271308950-EASA-Part-66-Module-3-Electrical-Fundamentals-Part-A.pdf

JAR 66 CATEGORY B1

uk

engineering

MODULE 3 (part A) ELECTRICAL FUNDAMENTALS

Index 1

ATOMIC STRUCTURE ........................ ........... ........................... .......................... ......................... ............... .. 1-1 MATTER ................................................................................ 1-1 1.1 1.1.1 States of Matter .......................... ............. ........................... .......................... .............. .. 1-1 1.1.2 Chemical classification of matter......................... ............ ................ ... 1-1 1.1.3 Atomic classification of matter........................ ........... ..................... ........ 1-1 MOLECULES .......................................................................... 1-2 1.2 1.3 ATOMS ................................................................................. 1-2 1.3.1 The Structure of an Atom ......................... ........... ........................... ............... 1-3 1.3.2 The Fundamental Particles .......................... ............. ....................... .......... 1-3 1.3.3 Particle function ......................... ............ ........................... .......................... .............. .. 1-4 1.3.4 ions ........................ ............ ......................... ........................... ........................... ..................... ........ 1-5 ELECTRICAL MATERIALS ......................................................... 1-5 1.4 1.4.1 Electron distribution .......................... ............. .......................... ..................... ........ 1-6 1.4.2 Ionisation......................... ............. .......................... ........................... ......................... ............ 1-7 1.4.3 Energy levels ......................... ............ .......................... .......................... ................... ...... 1-7 1.4.4 Conductors........................ ............ .......................... ........................... ....................... .......... 1-7 1.4.5 Insulators ........................ ........... ........................... ........................... ......................... ............ 1-7 1.4.6 Semi-conductors ........................ ............ .......................... .......................... .............. .. 1-7

2

STATIC ELECTRICITY .......................... ............. ........................... .......................... ......................... ............. 2-1 2.1 ATTRACTION & REPULSION ..................................................... 2-3 UNIT OF CHARGE ................................................................... 2-3 2.2 STATIC ELECTRICITY & AIRCRAFT ............................................ 2-3 2.3

3

ELECTRICAL TERMINOLOGY ........................ ........... ........................... .......................... .............. .. 3-1 VOLTAGE .............................................................................. 3-1 3.1 3.1.1 Potential ........................ ........... ........................... ........................... ......................... .............. .. 3-1 3.1.2 Potential Difference......................... ............ .......................... ....................... .......... 3-1 3.1.3 Electromotive Force – emf ......................... ............ ......................... ............ 3-2 CURRENT .............................................................................. 3-2 3.2 3.2.1 Movement of charge ......................... ............ .......................... ..................... ........ 3-2 3.2.2 Conventional flow .......................... ............. .......................... ......................... ............ 3-3 3.2.3 Electron flow .......................... ............. .......................... .......................... ................... ...... 3-3 RESISTANCE ......................................................................... 3-3 3.3 3.3.1 Factors affecting resistance ......................... ............ ....................... .......... 3-4 3.3.2 Units of resistance .......................... ............. .......................... ....................... .......... 3-4 3.4 CONDUCTANCE AND CONDUCTIVITY ........................................ 3-4

4

PRODUCTION OF ELECTRICITY......................... ............ .......................... ....................... .......... 4-1 BY FRICTION .......................................................................... 4-1 4.1 BY PRESSURE ....................................................................... 4-1 4.2

Issue 1 - 30 August 2001

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engineering 4.3 4.4 4.5 4.6


BY MAGNETISM ......................................................................

4-2 BY HEAT ............................................................................... 4-2 BY LIGHT ............................................................................... 4-3 BY CHEMICAL ACTION ............................................................. 4-3

5

CELLS & BATTERIES......................... ............ ........................... .......................... ......................... ............... .. 5-1 PRINCIPLES ........................................................................... 5-1 5.1 5.1.1 Cell & Battery symbols ......................... ........... .......................... .................. ...... 5-1 5.1.2 Construction & chemical action ........................ ............ .................. ...... 5-1 5.1.3 Primary & secondary cells.......................... ............. ......................... ............ 5-2 5.1.4 Cell emf ......................... ............ ........................... ........................... ......................... .............. .. 5-2 5.1.5 Cell capacity......................... ............ .......................... .......................... ..................... ........ 5-3 5.1.6 Interconnection of cells .......................... ............ .......................... ................ .... 5-3 LEAD ACID BATTERIES ............................................................ 5-4 5.2 5.2.1 Conventional construction .......................... ............. ......................... ............ 5-4 5.2.2 Solid block type construction.................................. construction.................................. 5-5 5.2.3 Chemical action ......................... ............. .......................... .......................... .............. .. 5-6 5.2.4 Voltage & Specific Gravity characteristics .............. ............. . 5-7 5.2.5 Common lead acid battery faults......................... ............ ................ ... 5-7 NICKEL CADMIUM BATTERIES .................................................. 5-8 5.3 5.3.1 Construction ......................... ............ .......................... .......................... ..................... ........ 5-8 5.3.2 Chemical action ......................... ............. .......................... .......................... .............. .. 5-9 5.3.3 Advantages & disadvantages......................... ............ ..................... ........ 5-10 5.3.4 Thermal runaway ......................... ............. .......................... .......................... ............ 5-11 SMALL ALKALINE CELLS .......................................................... 5-11 5.4

6

OHM’S LAW ........................ ............ ......................... ........................... ........................... .......................... ................. .... 6-1 TRANSPOSITION OF OHM’S LAW ............................................... 6-1 6.1 THE OHM’S LAW TRIANGLE ...................................................... 6-2 6.2

7

ELECTRICAL MEASURING INSTRUMENTS ......................... ........... ................... ..... 7-1 CONNECTING METERS TO A CIRCUIT ........................................ 7-1 7.1 7.1.1 Voltmeters ......................... ............. .......................... ........................... ....................... .......... 7-1 7.1.2 Ammeters........................ ........... ........................... ........................... ......................... ............ 7-2 7.1.3 Ohmmeters ......................... ............. .......................... ........................... ..................... ........ 7-2 7.2 ANALOGUE MULTIMETERS ....................................................... 7-3 7.2.1 DC voltage measurements......................... ............ ......................... ............ 7-4 7.2.2 DC current measurements ......................... ............ ......................... ............ 7-5 7.2.3 DC high-current measurement .......................... ............. .................. ..... 7-6 7.2.4 AC voltage measurements ......................... ............ ......................... ............ 7-7 7.2.5 Resistance measurements......................... ............ ......................... ............ 7-7 7.2.6 Continuity testing ......................... ............. .......................... .......................... ............ 7-9 7.2.7 Battery testing .......................... ............. ........................... .......................... ................ .... 7-10 7.2.8 DO's & DON'Ts of using an analogue multimeter .. 7-10


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engineering 4.3 4.4 4.5 4.6


BY MAGNETISM ......................................................................

