maximum power transfer conditions, since to do so would result in thesame amount of power being dissipated in the source as was supplied tothe load, which is wasteful of energy. Thus power systems are designed tohave the minimum internal resistance to minimise loses in the power supply.

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12 CAPACITANCE & CAPACITORS

When a voltage is applied to a capacitive circuit there is a change in the electricflux. The ease with which this change takes place is a measure of thecapacitance of the circuit.

In d.c. circuits, capacitance is only effective when the voltage is switched on andoff, but in a.c. circuits where the voltage varies continuously, the effect ofcapacitance is continuous.

A device used specifically to introduce capacitance into a circuit is known as acapacitor (sometimes called a condenser).

12.1 CHARGING A BODY

A conductor is given a positive charge when electrons are forcibly removed fromthe conductor, eg, by connecting it to the positive pole of a d.c. source. Similarly,when additional electrons are pushed on to a conductor, it is given a negativecharge.

The use of force means that energy has been expended by the source of d.c. andthis energy is stored in an electric field. An electric field is represented by lines offlux whose direction is the direction of force which would be experienced by a freepositive charge placed in the field. Lines of electric flux behave in an analogousmanner to lines of magnetic flux.

As the charge on a body increases, it repels further charge with greater force untileventually the repelling force equals the charging force and the conductor is fullycharged.

The charge on a fully charged body may be changed by changing the voltagesupplying the charging force, but the conductor will oppose this charge due to thecharge it already possesses.

Any conductor will hold a charge, the magnitude of the charge depends upon themagnitude of the voltage applied, but for a single conductor, even a large voltageproduces only a relatively small charge.

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12.2 THE BASIC CAPACITOR

If we have two metal plates close together, but separated by an insulator ordielectric (which could be air) and we apply a voltage across them, electrons areremoved from one plate and applied to the other and each becomes charged.The charge held by the combination may be very large because of theconcentration of the electric field between the plates. This represents a basiccapacitor.

Thus, a capacitor is a device whichopposes voltage change in a circuitthrough its capacity to store electricalenergy (or charge) in the form of anelectric field.

12.3 CAPACITANCE

If we increase the voltage between the plates, the charge increases, but the ratioof charge to voltage remains the same. This ratio gives the capacitance (C) ofthe capacitor.

ChargeVoltage = A constant called capacitance

When the charge (Q) is in coulombs and the voltage (V) in volts, then thecapacitance (C) is in farads (F).

C = Q (and also Q = VC, V = QV C )

A capacitor has a capacitance of one Farad when a charging current of oneampere, flowing for one second, causes a change of voltage of one volt betweenits plates. The Farad is a huge unit and smaller units are used in practice.

1 microfarad (F) = 10-6 farad

1 picofarad (pF) = 10-12 farad

12.4 FACTORS AFFECTING CAPACITANCE

The factors which affect the capacitance of a parallel-plate capacitor are:

Page 12-2

Overlapping area of the plates (A). The capacitance increases as the areaof overlap increases since a larger plate area provides more room toaccommodate the increase charge.

Distance between the plates (d). The capacitance increases as thedistance between the plates decreases, since the electric field thenbecomes more concentrated.

Material between the plates. This introduces a constant called the absolutepermittivity (). The constant is actually the product of two constants, thepermittivity of space (o) which has a value of 8·85 x 10-12 Fm-1 and therelative permittivity (r), which is basically a multiplication factor (no units)that indicates how many more times the material is able to concentrate theelectric flux compared with space. For example, if waxed paper is insertedbetween the plates instead of air, the ability to concentrate a flux (thepermittivity) is multiplied by approximately 3, therefore the relativepermittivity (r) of waxed paper is approximately 3.

We may summarise this in equation form as:

AC = d

The units of ‘C’ are Farads if the units of the other quantities are:

Area (a) - square metres (m2).

Distance between plates (d) - metres (m).

Absolute permittivity () - farads per metre (Fm-1).

In the case of multi-plate capacitors, capacitance is calculated using the formula:

C(n - 1) A

d

Where n is the number of plates and A is the area of a single plate.

12.5 ENERGY STORED IN A CAPACITOR

Energy is stored in the electric field of a charged capacitor. If a dielectric is

inserted, extra energy is stored above that stored in free space, due to the

distortion of electron orbits in the atoms. The energy stored is given by the

equation:

Energy = ½CV2 joules

= ½QV since CV = Q

= ½Q2/C since V = Q/C

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12.6 CAPACITOR CONSTRUCTION

12.6.1 FIXED CAPACITORS

Fixed capacitors usually consist of sheets of metal foil between which issandwiched the dielectric, or alternatively the metal, such as aluminium, is

deposited onto both sides of the dielectric. The characteristics and quality of thecapacitor depends mainly on the dielectric, which may be paper, chemicallyimpregnated paper, plastics mica or ceramic.

12.6.2 VARIABLE CAPACITORS

Variable capacitors are usually meter plates with air as the dielectric. Thevariation is achieved by varying the area of overlap of the plates.

Preset capacitors may use air, mica or ceramics as the dielectric.

12.6.3 ELECTROLYTIC CAPACITORS

Electrolytic capacitors use the metal oxide as the dielectric which is formeddirectly on the metal plates. High values of capacitance can be achieved herewith small physical size. Most electrolytic capacitors must be connected intocircuit with the correct polarity or damage (possibly including explosion) mayresult.

12.6.4 SAFE WORKING VOLTAGE

The safe working voltage is the maximum d.c. voltage that can safely be appliedto a capacitor without causing the dielectric to break down.

When breakdown occurs, the electric field is strong enough to ‘tear’ electrons freefrom their orbits. A current then flows with the production of a large amount ofheat. The dielectric is commonly burned through rendering the capacitorunserviceable.