4-2 BY HEAT ............................................................................... 4-2 BY LIGHT ............................................................................... 4-3 BY CHEMICAL ACTION ............................................................. 4-3

5

CELLS & BATTERIES......................... ............ ........................... .......................... ......................... ............... .. 5-1 PRINCIPLES ........................................................................... 5-1 5.1 5.1.1 Cell & Battery symbols ......................... ........... .......................... .................. ...... 5-1 5.1.2 Construction & chemical action ........................ ............ .................. ...... 5-1 5.1.3 Primary & secondary cells.......................... ............. ......................... ............ 5-2 5.1.4 Cell emf ......................... ............ ........................... ........................... ......................... .............. .. 5-2 5.1.5 Cell capacity......................... ............ .......................... .......................... ..................... ........ 5-3 5.1.6 Interconnection of cells .......................... ............ .......................... ................ .... 5-3 LEAD ACID BATTERIES ............................................................ 5-4 5.2 5.2.1 Conventional construction .......................... ............. ......................... ............ 5-4 5.2.2 Solid block type construction.................................. construction.................................. 5-5 5.2.3 Chemical action ......................... ............. .......................... .......................... .............. .. 5-6 5.2.4 Voltage & Specific Gravity characteristics .............. ............. . 5-7 5.2.5 Common lead acid battery faults......................... ............ ................ ... 5-7 NICKEL CADMIUM BATTERIES .................................................. 5-8 5.3 5.3.1 Construction ......................... ............ .......................... .......................... ..................... ........ 5-8 5.3.2 Chemical action ......................... ............. .......................... .......................... .............. .. 5-9 5.3.3 Advantages & disadvantages......................... ............ ..................... ........ 5-10 5.3.4 Thermal runaway ......................... ............. .......................... .......................... ............ 5-11 SMALL ALKALINE CELLS .......................................................... 5-11 5.4

6

OHM’S LAW ........................ ............ ......................... ........................... ........................... .......................... ................. .... 6-1 TRANSPOSITION OF OHM’S LAW ............................................... 6-1 6.1 THE OHM’S LAW TRIANGLE ...................................................... 6-2 6.2

7

ELECTRICAL MEASURING INSTRUMENTS ......................... ........... ................... ..... 7-1 CONNECTING METERS TO A CIRCUIT ........................................ 7-1 7.1 7.1.1 Voltmeters ......................... ............. .......................... ........................... ....................... .......... 7-1 7.1.2 Ammeters........................ ........... ........................... ........................... ......................... ............ 7-2 7.1.3 Ohmmeters ......................... ............. .......................... ........................... ..................... ........ 7-2 7.2 ANALOGUE MULTIMETERS ....................................................... 7-3 7.2.1 DC voltage measurements......................... ............ ......................... ............ 7-4 7.2.2 DC current measurements ......................... ............ ......................... ............ 7-5 7.2.3 DC high-current measurement .......................... ............. .................. ..... 7-6 7.2.4 AC voltage measurements ......................... ............ ......................... ............ 7-7 7.2.5 Resistance measurements......................... ............ ......................... ............ 7-7 7.2.6 Continuity testing ......................... ............. .......................... .......................... ............ 7-9 7.2.7 Battery testing .......................... ............. ........................... .......................... ................ .... 7-10 7.2.8 DO's & DON'Ts of using an analogue multimeter .. 7-10


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JAR 66 CATEGORY B1 MODULE 3 (part A)

uk

ELECTRICAL FUNDAMENTALS

engineering 7.3

DIGITAL MULTIMETERS ...........................................................

7.3.1 7.3.2 7.3.3 7.3.4 7.3.5 7.3.6 7.3.7 7.3.8

7-12 DC voltage measurements......................... ............ ......................... ............ 7-13 DC current measurements ......................... ............ ......................... ............ 7-13 High current measurements ......................... ............ ....................... .......... 7-14 AC voltage measurements ......................... ............ ......................... ............ 7-14 Resistance measurements......................... ............ ......................... ............ 7-15 Capacitor measurements ......................... ............ .......................... ............... 7-15 Continuity testing ......................... ............. .......................... .......................... ............ 7-16 DO's & DON'Ts DON'Ts of using a digital multimeter.......... 7-16

8

RESISTANCE & RESISTORS ........................ ........... .......................... .......................... ................. .... 8-1 RESISTIVITY .......................................................................... 8-1 8.1 CHANGES OF RESISTANCE WITH TEMPERATURE........................ 8.2 ............ ............ 8-1 TEMPERATURE CO-EFFICIENT OF RESISTANCE........................ 8.3 ............ .............. .. 8-2 RESISTORS ........................................................................... 8-3 8.4 8.4.1 Fixed resistors.......................... ............. ........................... .......................... ................ .... 8-3 8.4.2 Colour codes .......................... ............. .......................... .......................... ................... ...... 8-4 8.4.3 Preferred values and tolerances ......................... ............ ................ ... 8-5 8.4.4 Letter & digit codes ......................... ............ .......................... ....................... .......... 8-6 8.4.5 Power rating ......................... ............ .......................... .......................... ..................... ........ 8-6 8.4.6 Potentiometers ......................... ............ ........................... .......................... ................ .... 8-7 8.4.7 Rheostats ........................ ........... ........................... ........................... ......................... ............ 8-7 8.4.8 Voltage Dependent Resistors ........................ ........... ..................... ........ 8-7 THERMISTORS ....................................................................... 8-7 8.5

9

RESISTORS IN DC CIRCUITS .......................... ............ ........................... ......................... .............. .. 9-1 RESISTORS IN SERIES ............................................................ 9-1 9.1 9.1.1 Kirchoff’s Second Law................... ......................... ............. ............ 9-2 9.1.2 Voltage division ........................ ........... ........................... .......................... ................ .... 9-3 9.1.3 The Potential Divider......................... ............ .......................... ..................... ........ 9-3 9.1.4 Voltages relative to Earth ......................... ............ .......................... ............... 9-4 INTERNAL RESISTANCE ........................................................... 9-4 9.2 RESISTORS IN PARALLEL ........................................................ 9-6 9.3 9.3.1 Two resistors in parallel ......................... ............ ......................... ................ .... 9-7 9.3.2 Equal resistors connected in parallel ..................... ........... .......... 9-7 9.3.3 Effective value of resistors in parallel ..................... ........... .......... 9-8 9.3.4 Resistor size and current flow ........................ ........... ..................... ........ 9-8 9.3.5 Kirchoff’s First Law.......................... ............. .......................... ....................... .......... 9-8 RESISTORS IN SERIES / PARALLEL COMBINATIONS ..................... 9.4 ............. ........ 9-9 9.4.1 Physical arrangement of resistors ......................... ............ ............... 9-9 9.4.2 Solution of resistor networks using Ohm’s Law...... 9-9 THE EFFECTS OF OPEN CIRCUITS............................................. 9-11 9.5 THE EFFECTS OF SHORT CIRCUITS........................ 9.6 ........... .......................... ................... ...... 9-12