Higher voltage require thicker dielectrics, but this reduces capacitance. Thus, agiven value of capacitance requires a larger capacitor (greater plate area ‘a’) forgreater voltage working.

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12.7 CAPACITOR SYMBOLS

The diagram below gives the symbols for capacitors. The pre-set capacitor(sometimes referred to as a padder or trimmer) allows slight variations to bemade about its fixed value.

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13 CAPACITORS IN DC CIRCUITS

13.1 CAPACITORS IN SERIES

When three capacitors are connected in series. If one electron moves from thenegative terminal of the cell to the right hand plate of C3, and one electron movesfrom the left hand plate of C1 to the positive terminal of the cell, one electron willmove between C1 and C2 and between C2 and C3. Thus, the total charge movedis one electron and the charge on each capacitor is one electron. Thus:

QTOTAL = Q1 = Q2 = Q3

but V = V1 + V2 + V3 (Kirchoff’s second law)

also V = QC

Therefore Q = Q + Q + QCTOTAL C1 C2 C3

Hence 1 = 1 + 1 + 1

C C1 C2 C3

Therefore, the three single capacitors may be replaced by a single capacitorwhose capacitance (C) is given by the above equation, provided its safe workingvoltage is of a sufficiently high value to withstand the applied voltage.

Page 13-1

13.2 CAPACITORS IN PARALLEL

Three capacitors are connected in parallel. If on closing the switch S a current Iflows in the circuit, then from Kirchoff’s first law:

I = I1 + I2 + I3

therefore It = I1t + I2t + I3t (where ‘t’ is the time)

but Q = It

therefore QTOTAL = Q1 + Q2 + Q3

therefore

but

QTOTAL = Q1 + Q2 + Q3

V V V V

Q = CV

Therefore C = C1 + C2 + C3

Thus, we may replace capacitors in parallel by a single capacitor whose value isgiven by the above equation.

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13.3 CAPACITORS IN SERIES / PARALLEL COMBINATIONS

When capacitors are connected in series and parallel combinations, the processof finding the total capacitance is basically the same as that used to find the totalresistance of a resistor network. It must of course be noted, that the formulaeused for capacitors in series and parallel are different from those used forresistors connected the same way.

Where capacitors appear in both series and parallel, they may be reduced to asingle effective capacitance using a step-by-step sequence as follows;

Combine any simple parallel groupings within branches.

Replace any simple series groups by a single equivalent capacitor.

Repeat the process until a single capacitor remains.

13.4 CHARGE & DISCHARGE CHARACTERISTICS

A capacitor opposes voltage change in a circuit; indeed, if we had a perfect d.c.circuit and a perfect capacitor, then only an instantaneous current would flow,charging the capacitor instantaneously to equal the applied voltage (but in thereverse sense) and so preventing further current flow. However, in any realcircuit, resistance is present in the form of:

the connecting wires.

Internal resistance within the d.c. source.

This causes the capacitor to take a finite time to charge up.

13.4.1 CHARGING A CAPACITOR

In the diagram below, all of the resistance in the circuit is added together andshown as a single value R.

With S1 closed and S2 open, the capacitorwill charge up.

Note that Kirchhoff’s second law alwaysapplies, that is:

E = VR + VC

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The charging sequence is as follows:

On closing S1, no current has yet flowed, the capacitor plates have no

charge on them and hence, there is no voltage across it.

The whole of the applied voltage is developed across the resistor:

VR = E

The initial charging current is equal to the current through the resistor:

V EI R INIT R I

As C charges, the potential difference across it (VC) increases, opposing theapplied voltage (E) so that the charging current is progressively reduced.

Finally the capacitor is fully charged (VC = E) and current ceases(consequently VR = O).

This sequence is shown graphically below.

The curves are called ‘exponential’ curves and it can be seen that the slopes dVcdt

and dIdt are progressively decreasing as time increases.

13.4.2 TIME CONSTANT

It is found that the time taken to charge up the capacitor depends on the productof capacitance and resistance. This product is called the ‘time constant’ of thecircuit and its value is in seconds, providing R is in ohms and C in farads.

TIME CONSTANT = CR

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The time constant is defined as either:

The time which would be taken for the capacitor voltage to reach its

maximum value if it continued to increase at the initial value, or

The time for the capacitor voltage to reach 0.632 of its maximum value (or

63.2%, this is sometimes taken as 2/3 in calculations).

It is difficult to say at exactly what point the capacitor is fully charged, however,

for all practical purposes it may be considered fully charged after five time

constants:

TIME TO FULLY CHARGE = 5CR

13.4.2.1 Proof of time constant

When C is fully charged, then Q = CE. The time taken to fully charge at the initial

charging rate is equal to the time constant (TC).

Thus Q I TC (but IE

) so CE E

TCinitial

Therefore CEE

R

initial

TC

R R

Hence Time Constant TC = CR

13.4.3 DISCHARGING A CAPACITOR

On opening S1 and closing S2 (after the capacitor is fully charged), the capacitordischarges, thus current flows (in the opposite direction to the original current)and the voltage across the capacitor falls to zero exponentially.

In this case the voltage across the capacitor falls by 63.2% to 0.368E in CRseconds and takes 5CR seconds to fall to zero (0.368 is sometimes taken as 1/3in calculations).

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13.4.4 A CAPACITOR IN A DC CIRCUIT

It can be seen that although current does flow for a period of time in a d.c. circuitcontaining a capacitor (until the capacitor is fully charged), the current iseventually reduced to zero. Thus, a capacitor inserted in a d.c. circuit preventscurrent flow and is sometimes called a dc blocking capacitor.

Two points should be noted;1. Current does not flow through a capacitor, it only appears to, because the

number of electrons arriving at one plate is the same as the number leavingthe other plate.

2. Alternating current always appears to pass through a capacitor. The degreeof opposition to a.c. current flow is determined by a variety of factors whichwill be studied later in a.c. circuits. The study of capacitors in a.c. circuits willalso provide additional reasons for using them in d.c. circuits.

13.5 THE EFFECTS OF OPEN & SHORT CIRCUITS

A capacitor is in effect an open circuit, however, if the connection to a capacitorwere to go open circuit then it would be unable to charge and there would beabsolutely no current flow. If this occurred in a parallel combination, the totalcapacitance of the circuit would decrease, in a series combination the capacitorswould be ineffective because of the lack of current flow.

When a capacitor is short circuited it is unable to charge, if one capacitor in aparallel combination is short circuited it will prevent the other paralleled capacitorsfrom charging. In a d.c. circuit, a shorted capacitor will no longer act as a d.c.block and will allow the flow of both d.c. and a.c. current.

The effects of open and short circuited capacitors will be examined in more detailas there uses in various circuits are studied.

13.6 SAFETY & TESTING

A charged capacitor can store a large amount of energy which it releases ondischarge. It is therefore important to ensure that capacitors, especially largeones, are discharged before you attempt to touch them. Particular care isrequired when servicing faulty high voltage equipment.

A capacitor can be tested using an ohmmeter. When connected across acapacitor, the ohmmeter's battery charges the capacitor. The charging of thecapacitor is indicated by a changing value of resistance, from zero to infinity asthe capacitor charges. If the charging process is too quick to see, a resistor canbe placed in series with the meter and capacitor to slow it down (time constant =CR). In many cases it is necessary to remove the capacitor from the circuit inorder to test its serviceability.

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13.7 CIRCUITS INVOLVING CAPACITIVE DECAY

Consider the circuit shown below. Depending on the time constant of the circuit,relative to the period of the square wave applied to it, the response of the circuitcan vary widely. Assuming T is half the period of the square wave.

If CR is slightly less than T, the waveform in the top diagram is produced at theoutput (across C).

If Cr<<T, the square wave is hardly affected, centre diagram.

If CR>>T, the circuit is an integrating circuit, since the output waveform is thatof the integral of the square wave, that is the area underneath it. This is shown inthe lower diagram.

If the positions of the resistor and capacitor are reversed and the voltage acrossthe resistor measured, then the waveform produced will be that of the current,since V=IR.

If CR is short enough then a stream of pulses is produced when a square wave isapplied to the input. Shown in the top diagram.

If CR<<T the circuit is called a differentiating circuit, since the pulsesapproximate to the slope of the input waveform as in the centre diagram.

When CR>>T the circuit is called a coupling circuit. A coupling circuit allowsthe input waveform to pass to the output whilst blocking the passage of any d.c.

Page 13-7

14 MAGNETISM

Everyone has seen and handled a magnet in the form of a straight or horseshoe-shaped bar of steel or steel-alloy. The magnet was originally a piece of steelbefore it was magnetised.

A material called magnetite is a naturally occurring magnet (also calledlodestone) which was used at sea for primitive navigation.

A magnet is easily recognised by its ability to attract pieces or iron and steel; andif suspended freely on a piece of string, will swing to align with the earth’s ownmagnetic field.

14.1 MAGNETIC THEORIES

14.1.1 MOLECULAR THEORY

If we continue cutting our magnet into smaller and smaller pieces we wouldeventually arrive at the smallest piece, which would be a molecule and thismolecule would be a magnet. Thus the molecular theory of magnetism statesthat:

All materials contain molecules with magnetic properties.

In unmagnetised substances, these molecules are arranged in a randommanner and no external magnetic effect is produced.

When the material is being magnetised, we are aligning the molecules. Thenumber aligned increases, as we further magnetise the specimen and whenall are aligned no further increase in magnetisation is possible and thespecimen is said to be magnetically saturated.

In theory all substances could be magnetised, but in practice it is impossibleto align the molecules of most substances.

14.1.2 DOMAIN THEORY

In domain theory it is assumed that magnetic materials are composed of tinyindividual magnets called domains, a single domain is very small - about 1012

atoms.

Considering each atom - orbital electrons not only orbit the nucleus but spinaxially on their own axis.

In non magnetic materials the same number of electrons spin clockwise asanti-clockwise. In magnetic materials more electrons spin one way than the otherway

The unbalanced spin creates twists called magnetic moments.

In unmagnetised state the moments of the electrons are in the same direction ina single domain, but the domains produce random pockets of magnetism.

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As the magnetic material becomes magnetised the domains become partiallyaligned. In fully magnetised material all domains become fully aligned.

14.2 MAGNETIC PROPERTIES

14.2.1 MAGNETIC POLES

The two regions near the ends of a magnet at which the attracting forces appearto be concentrated are called the magnetic poles.

The pole (when freely suspended) which points towards the earth’s geographicnorth pole is called the North Seeking Pole ‘N’ (or north pole for short) and thatwhich points to the south geographic pole, the South Seeking Pole ‘S’ (or southpole).

It is observed that two north poles repel each other and likewise with two southpoles; however a north pole and a south pole will attract each other. This issummarised in the fundamental law of magnetism:

Like Poles Repel, Unlike Poles Attract

To test a specimen for the presence of magnetism it is necessary to observerepulsion. Attraction simply means that the specimen is magnetic but it may notbe magnetised. Thus the test for magnetism is repulsion.

14.2.2 MAGNETIC FIELD

The region around a magnet in which it exerts a force is called the ‘magneticfield’. The magnetic field is three-dimensional and it may be shown visually bydrawing imaginary lines called ‘lines of magnetic flux’.

14.2.3 LINES OF FLUX

A line of flux is a line indicating the direction in which a free north pole wouldtravel, if placed in the field at that point. Alternatively it is the direction in whichthe north pole of a compass needle would point. The direction which would betaken is indicated on the lines of flux by arrow heads.

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Therefore lines of flux emanate from north poles and re-enter at south poles, seediagram below.