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10 THE WHEATSTONE BRIDGE...................................................... 10-1 10.1 CONSTRUCTION ..................................................................... 10-1 10.2 CALCULATING UNKNOWN RESISTANCES ................................... 10-1 10.3 USES ON AIRCRAFT ................................................................ 10-2 11 ENERGY & POWER IN DC CIRCUITS ........................................ 11-1 11.1 ELECTRICAL WORK ................................................................ 11-1 11.2 ELECTRICAL ENERGY ............................................................. 11-1 11.3 ELECTRICAL POWER ............................................................... 11-2 11.4 POWER RATINGS ................................................................... 11-2 11.4.1 Power ratings of resistors....................................... 11-3 11.4.2 Size and power rating ............................................ 11-3 11.4.3 The Kilowatt Hour .................................................. 11-3 11.5 MAXIMUM POWER TRANSFER .................................................. 11-4 12 CAPACITANCE & CAPACITORS ................................................ 12-1 12.1 CHARGING A BODY ................................................................. 12-1 12.2 THE BASIC CAPACITOR ........................................................... 12-2 12.3 CAPACITANCE ....................................................................... 12-2 12.4 FACTORS AFFECTING CAPACITANCE ........................................ 12-3 12.5 ENERGY STORED IN A CAPACITOR ........................................... 12-4 12.6 CAPACITOR CONSTRUCTION ................................................... 12-4 12.6.1 Fixed capacitors ..................................................... 12-4 12.6.2 Variable capacitors ................................................ 12-4 12.6.3 Electrolytic capacitors ............................................ 12-4 12.6.4 Safe working voltage .............................................. 12-4 12.7 CAPACITOR SYMBOLS ............................................................. 12-6 13 CAPACITORS IN DC CIRCUITS .................................................. 13-1 13.1 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 ............................... 13-3 13.4.1 Charging a capacitor .............................................. 13-3 13.4.2 Time Constant........................................................ 13-4 13.4.3 Discharging a capacitor.......................................... 13-5 13.4.4 A capacitor in a dc circuit ....................................... 13-6 13.5 THE EFFECTS OF OPEN & SHORT CIRCUITS ............................... 13-6 13.6 SAFETY & TESTING ................................................................ 13-6 13.7 CIRCUITS INVOLVING CAPACITIVE DECAY.................................. 13-7 14 MAGNETISM ................................................................................ 14-1 Issue 1 - 30 August 2001

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engineering 14.1

14.2

14.3 14.4

14.5


MAGNETIC THEORIES .............................................................

14-1 14.1.1 Molecular Theory ................................................... 14-1 14.1.2 Domain Theory ...................................................... 14-1 MAGNETIC PROPERTIES .......................................................... 14-2 14.2.1 Magnetic poles ....................................................... 14-2 14.2.2 Magnetic field ......................................................... 14-2 14.2.3 Lines of flux ............................................................ 14-3 THE EARTH’S FIELD ................................................................ 14-4 MAGNETIC MATERIALS ............................................................ 14-4 14.4.1 Ferromagnetic materials ........................................ 14-4 14.4.2 Paramagnetic materials ......................................... 14-5 14.4.3 Diamagnetic materials............................................ 14-5 PRODUCTION OF A MAGNET .................................................... 14-5 14.5.1 Stroke method........................................................ 14-5 14.5.2 Induction ................................................................ 14-6 14.5.3 Use of electrical current ......................................... 14-7

15 ELECTROMAGNETISM ............................................................... 15-1 15.1 PRODUCTION OF A BAR MAGNET.............................................. 15-1 15.1.1 End Rule ................................................................ 15-2 15.1.2 Right Hand Gripping Rule ...................................... 15-2 15.2 THE MAGNETIC CIRCUIT .......................................................... 15-2 15.2.1 Magnetomotive force (mmf) ................................... 15-2 15.2.2 Magnetising force ................................................... 15-2 15.2.3 Flux & Flux density ................................................. 15-3 15.2.4 Permeability ........................................................... 15-3 15.2.5 Reluctance ............................................................. 15-4 15.2.6 Composite paths and airgaps ................................ 15-4 15.3 BH CURVE ............................................................................. 15-5 15.4 HYSTERESIS LOOP ................................................................. 15-5 15.5 COMPARISON OF ELECTRICAL & MAGNETIC CIRCUITS ................ 15-7 15.6 MAGNETIC SCREENING ........................................................... 15-8 16 INDUCTION .................................................................................. 16-1 16.1 ELECTRICITY FROM MAGNETISM .............................................. 16-1 16.1.1 Factors affecting induced emf ................................ 16-1 16.1.2 Faradays Law ........................................................ 16-2 16.1.3 Lenz’s Law ............................................................. 16-2 16.1.4 Flemings Right Hand Rule ..................................... 16-3 16.2 SELF INDUCTANCE ................................................................. 16-3 16.3 MUTUAL INDUCTANCE ............................................................. 16-4 16.4 COUPLING FACTOR ................................................................ 16-5 16.5 ENERGY STORED IN MAGNETIC FIELD ....................................... 16-5 Issue 1 - 30 August 2001

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16.5.1 Spark suppression ................................................. 16-5 17 INDUCTORS ................................................................................. 17-1 17.1 CONSTRUCTION ..................................................................... 17-1 17.2 INDUCTOR SYMBOLS .............................................................. 17-2 18 INDUCTORS IN DC CIRCUITS .................................................... 18-1 18.1 INDUCTORS IN SERIES ............................................................ 18-1 18.2 INDUCTORS IN PARALLEL ........................................................ 18-1 18.3 INDUCTORS IN A DC CIRCUIT ................................................... 18-2 18.3.1 When dc current is applied..................................... 18-2 18.3.2 Time constant ........................................................ 18-3 18.3.3 The Effects of back emf on circuit current .............. 18-4 18.3.4 When dc current is removed .................................. 18-5 18.3.5 Safety ..................................................................... 18-6 19 CIRCUIT SYMBOLS ..................................................................... 19-1


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1

ATOMIC STRUCTURE

1.1

MATTER

Matter is defined as anything that occupies space and may be classified in a number 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 its container. Gas. A gas has definite mass but takes the volume and shape of its container. 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 chemical process 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 more elements 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 brought together 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 the atomic view of matter. This view gives us a better understanding of electrical and electronic 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 what happens 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. The resulting smaller and smaller droplets will soon become invisible to the naked eye, but it is known what happens if the process could be carried far enough; a point would eventually be reached where the particles of water are of such a size that further sub-division would split them into the hydrogen and oxygen of which they are composed. These last minute particles of water are known as molecules and are the smallest particles of water which can exist alone and still behave chemically as water. Every material is built-up from molecules and there are as many different molecules as there are different substances in existence. Molecules. The molecule of an element or compound is the smallest particle of it which can normally exist separately. It consists of one or more atoms, of the same or different types joined together. The term ‘molecular structure’ is used when compounds are discussed. 1.3

ATOMS

If a water molecule could be magnified sufficiently it would be seen to consist of three 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. Every element has atoms of its own type. There are 92 naturally occurring elements and therefore 92 types of naturally occurring atoms. Every molecule consists of atoms. Molecules of elements contain atoms of the same types, for example the hydrogen molecule consists of two atoms of hydrogen joined together, the oxygen molecule consists of t wo atoms of oxygen joined together, but the molecules of compound contain different atoms joined together. Most molecules contain more than one atom but some elements can exist as single atoms. In such a case the atom is also the molecule. For example the Helium atom is also the Helium molecule. An atom is the smallest indivisible particle of an element which can take part in a chemical change. The term ‘atomic structure’ is use when talking about elements.


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1.3.1 THE STRUCTURE OF AN ATOM

The Nucleus and Electrons. Atoms themselves are also composed of even smaller particles. Let us take an atom of hydrogen as an example. A hydrogen atom is very small indeed (about 10 –10 in diameter), but if it could be magnified sufficiently it would be ‘seen’ to consist of a core or nucleus with a particle called an electron travelling around it in an elliptical orbit. The nucleus has a positive charge of electricity and the electron an equal negative charge; thus the whole atom is electrically neutral and the electrical attraction keeps the electron circling the nucleus. Atoms of other elements have more than one electron travelling around the nucleus, the nucleus containing sufficient positive charges to balance the number of electrons. Protons and Neutrons. The particles in the nucleus carrying a positive charge are called protons. In addition to the protons the nucleus usually contains electrically neutral particles called neutrons. Neutrons have the same mass as 1 protons, whereas electrons are very much smaller – only of the mass of a 1836 proton 1.3.2 THE FUNDAMENTAL PARTICLES

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

1 unit of mass but it carries a unit 1836

negative charge. Thus, although we have 92 types of naturally occurring atoms, they are all builtup from different numbers of these three fundamental particles.


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

Molecules Hundreds of different kinds

Atoms 92 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 atomic number of copper is 29. 1.3.3.2

Neutrons

The neutron simply adds to the weight of the nucleus and hence the atom. There is no simple rule for determining the number of neutrons in any atom. In fact atoms of the same kind can contain different numbers of neutrons. For example chlorine may contain 18 – 20 neutrons in its nucleus. The atoms are chemically indistinguishable and are called isotopes. The weight of an atom is due to the protons and neutrons (the electrons are negligible in weight), thus the atomic weight is virtually equal to the sum of the protons and the neutrons. Issue 1 - 30 August 2001

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Electrons

The electron orbits define the size or volume occupied by the atom. The electrons 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 properties of the atom are determined by how tightly the electrons are bound by electrical attraction to the nucleus. 1.3.4 IONS

A neutral atom contains an equal number of positive charges (protons) and negative charges (electrons). It is possible for an atom to gain or loose an electron. An atom (or possibly a group of atoms) which loses an electron has lost one of its negative charges and is therefore left with an excess of one positive charge; it is called a positive ion. An atom that gains an electron has an excess of negative charge and is called a negative ion. 1.4

ELECTRICAL MATERIALS

Materials which allow an electric current to flow easily are known as conductors and those which prevent the flow of an appreciable current are known as insulators. Conductors and insulators are used in electrical circuits to provide paths for and to control the flow of, electric current. Practically all normal materials are either good conductors or good insulators. There are, however, a few materials which fall between these two categories and these are called semiconductors. Semiconductors will be studied in detail when we begin the electronics phase of the course. The best electrical conductor is silver, but for most purposes its high cost is prohibitive so copper is the standard conductor material. Aluminium is an alternative, but it is not such a good conductor. Brass, which is harder than copper, is commonly used for terminals, switches etc. Tungsten and nickel are used in the construction of lamps and thermionic valves.


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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 energy shells or levels. The potential energy (energy of position) increases with distance out from the nucleus. The outermost occupied energy level is called the valence shell. This is a higher energy level than the energy levels of electrons in the other shells since the electrons are rotating further from the nucleus. The electrons in the valence shell can most easily pass from one atom to another and thus constitute an electric current. Furthermore, the valence electrons are the 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 valence electron may acquire sufficient energy to jump through a forbidden (energy) gap and on into the conductor band where it is free of any influence of the positive nucleus and becomes a carrier of electricity, ready to take the place of another electron that has just left its own atom, in the same manner.


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1.4.2 IONISATION

If the amount of external energy is large enough the valence electron can gain sufficient kinetic energy (energy of movement) to be removed completely from its atomic orbit and may not be replaced by another accelerated electron. This process is known as ionisation, since an atom which now contains one more proton than can be neutralised by the remaining electrons is a positive ion. Gasfilled devices such as Neon tubes make use of this process. In a solid where atoms are close together, simple ionisation does not occur as with individual items. 1.4.3 ENERGY LEVELS

The energy levels, measured in electron volts (e.v.) in which orbiting electrons exist comply with a law of physics which states that energy can be given to electrons only in discrete amounts (quanta) which means that there are energy values that an electron cannot acquire. From this it can be deducted that there is a 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 and the bottom of the conduction band determine the electrical conducting properties of materials. 1.4.4 CONDUCTORS

Elements with 1 or 2 electrons in their outer orbits readily transfer them from atom to 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 conduction bands because the forbidden gap is to large. Sulphur and rubber elements are insulators. 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 are semi-conductors.


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engineering 2


STATIC ELECTRICITY

If electrons are removed from one material and placed on another, or if they are moved from one region of a piece of material to another, we have a separation of charge. The material, or area, that receives the electrons becomes negatively charged and the material or region that loses electrons becomes positively charged. 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 you touch 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 moved from one material to the other. This type of static charging between two or more dissimilar materials is known as triboelectric charging and is a very important factor in the design of aircraft and aircraft f urnishings and equipment. The nature and size of the charge produced depends on the materials, some loose or gain electrons more easily than others. The Triboelectric series on the next page list materials in the order in which they gain or loose electrons. The list is arranged such that, if any two materials are selected and rubbed together the one 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 become negatively 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, the electrons are not free to move through the material. The charge therefore remains at the point of friction. If a conductor is charged through rubbing, the electrons are free to move and the charge will dissipate unless the conducting material is insulated from its surroundings. If two statically charged items are brought into contact with one another, electrons will transfer from the more negative to the more positive one. This movement of electrons 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 electric field, the electric field is analogous to a magnetic field, which will be studied later in the course. The electric field is represented in magnitude and direction by electric lines of force. The density or magnitude of the force may be represented by the number of lines, and the direction is indicated by arrows that point f rom positive to negative. Isolated positive and negative charges


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Triboelectric Series Air Human Skin Asbestos Rabbit Fur Glass Mica Human Hair Nylon Wool Fur Lead Silk Aluminium Paper Cotton Steel Wood Amber Sealing Wax Hard Rubber Nickel, Copper Brass, Silver Gold, Platinum Sulphur Acetate Rayon Polyester Celluloid Orion Saran Polyurethane Polyethylene Polypropylene PVC (vinyl) Kelf (ctfe) Silicon Teflon Issue 1 - 30 August 2001

Increasingly Positive

Increasingly Negative

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engineering 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 charged bodies are brought together there is a force of repulsion. However, if a positively charged body is brought close to a negatively charged body, they attract each other. 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 charge called a Coulomb, has been chosen: One Coulomb =

2.3

6.29 x 1018 electrons

STATIC ELECTRICITY & AIRCRAFT

As mentioned earlier, the effects of static electricity are of considerable importance in the design of aircraft and aircraft equipment. An aircraft in flight picks up static charges as it flies through rain, cloud, snow, dust and other particles in the atmosphere. This build-up of statics is referred to as precipitation static. The amount of charge that builds up in any particular part of the aircraft depends on the atmospheric conditions to which it is subjected, and the material of which it is made. If two adjacent pieces of material are able to build up charges at different rates, a potential difference will exist between them. Eventually the potential difference will be sufficient to break down the insulation and current will jump as a spark between the 2 materials. This spark creates numerous problems; it damages the materials, it causes corrosion, it radiates radio frequencies that interfere with radio and navigation equipment and it could ignite fuel or oil vapour. In order to prevent this happening, it is essential that all of the aircraft structure and equipment is interconnected or bonded. Bonding allows small currents to continuously flow between materials and equipment, thereby preventing the build up of large static charges.