14.2.3.1 Properties of Lines of Flux

To make the imaginary lines of flux describe the behaviour of the magnetic fieldwe must give them appropriate properties. Thus lines of flux have the followingproperties:

They are imaginary.

By definition they emerge from a north pole and re-enter at a south pole.

They are continuous and never ending (thus they travel inside the magnetfrom the south to north).

They never cross each other (a compass placed at a given point can onlypoint in one direction).

They can bend, but resist bending or distortion.

They behave as though elastic (and therefore try to shorten themselves).

They repel each other sideways (they fill evenly the volume available -there are no abrupt discontinuities).

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14.3 THE EARTH’S FIELD

The earth acts as a magnet and the lines of force produced by it follow thepattern shown in the diagram below.

If the Earth were completely symmetrical, thenorth and south magnetic poles wouldcoincide with the axis of the Earth. Themagnetic poles are, in fact, separated fromthe true poles by about 1000 Miles, the northmagnetic pole being in the area 70 - 75degrees North and roughly 95 degrees West.

Since the North pole of a magnet is really aNorth seeking pole and similarly the Southpole is really a South seeking pole it followsthat at the Earth's North pole there must be asouth seeking magnet and similarly at theEarth's South pole there must be a Northseeking magnet. Unfortunately before thesignificance of the Earth's magnetism wasrealised, navigators had dropped the word"seeking" leaving the embarrassing statementthat there is a magnetic south pole at theNorth pole and a magnetic North pole at theSouth pole.

This problem is overcome by defining the North seeking pole as the Red Poleand the South seeking pole as the Blue Pole.

14.4 MAGNETIC MATERIALS

14.4.1 FERROMAGNETIC MATERIALS

Ferromagnetic materials can be easily magnetised and exhibit strong magneticproperties. This group can be further subdivided into hard and soft magneticmaterials.

Above certain temperatures ferromagnetic materials behave as paramagneticmaterials.

Page 14-4

14.4.1.1 Hard Iron

Hard magnetic materials are more difficult to magnetise but retain most of theirmagnetism when the magnetising force is removed.

Examples - steel and nickel alloys such as:

Ticonal - Iron-Cobalt / Nickel / Aluminium / Titanium and Copper

Alnico - Iron-Nickel / Cobalt And Aluminium

These materials are used for permanent magnets

14.4.1.2 Soft Iron

Soft magnetic materials become magnetised very easily, but they loose most ofthe magnetism when the magnetising force is removed.

Examples - alloys such as stalloy and mumetal

These materials are used for temporary magnets

14.4.2 PARAMAGNETIC MATERIALS

Most materials fall into this group. These materials can only be magnetised with agreat amount of effort, usually resulting in their destruction. If magnetised thematerial only exhibits small magnetic properties.

Examples - Wood / Glass /Air / Water / Aluminium

14.4.3 DIAMAGNETIC MATERIALS

This is a small group of materials that actually oppose a magnetising force. Ifplaced in a magnetic field they will decreases its strength. If suspended in amagnetic field, they will swing to adopt a position at 90 degrees to the lines offlux.

Examples - Copper / Brass / Bronze / Mercury / Bismuth

14.5 PRODUCTION OF A MAGNET

Magnets can be produced in a variety of ways, generally the method used isdetermined by the type of magnet required.

14.5.1 STROKE METHOD

Using the stroke method of producing a magnet, a piece of steel is stroked by apermanent magnet or magnets. Backward and forward movement of the steelshould be avoided and magnets should follow the assumed lines of force whenstroking the steel.

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Magnets with same polarity at either end can be produced using the doublestroke method. This entails stroking the steel from the centre to the end,

reversing the direction of the magnet for each end. Such a magnet is said to haveconsequent poles.

14.5.2 INDUCTION

The property of magnetism may be induced in a piece of material that does notnormally have that characteristic.

If a piece of soft iron is placed in the magnetic field of a permanent magnet, thesoft iron will assume the properties of a magnet and become magnetised. Thisaction is called magnetic induction. It occurs because the lines of flux tend to flowthrough the path of least opposition, and air offers more opposition than soft iron.

When the lines of flux pass through the soft iron, the molecules of soft iron line upwith the lines of force, their north poles pointing in the direction in which the linesof force are travelling through the iron. The end at which the lines of flux enter thesoft iron becomes a south pole, the end at which they leave, a north pole.

If the magnetic field is removed, the soft iron will loose its magnetism.

It should be noted that a piece of soft iron sitting in the earth's magnetic field willconcentrate the lines of flux and become magnetised.

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14.5.3 USE OF ELECTRICAL CURRENT

When a conductor carries an electric current, a magnetic field is produced aroundthat conductor. This phenomenon was discovered by Oersted in 1820.

Oersted found that a wire carrying an electric current produces a magnetic fieldaround the wire for as long as current continues to flow. The direction of themagnetic field depends upon the direction of the current. The field is symmetricalaround the wire and is represented by lines of flux drawn as concentric circlesaround the wire.

By convention current flowing into a diagram is represented by a cross, currentflowing out of the diagram by a dot. One can liken this to the view obtained from adart thrown towards you, or away from you.

14.5.3.1 Corkscrew Rule

Knowing the direction of the current, it is possible to determine the direction of themagnetic field using Maxwell’s Corkscrew rule, usually abbreviated to theCorkscrew Rule (or sometimes the right hand screw rule).

Page 14-7

The Corkscrew Rule states; if a corkscrew is turned so that it moves in thedirection of conventional current flow, then the direction of rotation of the

corkscrew corresponds to the direction of the magnetic field, see diagram below.

14.5.3.2 Attraction & Repulsion

Two parallel wires, which are close together, each carrying an electric current,produce magnetic fields which interact with one another. If the currents flow inthe same direction, the wires experience a force of attraction. If the currents flowin opposite directions, the wires experience a force of repulsion, see diagrambelow.