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An aircraft often accumulates very high electric charges, not only from precipitation but also from the high velocity gases exiting the engine exhausts. When the charge is sufficiently large, it will start to dissipate into the surrounding atmosphere from any sharp or pointed parts of the aircraft, such as the trailing edges of aerofoil sections. The point at which this occurs is called the corona threshold. The corona discharge produces severe radio interference and needs to be controlled. This is achieved using special devices called wicks, that allow the charge to dissipate in a controlled manner from specific points on the aircraft so that it causes minimum interference. The subject of static electricity can be considered amusing or annoying when one suffers from its effects. However, it must be taken very seriously by aircraft maintenance engineers. The following are a few points to consider.

• It essential to maintain the integrity of bonding when carrying out any maintenance work on aircraft.

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

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

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

• When an aircraft is inside a hangar for maintenance it should be correctly grounded.


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MODULE 3 (part A)

engineering 3


ELECTRICAL TERMINOLOGY

3.1 VOLTAGE Voltage is the electrical equivalent of mechanical potential. If a person drops a rock from the first storey of a building, the velocity it will reach when dropped will be fairly small. However, if the rock is dropped from the twentieth floor, it will have reached a much greater velocity on reaching the ground. On the twentieth floor the rock had much more potential energy. The potential energy of an electrical supply is given by its voltage. The greater the voltage of a supply source, the greater its potential to produce a current f low. Thus, a 115 volt supply has 115 times the potential to produce a current flow than a 1 volt supply. 3.1.1 POTENTIAL

If one coulomb of electrons is added to a body and one joule of work has been done, then the body will acquire of potential of – 1 volt. If the electrons had been removed, then the body would have acquired a potential of +1 volt. The unit of potential is the volt. 3.1.2 POTENTIAL DIFFERENCE

When charges move from one point to another, it is not the actual values of potential 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 gym floor and the height of one’s body. In cases where an actual level of potential is required, the zero of potential is taken as Earth and whenever the potential at a point is given, it means the difference in potential between the point and the earth’s surface. If one coulomb of electricity requires one joule of work to move it between two points, then there is a potential difference of 1 volt between them. It is sometimes helpful 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 between any two points in that circuit and each point in the circuit must be at a different potential. However because there is very little opposition to current flow in conducting wires, very little potential difference is required to push the current along the wires and it is normally assumed to be zero. Whenever the opposition to current flow is not negligible, then a potential different exists across that component to push the electrons through the device.


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The converse is also true, if no current is flowing, then no potential difference exists. The larger the potential difference the larger the current. 3.1.3 ELECTROMOTIVE FORCE – EMF

To make use of electricity by provision of an electric current, the potential different must be maintained. That is, the positive and negative charge must be continuously replenished. A cell (or battery) uses chemical energy to maintain the potential difference. Another device used for this purpose is the generator, which uses electromechanical energy to maintain the potential difference. The potential difference across the terminals of the source (cell, battery or generator) when it is not supplying current, is called Electromotive Force (emf), since this is a measure of the force available to push electrons around the circuit. In a circuit with a current flowing, the potential difference across the terminals of the source is always less than 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 current is 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 a conductor, it should be noted that more exactly, any movement of electric charge constitutes an electric current. Thus, passage of electricity may occur through a:

• conductor such as metal, due to the movement of the loosely held outer electrons 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 acids and 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 ampere is flowing in a conductor, one coulomb of charge passes any point in the conductor 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 Q or I = Seconds 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 (λ). Resistance is directly proportional to length, thus if the length is doubled (other factors remaining constant), resistance is doubled.

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

• Temperature. Temperature affects the number of free electrons and hence resistance. 3.3.2 UNITS OF RESISTANCE

Resistance is measured in ohms, symbol Ω (omega). The resistance of a piece of material is one ohm if a potential difference of one volt applied across it causes a 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 ρλ/a

= σ×

a

λ

The conductivity of a material is the reciprocal of its resistivity. It is given the Greek symbol σ (sigma) and has the units siemens per metre (s/m). Thus at 0°C copper has a conductivity of;

σ =

1

ρ

=

1 1 ⋅ 55 × 10 -8

= 64 ⋅ 52 × 10 6 s/m

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


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PRODUCTION OF ELECTRICITY

Very large amounts of electrical energy lie dormant in the atoms of every speck of material 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 of external energy that will separate the electrons from their nuclei. In this way, the external energy that is applied will give rise to electrical energy. There are six sources of external energy that are capable of separating the electrons from their nuclei, these are friction, pressure, magnetism, heat, light and chemical action. 4.1

BY FRICTION

Static electricity, that is the separation and build-up of charge is an everyday phenomenon that is often caused by friction – the physical stripping of electrons from one body and depositing on another. Early examples in science were the rubbing of a glass rod (which loses electrons and gains a positive charge) with a silk stocking! (gains electrons, receives negative charge) and the rubbing of an ebonite rod (receives negative charge) with cats f ur (becomes positively charged). Everyday examples are:

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

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

• The receiving of ‘electric shock’ from cars (also aircraft) when touching them on the outside. Here the charge has been produced by the friction of air passing around the vehicle.

• The rapid collection of dust by records. The dust is attracted by the charge built 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, static electricity is generated by friction as the aircraft moves through the air and will therefore be considered at various points throughout the course. 4.2

BY PRESSURE

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


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This effect is used in a number of devices including semi-conductor strain gauges and vibration sensors. As the mechanical pressure on the crystal is altered, a varying voltage which is related to the pressure is produced by the crystal. The voltage can be as small as a fraction of a volt or as large as several thousand volts depending on the crystal material and the pressure. Aircraft systems employing the piezoelectric effect generally only produce very small emf’s, the very high voltages produced by materials such as lead zirconate titanate are used in 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 manner which will be studied in great detail later in the course, large amounts of electrical energy are produced by machines called generators. Energy is used to drive the generator, which when it turns, makes use of the properties of magnetism to produce the external energy necessary to break the electrons away from their nuclei and so make it possible for electric current to flow. 4.4

BY HEAT

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

If two metals, say copper and iron, are joined at t wo points as shown in the diagram 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 the circuit, that is to say, current flows.


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engineering


The magnitude of the voltage produced by this method is small – only a few millivolts per degree centigrade – but it is sufficient to be measured. The current flow is a measure of the difference in temperature between the ‘hot’ junction and the ‘cold’ junction. Each junction is known as a thermocouple and if a number of thermocouples are connected in series so that alternate junctions are ‘hot’ and the other junctions are ‘cold’, the total emf is increased; this arrangement is known as a thermopile. On aircraft, thermocouples are used for temperature measurement and will be examined in more detail at a later date. 4.5

BY LIGHT

The Photovoltaic Cell or Solar Cell. A photovoltaic cell generates an emf when light falls onto it. Several forms of photovoltaic cell exist, one of the earliest types being the selenium photovoltaic cell in which a layer of selenium is deposited on iron and any light falling on the selenium produces an emf between the selenium and 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 ptype and the other is n-type. The most efficient photovoltaic cells incorporate semi-conductor p-n junctions in which one of the regions is a very thin layer (about 1µm thick) through which light can pass without significant loss of energy. When the light reaches the junction of the two regions it causes electrons and holes 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 when semi-conductor materials and devices are studied. 4.6

BY CHEMICAL ACTION

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


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CELLS & BATTERIES

To study electrical principles further we require a source of emf. Although an emf can be produced by any of the six methods discussed above, large amounts of useable power can only be produced chemically or by generation. Generation requires a more in depth study of magnetism and therefore cells and batteries will be studied first. On an aircraft, the battery may be used for engine starting, but f ar more importantly, the battery is the source of emergency power when the generator fails. Although aircraft battery systems and servicing will be studied at a later date, battery principles and battery construction will be studied now and will not be 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 a principle 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 the polarity of the terminals, a long thin line is used to represent the positive terminal and a short thick line the negative terminal. Sometimes the terminal voltage is indicated.

5.1.2 CONSTRUCTION & CHEMICAL ACTION

In cells, an electrolyte separates two charge collecting materials called electrodes, to which external connections are made. The electrolyte pushes electrons onto one of the plates and takes them off the other. This action results in an excess of electrons, or a negative charge, on one plate and a loss of electrons, or a positive charge, on the other plate. Electrolytes are chemical solutions manufactured to allow the generation and free movement of both types of ions, and are normally acid or alkaline pastes or liquids.


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The action of the electrolyte in carrying electrons from one plate to the other is actually a chemical reaction between the electrolyte and the two plates. This action changes chemical energy into electrical charges on the cell plates and terminals. With nothing connected to the cell terminals, the electrons would be pushed onto the negative plate until there was no more room. At the same time the electrolyte would take electrons from the positive plate to make up for those it had pushed onto the negative plate. Both plates would then be fully charged and the movement 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 the wire to the positive terminal. The electrolyte would carry more electrons across from the positive plate to the negative plate. Whilst the electrolyte is carrying electrons you would see the negative plate being used up and you would see bubbles 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 dissolved the negative plate into the electrolyte, at which point the cell would be exhausted and of no further use. In a secondary cell, the chemical action that takes place whilst the cell is producing 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 entails passing a current through the cell in the opposite direction to the discharge current. 5.1.4 CELL EMF

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

• internal resistance of the cell. • size of the discharge current. • charge state of the cell.


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• The size of the discharge current. As a general rule, whenever a cell is providing current, the terminal voltage will be less than the cell emf. The larger the discharge current, the greater the difference between the cell emf and its terminal voltage.

• The internal voltage of the cell. All sources of electricity have internal resistance which affects the terminal voltage, this will be examined in more detail 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 its useful 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 the current the lower the capacity, therefore capacity is normally quoted at a standard rate. The 1hr rate is the internationally accepted standard for Nickel Cadmium cells, 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 10 hours. A battery quoted at 40A-h at the 1 hr rate will provide 40 Amps continuously for 1 hour. A 40 A-h cell will only be able to provide a discharge current of 80 amps for approximately 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 than the expected 2 hrs. The capacity of a cell is also affected by its age, the older a cell, the lower its capacity, 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 order to form a battery. When cells are connected to form a battery t hey should be of similar construction, and have the same terminal voltage, internal resistance and capacity. 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.


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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 aircraft battery would consist of 12 cells connected in series. The active material in the positive plates is Lead Peroxide (Pb0 2) 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 solid block, often referred to as a Varley type battery. In the conventional battery the plates consist of lead grids into which the active materials are pressed. The positive and negative plates are then interleaved and connected to a lug that forms both a mechanical support and the terminal. Cells are generally constructed with an additional negative plate, making both outside plates negative. This ensures that chemical action takes place on both sides of each positive plate. When chemical action only takes place on one side of a positive plate it tends to buckle.


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The plate arrangement is then inserted into a composite material container which is fitted with a lid. The inside of the container is ribbed to provide additional support for the plates, which are raised clear of the bottom of the container to prevent shorting by any sediment that forms. To provide further support for the plates and to ensure they cannot touch, separators are fitted, these were originally cedar wood but modern batteries use micro-porous plastic materials. Each cell is fitted with a special non spill valve that allows gasses to escape, but prevents the spillage of electrolyte, this valve can be removed for checking and adjusting the electrolyte level. The electrolyte used is sulphuric acid diluted with pure distilled water, the specific gravity of the electrolyte used is determined by the manufacturer, however, it is generally lower than 1300. 5.2.2 SOLID BLOCK TYPE CONSTRUCTION

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

The plates are completely supported and therefore a more porous active material paste can be used, this gives better absorption and an enhanced electrochemical activity. 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 for the plates. All of these advantage result in a battery that is stronger, less susceptible to vibration damage and has a higher capacity to weight ratio than its conventional counterpart.


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5.2.3 CHEMICAL ACTION

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

The H2 ions go to the positive plate and combine with the oxygen of the lead peroxide (PbO2) forming water (H2O), during the process they take electrons from the 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 an excess of electrons on the negative plate. When a circuit is connected to the battery, electrons flow from the negative plate to the positive plate. This process will continue until both plates are coated with lead sulphate. The lead sulphate is highly resistive, and it is mainly the formation of the lead sulphate which gradually lowers the battery capacity until it is discharged. During charging, current is passed through the battery in a reverse direction. The SO4 ions are driven back into solution in the electrolyte, where they combine with the H2 ions of the water, thus forming sulphuric acid. The plates are thus returned to their original compositions. The sulphuric acid is effectively used up as the battery is discharged, and returned to the electrolyte as it is charged, a test of the specific gravity of the electrolyte will give a good indication of the state of charge of the battery.