The force between two such conductors forms the basis for the definition of theunit of current- the ampere.

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15 ELECTROMAGNETISM

If a straight wire carrying a current is formed into a circular loop, the magneticfield is as shown. The field may be deduced by taking elements of the loop andlooking at the field around each part of the loop.

15.1 PRODUCTION OF A BAR MAGNETIf a length of wire is bent into a series of loops, it forms a solenoid. The directionof the magnetic field around any small part of it can be obtained by using thecorkscrew rule. If the fields for a series of such loops are combined, the resultwill be a field pattern similar to that of a bar magnet.

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15.1.1 END RULE

The direction of the magnetic field depends upon the direction of conventionalcurrent flow. We can find out which end of the coil is acting as the north pole andwhich is the south pole by observing the direction of current flow at each end.This is called the End Rule or sometimes, the clock rule, see diagram below.

15.1.2 RIGHT HAND GRIPPING RULE

The right hand gripping rule can also be used to determine the north pole of acoil. The coil is gripped by the right hand with the fingers pointing along theconductors in the direction of conventional current flow, when the thumb is thenextended, it indicates the end of the coil that has a magnetic north polarity.

15.2 THE MAGNETIC CIRCUIT

15.2.1 MAGNETOMOTIVE FORCE (MMF)

In an electric circuit, a current is established due to the existence of anelectromotive force. In the same way, in a magnetic circuit, a flux is establisheddue to the existence of a magnetomotive force. The mmf is produced by thecurrent flowing in the coil and its value is the product of the current and thenumber of turns on the coil.

Magnetomotive Force = Current x Number of Turns on the Coil

Note that, although mmf is quoted in ampere turns, the actual unit dimension is inamperes.

15.2.2 MAGNETISING FORCE

The magnetomotive force can be expressed in terms of the length of the magnet.It is then referred to as the magnetising force or magnetic field strength and giventhe symbol H. The magnetising force is a measure of the intensity of the magneticeffects at any given point in the magnetic field.

Magnetising Force (H) = Magnetomotive ForceLength of magnet

Page 15-2

Note that:

The unit of field strength is ampere per metre, although it may be quoted asampere turns per metre.

The length of a solenoid ‘l’, is the length along its axis and not the length ofwire from which the solenoid is made.

It will therefore be seen that a solenoid having 10 turns per metre carrying acurrent of 6A (10 6 = 60 ampere/metre) will produce the same strength ofmagnetic field as one of 12 turns per metre carrying 5A (12 5 = 60ampere/metre).

15.2.3 FLUX & FLUX DENSITY

A magnetising force produces a certain amount of magnetic flux (),measured in Webers. The magnetic field is represented by imaginary lines ofmagnetic flux. The number of lines of flux passing though a given area is calledthe ‘flux density’. Flux density is denoted by the symbol B and given the unitTesla.

Flux density (B) = A Teslas

The unit of flux density is actually Webers per m2, so:

1 Tesla = 1 Wm2ber

15.2.4 PERMEABILITY

When an mmf produces a magnetising force H, a certain flux density B isestablished.

Ratio BH is termed 'the permeability of the material'.

Permeability is an indication of the ability of the flux to permeate the material. Ifthe material in which the flux is established is a vacuum, or free space, then theratio is called‘the permeability of free space' and given the symbol o. Thisvalue is considered to be a constant, 4 10-7 H/M

If a flux is established in any material other than air or free space, then the fluxdensity will increase. The number of times by which the flux density increases iscalled the ‘relative permeability of the material’ denoted by the symbol r.This is not a constant but varies with different material. i.e. steel= 800.

The product of o and r is called the ‘absolute permeability’ and is denotedby the symbol .

Page 15-3

For all materials

15.2.5 RELUCTANCE

B

H = = o x r

The opposition experienced by a magnetising force to the creation of a flux is

called ‘reluctance’ and denoted by the symbol S. The following derivation is for

information only.

Total Flux = B × A Webers (1)

IN

(from flux density B = A )

mmf = I.N and H = length

therefore H x length = IN and

using equations (1) and (2) above

mmf = H × length (2)

x Ammf = H xlength

But B H = o x r

ATherefore

mmf = o x r x length

lengthAnd reluctance (S) = mmf= o x r x A

The units of reluctance are Ampere TurnsWeber

15.2.6 COMPOSITE PATHS AND AIRGAPS

A magnetic circuit may be composed of paths of different materials. Such

magnetic path is called a composite path. The total reluctance of a composite

path is equal to the sum of the individual reluctance's.

In many devices such as transformer motors and generators the magnetic flux

has parallel paths. The purpose is to reduce the total reluctance given two

parallel paths S1 and S2.

For more than two parallel paths:

Page 15-4

1 1 1 1 1 S S S S ST OT AL 1 2 3 n

S SS

T OT AL1 2

S S1 2

15.3 BH CURVE

For any ferromagnetic material there is a definite value of flux density (B),corresponding to a specified value of magnetising force (H). These values can

be ascertained from graphs of B against H for each material. A BH curve can onlybe obtained using a piece of material that has never been magnetised before.Once the material has been magnetised and the curve obtained, the productionof another BH curve, from the same piece of material, is not possible.

The BH curve is the line O to Q on the hysteresis curve shown below.

The gradient of the BH curve gives the permeability of the material. In practice itis found that the magnetic property of different specimens of the same materialvary considerably. The fact that permeability varies for a given material may alsobe seen from the shape of the curve, if the permeability was a constant, the graphof B against H would be a straight line.

15.4 HYSTERESIS LOOP

A ferromagnetic material retains some magnetism after the magnetising force isremoved. The BH curve (O to Q) will therefore only be followed once, on initialmagnetisation.