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engineering 5.2.3.1


A simple overview of the charge and discharge characteristics

During discharge the plates are converted into lead sulphate, the water content of the electrolyte increases, the internal resistance of the cell increases and the terminal voltage decreases. By passing a current through the battery in the opposite direction these effects are reversed. The plates are converted back to their original form, the water content of the electrolyte decreases, the internal resistance decreases and the terminal voltage increases. The process of recharging takes approximately 8 t o 10 hours. During most of the charge and discharge cycle the battery terminal voltage remains constant at 1.95V, it therefore gives no indication as to the battery’s state of charge. The specific gravity of the electrolyte however changes at a regular rate as the battery is charged, or discharged and can therefore be used to determine the battery’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 and appears as random greyish white patches. Sulphation causes an increase in the internal resistance of the battery, leading to possible overheating and buckling of the plates. Sulphation is caused by continually undercharging the battery or by discharging below 1.8 Volts or 1150 SG and is severe there is no cure, however if mild it can sometimes be cured by giving the battery a long low charge.


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Buckling is twisting and bending of the plates. Because the active material is squeezed out of the plates the capacity of the battery may be reduced, if severe it can lead to internal shorting of the battery. Buckling is caused by excessive charge and discharge currents being imposed on 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 t he bottom 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 steel screen with nickel carbonyl powder. The resultant plaques are then impregnated with the active materials, Nickel salts on the positive, cadmium salts on the negative. The plaques are then placed in electrolyte and subjected to a small current to convert them to their final form. After washing and drying the plaques are cut into plates, each one having a nickel 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 its container, which is sealed and pressure tested. The separator used is normally a triple layer type, one layer of cellophane, two of woven nylon cloth. Cellophane is used because it has a low resistance and is a good barrier material, it prevents metal particles from shorting the plates whilst allowing current to flow. The cellophane also acts as a gas barrier, preventing oxygen given off by the positive plate during overcharge, from passing to the negative plates. At the negative plates the oxygen combines with the cadmium, reducing the cell voltage and producing heat.


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

In a typical Ni-Cad battery the cells are mounted in a m etal case that incorporates 2 venting outlets, carrying handles, a quick release connector and a lid. Each cell is separated from its neighbour by its moulded plastic case and electrically connected by nickel plated steel links between the terminals. 5.3.2 CHEMICAL ACTION

As the battery discharges, hydroxide ions (OH) from the electrolyte combine with the cadmium in the negative plates and release electrons to the plate. The cadmium is converted to cadmium hydroxide during the process. At the same time, hydroxide ions from the nickel hydroxide positive plates go into the electrolyte carrying extra electrons with them. Thus electrons are removed from the positive plate and delivered to the negative plate during discharge. The composition of the electrolyte remains a solution of potassium hydroxide because hydroxide ions are added to the electrolyte as quickly as they are removed. For this reason the specific gravity of the electrolyte remains essentially constant at any state of charge. It is therefore impossible to use the specific gravity as an indication of the charge state of the battery. When the battery is charged, the hydroxide ions are caused to leave the negative plate and enter the electrolyte. Thus the cadmium hydroxide of the negative plate is converted back to metallic cadmium. Hydroxide ions from the electrolyte recombine with the nickel hydroxide of the positive plates, and the active material is brought to a higher state of oxidation. This process continues until all the active material of the plates have been converted. If charging is continued, the battery will be in overcharge, and the water in the electrolyte will be decomposed by electrolysis. Hydrogen will be released at the negative plates and oxygen at the positive plates. This combination of gases is highly explosive.


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A simple overview of the charge and discharge characteristics

During charging and discharging the electrolyte acts only as an ionised conductor, transporting electrons from one plate to the other, its specific gravity remaining constant. On discharge the terminal voltage initially falls rapidly and then remains constant for most of the discharge cycle, dropping rapidly again when the battery is nearly fully discharged. When charged, the terminal voltage initially rises rapidly and then settles to a gradual increase. A second rapid rise takes place as the battery reaches the fully charged condition, at this time gassing takes place, hydrogen being released at the negative plates, oxygen at the positive plates, this combination of gases is explosive. Prolonged gassing should be avoided as it reduces the water content of the electrolyte and causes overheating of the battery, a slight amount of gassing, however, is necessary to ensure charging is complete. The terminal voltage remains constant for most of the batteries life and the specific gravity of the electrolyte remains unchanged, the only way of determining the state of charge of the battery therefore, is t o carry out a full charge followed by a capacity test. During discharge the plates absorb electrolyte to such an extent that the level may disappear from view. As the battery is charged, the electrolyte is forced back out 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 without causing 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 a battery.

• They are more susceptible to thermal runaway.


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5.3.4 THERMAL RUNAWAY

The battery looses heat by conduction and radiation. Provided the rate of heat loss is greater than the rate at which heat is generated there is no problem. Should the battery not be able to loose heat so quickly it will start to get hot. As its temperature goes up the internal resistance decreases and the current increases. This increase in current leads to an increase in chemical activity within the battery, this generates more heat and the cycle repeats. Nickel Cadmium batteries are very susceptible to thermal runaway which can result 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 as their primary counterparts. They are small, portable and maintenance free, but have the added advantage of being rechargeable. The plates are constructed in a similar manner to the larger Ni-Cad cells, the separator being a thin porous material. The electrolyte is fully absorbed by the plates and separator in a similar manner to the Varley type cell. With steel or plastic being used for the case. Special vents are fitted to each cell, these allow the escape of gas but prevent the entry of oxygen and electrolyte leakage. The nominal voltage of a fully charged cell is 1⋅25 volts and these can then be interconnected to form batteries. A 10 hour rate capacity is generally used with an end of life voltage of 1.1 volts, it is possible to discharge the cells further but damage will occur if allowed to go below 1 volt. Charging should be carried out using a constant current at the 10 hour rate, total charge taking approximately 14 hrs, the end of charge “on charge” voltage being 1⋅45 volts. Overcharging should be avoided, it produces heat and shortens the long term life of the cell.


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engineering 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 ratio

V I

= Constant

and this ratio is called the resistance of the conductor. Hence we may write V = R I

6.1

where V is in volts I is in amperes R is in ohms

TRANSPOSITION OF OHM’S LAW

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

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

I=V R

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

V = IR

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


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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 two is directly observed. You may check this against the equations in the above subchapter. This is not necessary if you are able to remember one form of the equation and derive the other two directly by transposition.


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ELECTRICAL MEASURING INSTRUMENTS

Quantities of electrical current, voltage and resistance are measured using instruments called meters. Until the advent of electronic displays and semiconductor components, meters comprised a movement, working on the motor principle, driving a needle across a scale. These types of meters were called 'moving coil meters' or 'analogue meters'. Moving coil meters will be studied in some depth later in the course, because the principle behind their operation is the same as the principle employed in many aircraft instruments. Modern meters are referred to as a 'digital meters' or 'digital voltmeters', more commonly abbreviated to DVM's, although they measure far more than just voltage. Digital meters are cheaper, more reliable, more robust and generally considered more accurate than their analogue counterparts, although some would 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 are instances where a digital meter cannot be used, leaving no choice but to revert to an analogue meter. 7.1

CONNECTING METERS TO A CIRCUIT

Irrespective of whether the meter is digital or analogue, the way that it is connected 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 between which the potential difference is required.

If the potential at A with respect to B is required, the red lead is connected to point A, the black lead point B. If the potential at B with respect to A is required, the red lead is connected to point B, the black lead point A. If the potential between a point and Earth or ground is required. The red lead is connected to the point and the black lead is connected to ground or Earth.