When a material is subjected to a changing magnetising force, the flux density isaffected by its previous magnetic history. There is tendency for the magneticconditions to lag behind the magnetising force that is producing them. This isknown as ‘hysteresis’ and comes from the Greek meaning late or lagging.

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If a piece of material is taken through a complete cycle of magnetising anddemagnetising the graph of B against H is as shown, this diagram is called ahysteresis loop.

O to Q - Initial magnetisation to saturation at point A

Q to R - Magnetising force is reduced to zero.

O to R - Represents remanence. Remanence is the flux density remaining inor the material after the magnetising force is removed. It is sometimes

0 to U called ‘retentivity’. If the material had not been taken to saturation thenOR or OU would represent the remanent

flux density.

R to S - The magnetising force is reversed.O to S - Represents the magnetising force required to reduce the flux densityorto zero. This is called the coercivity of the material. If the material

O to V had not reached saturation it is termed the ‘coercive force’.

S to T - Further increase in the reverse magnetising force. This causes thematerial to reach saturation in the opposite direction.

T to Q - Reversal of magnetising force again eventually makes the materialsaturate in original direction.

The term residual magnetism is used to describe the useful flux remaining afterthe magnetising force has been removed for a considerable time. It isproportional to the coercivity of the material and is also called coercivity. Thisterm should not be confused with remanence or remanent flux density.

The area of the loop represents the energy loss during each magnetic cycle, orthe power dissipated. It’s size is dependent upon the type of material andfrequency at which the magnetising force is switched.

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The following should be noted:

Soft iron saturates with much less magnetising force than steel.

The remanence of soft iron is greater than that of steel.

The area of the loop and coercivity for steel is much greater than for softiron. This indicates greater hysteresis loss and residual magnetism.

Materials with large loops are used for permanent magnets - ticonal.

Materials with small loops are used for temporary magnets - stalloy,

Mumetal.

15.5 COMPARISON OF ELECTRICAL & MAGNETIC CIRCUITS

It is useful to compare various electric and magnetic quantities and theirrelationships. Consider the electric and magnetic circuits shown below.

Tabulating the comparisons:

ELECTRIC CIRCUIT MAGNETIC CIRCUIT

Quantity Unit Quantity Unit

Emf Volt mmf Ampere turn

Current Ampere Magnetic Flux Weber

Resistance Ohm ReluctanceAmpere turns /

Weber

Current = emf / Resistance Magnetic Flux = mmf / Reluctance

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15.6 MAGNETIC SCREENING

The differing values of reluctance of air and soft iron are made use of in magneticscreening. Air had high reluctance whilst soft iron has a low reluctance. Thus ifthe equipment to be screened is surrounded by soft iron, most of the flux will passthrough the soft iron, rather than the air inside it, since lines of flux take the pathof least reluctance.

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16 INDUCTION

In 1831, a scientist called Michael Faraday discovered that an electric currentwas produced by the relative movement of a magnet and a coil, a phenomenonwhich is now known as electromagnetic induction.

16.1 ELECTRICITY FROM MAGNETISM

If a magnet is moved into or out of a coil of wire and if the coil is connected to ameter, the meter records a flow of current as long as the magnet is moving.

The same result is obtained if the magnet is kept stationary and the loop ismoved. The meter therefore shows that there is a current as long as there is

relative movement between the loop (coil) and the magnet (magnetic field). Notethat energy is not being produced but simply converted from mechanical energyto electrical energy.

16.1.1 FACTORS AFFECTING INDUCED EMF

By experiment, the following factors may be noted:

The faster the magnet (or coil) is moved, the greater is the deflectionobtained on the meter. This shows that the magnitude of the emf isproportional to the rate of relative movement.

Repeating the experiment using a stronger magnet results in greater meterdeflection for the same rates of movement. Hence the magnitude of the emfis proportional to the flux density.

Reversal of the direction of motion produces meter deflecting in the oppositesense. The direction of the induced emf therefore depends on the directionof motion.

Using the south pole of the magnet instead of the north results in meterdeflections in the opposite sense, showing that the direction of the inducedemf depends upon the direction of the magnetic field.

If more turns are used on the coil, meter deflection is greater and isproportional to the number of turns (N).

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These results are summarised in two laws, as follows.

16.1.2 FARADAYS LAW

When the magnetic flux through the coil is made to vary, an emf is induced in the

coil. The magnitude of the induced emf is proportional to the rate of change of

flux.

Hence, E d

dtwhere

d change of

flux

dt timetakentochange

The emf is also dependent on the number of turns on the coil (N), the greater the

number of turns on the coil, the greater emf. Hence, we may write:

E Nd

dtvolts

16.1.3 LENZ’S LAW

A change of flux in a closed circuit induces an emf and sets up a current. The

direction of this current is such that its magnetic field tends to oppose the change

of flux. See diagram below.

The direction of the induced emf as given by Lenz’s Law may be shown in our

equation by introducing a negative sign, but remember that the negative sign is

vectorial and not arithmetic.

Hence,E -Nd

dtvolts

This formula is not strictly correct. A conductor must cut 108 lines of flux per

second in order to induce 1 volt. That is the flux must be changing at a rate of

108 lines per second. The formula should therefore be written as:

E -Nd

dtx10 8 volts

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16.1.4 FLEMINGS RIGHT HAND RULE

When a straight wire is moved through a magnetic field, an emf is induced in it, inthe manner of the coil and magnet experiment. Once again, lines of flux arebeing cut by a conductor and if the wire forms part of a closed circuit, a currentwill flow. The same effect is observed if the wire is stationary and the magneticfield moves. The direction of the induced emf may be determined by Fleming’sRight Hand Rule.

The thumb, first finger and second finger of the right hand are held at right anglesto each other, then:

With the thuMb pointing in the direction of the conductor movement.

With the First finger pointing in the direction of the magnetic field (N to S).

Then the seCond finger points in the direction of conventional current flowand thus indicates the direction of the induced voltage.

16.2 SELF INDUCTANCE

When current through a coil changes, the changing flux induces an emf thatopposes the current flow. This emf is the result of self inductance and is called‘back emf’. The term ‘self inductance’ is often replaced merely by inductance.The value of back emf is given by:

E = -L x dIdt

Where L is the inductance in henries, and dIdt the rate of change of current.

The minus indicates back emf.

The unit of inductance is the henry and is based on the equation. If currentchanging at a rate of 1 amp a second induces an emf of 1 volt then theinductance is 1 henry.

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All circuits have inductance even a straight conductor, but if a straight piece ofwire is formed into a coil the number of flux linkages increases and so does theinductance.

A further increase in inductance is achieved by increasing the flux density. Thisdepends on the area, the length of the coil and the permeability of material inwhich flux is established,

Thus, L= N2 o r A

Henries l

N = Number of Turns

o r= Absolute Permeability

A = Area in square metres

I = Length of coil in metres (not wire)

2length lAs reluctance (S) =

o x r x Ao r A = S and L = S

Also by transposition of E = -L × dldt

L = -E × dtdl

16.3 MUTUAL INDUCTANCE

If the changing flux in a coil links with the turns of a second coil, the two coils aresaid to be mutually coupled and mutual inductance exists between them. Theunit of mutual inductance is Henry and is defined by:

If the primary current, changing at a rate of 1 amp per second, induces asecondary voltage of 1v, then the mutual inductance is 1 henry.

Thus: Es = M × dlprimarydt

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16.4 COUPLING FACTOR

If all the flux of a primary coil links with all the turns of a secondary then 100%coupling exists. Sometimes it is more convenient to use a coupling factor- k.

Maximum Coupling (100%) is represented by a k value of 1.

Thus if flux linkage is 97% the coupling factor is 0.97.

Given that mutual coupling depends on k then so does the mutual inductance.The relationship is given by: M = kL1 L2

Where L1 and L2 are individual inductance’s of the mutually coupled coils.

The value of k depends on:

Purpose of coils involved

Relative positions of the coils

Frequency or rate of change of current

and can be as high as 0.98 or as low as 0.0001.

16.5 ENERGY STORED IN MAGNETIC FIELD

If we consider the theoretical case of a circuit with inductance only, all of theenergy used in the circuit must go into the magnetic field. It can be shown thatthe energy stored in the magnetic field is given by equation:

Energy stored = ½ L I2 joules

Where L is the inductance of the coil in Henries and I is the current flowingthrough it in amps.

16.5.1 SPARK SUPPRESSION

If we consider a circuit with a large inductance, possibly one using a magneticrelay. At the instant the switch is opened, the current through the coil is changingat maximum rate, therefore the back emf induced in the coil is also at maximum.

This emf is applied to the air gap between the switch contacts and ionises the air,producing a spark which the burns the contacts. This increases their electricalresistance and radiates energy which may cause interference, therefore sparksmust be suppressed. Good design of switch contacts can help, but connecting acapacitor in parallel with the switch is the best method of eliminating sparking.

When using a capacitor the energy released by the coil charges the capacitorinstead of ionising air. When the switch is closed again the capacitor discharges.

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Page 16-6

17 INDUCTORS

Coils which are used for their opposition to current change in a circuit are knownas inductors or chokes.

17.1 CONSTRUCTION

Inductors with an air core have small inductance values and are used at highfrequencies within radio tuning circuits, or as r.f. chokes to stop radio frequencycurrents taking certain paths in circuits. Coils for use at high frequency are madeof Litz wire which consists of several thin copper wires insulated from each other.

Materials based on iron are used where a large inductance is required. Ironincreases the strength of the magnetic field several hundred times. Silicon steeland nickel iron are used at frequencies up to 20kHz.

Iron cores are laminated. The laminations reduce the conversion of electricalenergy to heat by making it difficult for currents in the coil to induce currents inthe core. These induced currents are called ‘eddy currents’ because they flow incircles through the iron core. If the laminations are at right angles to the plane ofthe coil windings, the core offers a large resistance to the eddy currents.

Iron based cores can be used at high frequencies if the material is in the form of apowder which has been coated with an insulator and pressed together.

Ferrite cores consist of ferric oxide combined with other oxides such as nickeloxide and may also be used at high frequencies.

Iron dust and ferrite cores increase the inductance of a coil considerably. Forexample, an air cored inductor of 1mH could be increased to 400mH by fitting aferrite core. These cores also have a high resistance, thereby reducing eddycurrents.

Page 17-1

17.2 INDUCTOR SYMBOLS

Air Core:

old symbol new symbol

Iron Core:

old symbol new symbol

Iron Dust or FerriteCore:

old symbol new symbol

Page 17-2

18 INDUCTORS IN DC CIRCUITS

18.1 INDUCTORS IN SERIES

If it is required to increases the value of inductance in a circuit, then two or moreinductors may be connected in series. The total inductance then depends on thesum of individual inductances and the mutual coupling between them.

With no mutual coupling:

LT = L1 + L2 etc

If the coils are positioned so that the mutual induced emf’s in each coil aid the selfinduced emf’s then the coils are said to be series aiding, and

LT = L1 + L2 + 2M

If the coils are positioned so that mutually induced emf’s in each coil oppose theself induced emf’s, the coils are said to be in series opposing, and

LT = L1 + L2 - 2M

Thus if the position of L2 reference to L1 can be reversed, then the totalinductance will vary between:

LT = L1 + L2 + 2M

and LT = L1 + L2 - 2M

giving a total variation of 4M.

A device which will achieve this is called variometer. It consists of two coilslocated one inside the other. The outer coil (stator) is stationary whilst the innercoil (rotor) is capable of rotation through 180 degrees. The coils are mutuallycoupled and connected in series, in one position the rotor field aids the statorfield, when the rotor is turned 180º the rotor field opposes the stator field. Thenthe coils are at 90 degrees to each other, mutual coupling is negligible.

18.2 INDUCTORS IN PARALLEL

If inductors are connected in parallel, the total inductance decreases.

With no mutual coupling:

1LT

=1

L1 +L2 +L3

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Or if only two inductors are connected:

LT = L1 L2 L1 + L2

18.3 INDUCTORS IN A DC CIRCUIT

If a circuit contained only pure resistance, then the current would rise to its full

value I = E in zero time when the switch is closed. R

In practice, there is no such thing as ‘pure’ resistance and it is normal to find a

circuit containing resistance and inductance in series. Also, there is no such

thing as pure inductance since any coil must have some resistance. Therefore,

the circuit to be considered will have inductance and resistance in series.

An inductance opposes any change in current by producing a back emf. The

back emf tries to prevent current flow when the circuit is switched ‘ON’ and tries

to maintain current flow when the circuit is switched ‘OFF’. Current can therefore

not rise instantly to a maximum, or fall instantly to zero.

18.3.1 WHEN DC CURRENT IS APPLIED

On moving the switch to position A in the diagram below, the current circuit will

start to rise. All times Kirchhoff’s second law applies.

By Kirchhoff’s second law

but

and

hence

E - Eb = VR (Eb = back emf)

Eb = -L dldt

VR = IR

E = L dl - IR voltsdt

In the above equation, E, L and R are constant, therefore as I increases,

dl

Dt (the slope of the graph at any point) must decrease.

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The current therefore follows a curve whose gradient is continually decreasingand which is called an ‘exponential curve’.

18.3.2 TIME CONSTANT

It is impossible to decide exactly when the maximum point is reached on anexponential curve, or when the curve has fallen to exactly zero. To enable

calculations to be performed a time constant is used. The time constant givesan indication of the time taken for the current to rise to its maximum value or fallto zero. The time constant is defined as either:

The time taken for a current to reach its maximum value if the initial rate ofincrease were maintained.

The time taken for the current to reach 0.632 of its maximum value (or63.2%).

The latter definition arises since it is found that after one time constant, thecurrent has always built up to 63.2% of its maximum value. The time constant fora series LR circuit is given by:

Time Constant = LR seconds

Therefore, although it is not possible to say exactly when the current reaches itsmaximum value, for all practical purpose it can be considered a maximum after 5time constants:

Maximum Current flows after 5LR

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18.3.2.1 Proof of Time Constant

At the instant of closing the switch (point A) I = O.

ButE = L dl

+ IR dt

Therefore E

But dl

= L dldt and dt = L

dt at A is the slope of the graph

at A.

The slope of AB = BC

AC = L

But if AC is the time constant and BC = ER

E 1 EThen

R

Time Constant

L

Therefore the Time Constant must equal LR

18.3.3 THE EFFECTS OF BACK EMF ON CIRCUIT CURRENT

In proving the time constant, it was stated that, at the instant the switch is closed,the current (I) is zero. This is because, at that instant in time the current in thecoil and the flux surrounding the coil are both changing at their maximum rate.This rate of change of flux produces maximum back emf, the value being equaland opposite to the applied voltage. Therefore, with no potential differenceacross the circuit, no current can flow. This fact is quite simple to prove using theequation for the self induced emf in a coil and elements of the ‘proof of timeconstant’ above:

E = -L x dIdt

The current starts from zero, and would rise to its maximum value in 1 timeconstant if the initial rate of change could be maintained.

The rate of change of current is therefore given by the gradient of line AB. The

gradient of AB = BCAC =

ime Constant .

Issue 1 - 20 March 2001 Page 18-4

IMAX can be calculated using VSupply , because when the current reaches itsRmaximum value it is no longer producing a changing flux and therefore not

producing a back-emf. At this time, the whole supply voltage is dropped acrossthe resistor.

18.3.4 WHEN DC CURRENT IS REMOVED

A similar situation occurs when the switch is moved from position A to position B.The current does not immediately fall to zero because the inductor opposes anychange and tries to maintain the current flow. Instead the current decaysexponentially to zero over a period of 5 time constants.

In the circuit shown, the resistor is kept in circuit, therefore the time constantcalculated will be the same as when the switch was moved to position A. If adifferent value of resistance is present then the time constant will be different.

It should be noted that in trying to keep the current flowing in the same directionaround the circuit, the polarity of the voltage across the inductor must be thereverse of what it was when the switch was moved to position A. ie +ve at thebottom of the coil and -ve at the top.

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18.3.5 SAFETY

As the current increases through an inductor, flux builds up and energy is storedin the magnetic field. On short circuiting an inductor, the magnetic field collapsesand the energy is returned to the circuit in the form of an emf that tries to maintainthe current flow. If the circuit is open-circuited rather than short-circuited by aresistor, as in the case of the circuit studied (moving the switch to B), then thecollapsing flux will produce a large back-emf that may cause sparking across theswitch contacts as they are opened. The sparks damage the contacts, produceheat, could ignite fuel vapour and transmit electromagnetic radiation whichinterferes with communication and navigation equipment. The large emf’s canalso cause electric shocks on what are considered safe, low voltage d.c. circuits.

Issue 1 - 20 March 2001 Page 18-6

19 CIRCUIT SYMBOLS

The following circuit symbols have been taken from a typical aircraft manual andare intended to be a small selection of what you will find being used in aircraftmaintenance documentation. You will be expected to memorise commonsymbols, as without them you will be unable to negotiate the aircraft schematicdiagrams and wiring diagram manuals. This applies irrespective of your intendedtrade.

For manuals produced i.a.w. the ATA specification 100, a list of circuit symbolscan be found in the WDM Chapter 20. For other aircraft no such list may existand you will have to rely on memory.

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