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7.1.2 AMMETERS

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

To connect an ammeter, the power must be switched off . The circuit is broken 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 red lead and out of the black lead. Once the meter is connected, circuit power is restored 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 when measuring resistance the circuit power must be switched off , power is derived from within the instrument. Secondly, great care must be taken to ensure there are no parallel paths that would affect the measurement. This is generally best confirmed by removing the component or device, or by disconnecting one end of it from the circuit concerned. Thirdly, it is essential that an analogue meter is zeroed before it is used. used. To measure resistance, the meter is simply connected across the component or device to be measured. The polarity of the leads is not important unless semiconductor type devices are present. (this will be discussed in a later module).


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When making resistance measurement, care must be taken to ensure the correct range is used. It is easy to mistake a low resistance value for a zero reading or short circuit. 7.2

ANALOGUE MULTIMETERS

Even the most basic analogue multimeter can prove to be invaluable when in the hands of an experienced experienced user. Simple measurements measurements of voltage, current and resistance can provide provide useful information on the state of almost any any circuit. What matters, of course, is the interpretation put on the the readings obtained. obtained. To get the best from such a simple instruments it is not only necessary to select an appropriate measurement function and range, but also to be aware of the limitation of the instrument and the effect that it might, or might not, have on the circuit under investigation. The diagram below shows the controls and display provided by a simple analogue multimeter.

The range selector allows you to select from a total of t wenty ranges and six measurement functions. These functions are: 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 MEASUREMENTS

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

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


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

7.2.2 DC CURRENT MEASUREMENTS

An example of how to make a DC current measurement is shown in the diagram below. Once again, the red and black test leads connected to the '+' and '-' sockets respectively. The range selector is set to DC, 50mA. The pointer is reading just less than midway between 45 and 50 on the range that has 50 as its full-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 high current range (e.g. 10A) is not only selected using the range selector switch but a separate input connection must also be made. The reason for this is simply that the 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 DC measurement 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 is reading midway between 8 and 10 on the range that has 10 as its full-scale indication. The actual reading indicated is thus 9A.


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7.2.4 AC VOLTAGE MEASUREMENTS

An example of how to make AC voltage measurements is shown in the diagram below. 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 is reading 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 diagrams below. In all three cases, the red and black test leads are connected to the '+' and '-' sockets respectively. Before making any measurements it is absolutely essential to zero the meter. This is achieved by shorting the test leads together and adjusting the 'zero adj' control until the meters reads full-scale (i.e., zero on the ohms scale).


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

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


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In the third diagram, the range selector is set t o OHM, × 1k. The pointer is reading exactly 5k and the resistance indicated is 5k × 1k or 5MΩ.

7.2.6 CONTINUITY TESTING

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


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7.2.7 BATTERY TESTING

Several analogue multimeters provide a battery testing facility. The diagram below 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 of the battery terminal voltage and ideally such a measurement should be carried out with the battery on-load (i.e. supplying current to a load resistance within the meter). The range selector is set to BAT, 9V. The indication on the meter shows that 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 function before attempting to connect the meter into a circuit.

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

• Do select a higher range than expected and then progressively increase the sensitivity 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 attempting to transport the meter.

• Do check and, if necessary, replace the internal batteries regularly. • Do use properly insulated test leads and prods. Issue 1 - 30 August 2001

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

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

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

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


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DIGITAL MULTIMETERS

Digital multimeters offer a number of significant advantages when compared with their more humble analogue counterparts. The display fitted to a digital multimeter usually consists of a 3½ digit seven-segment display - the '½' simply indicates that the first digit is either blank (zero) or 1. Consequently, the maximum indication on the 2V range will be 1.999V and this shows that the instrument is capable of offering a resolution of 1mV on the 2V range. The resolution obtained from a comparable analogue meter would be of the order of 50mV, or so, and thus the digital instrument provides a resolution which is many times greater than its analogue counterpart. The controls and display provided by a simple digital multimeter are shown in the diagram below. The mode switch and range selector allows you to select from a 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)


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7.3.1 DC VOLTAGE MEASUREMENTS

An example of how to make DC voltage measurements is shown to the left. The red and black test leads are connected to the 'VΩ' and 'COM' sockets respectively. The mode switch and range selector is set to DC, 200V and the display indicates a reading of 124.5V.

7.3.2 DC CURRENT MEASUREMENTS

An example of how to make a DC current measurement is shown to the right. Here, the red and black test leads are connected to the 'mA' and 'COM' sockets respectively. The mode switch and range selectors are set to DC, 200mA, and the display indicates a reading of 85.9mA.


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7.3.3 HIGH CURRENT MEASUREMENTS

In common with simple analogue multimeters, the meter used a shunt which is directly connected to a separate 10A terminal. The diagram shows the connections, mode switch and range selector settings to permit high-current DC measurements. The mode switch and range selectors are set to DC, 2000mA (2A), and the red and black test leads are connected to '10A' and 'COM' respectively. The display indicates a reading of 2.99A.

7.3.4 AC VOLTAGE MEASUREMENTS

An example of how to make a AC voltage measurement is shown to the left. Once again, the red and black test leads are connected to the 'V-Ω' and 'COM' sockets respectively. The mode switch and range selectors are set to AC, 2V, and the display indicates a reading of 1.736V.


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7.3.5 RESISTANCE MEASUREMENTS

The diagram shows an example of how to make resistance measurements. As before, the red and black test leads are connected to the 'V-Ω' and 'COM' sockets respectively. The mode switch and range selectors are set to OHM,200Ω, and the meter indicated a reading of 55.8Ω. Note that it is not necessary to 'zero' the meter by shorting the test probes together before taking any measurements (as would be the case with an analogue instrument).

7.3.6 CAPACITOR MEASUREMENTS

Many modern digital multimeters incorporate a capacitance measuring facility although this may be limited to just one or two ranges. The diagram below shows how to carry out a capacitance measurement. The capacitor on test is inserted into the twoway connector marked 'CAP' whilst the mode switch and range selector controls are set to DC, 200pF. The display indication shown corresponds to a capacitance of 329pF.


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7.3.7 CONTINUITY TESTING

An example of how to make continuity (buzzer) tests is shown in the diagram below. The mode switch and range selectors are set to DC, buzzer (note that this is indicated by means of an icon on the front panel of the instrument) and the red and black test leads are connected to the 'V-Ω' and 'COM' sockets as usual. When there is a low-resistance path between the two test probes, an audible buzz will be produced. No meter indication is produced (instead, the meter displays 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 function before attempting to connect the meter into a circuit.

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

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

• Do switch the meter to the 'off' position in order to conserve battery life when the 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.


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• Do check that a suitably rated fuse is used in conjunction with the current ranges.

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

• Don't rely on voltage and current readings made on circuits where high frequency signals may be present (as with analogue instruments, digital meters may produce readings that are wildly inaccurate or misleading in such circumstances).

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


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engineering 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: Rα

λ (length) A (cross sectional area)

R = Constant ×

R=

ρλ A

λ A

Ohms

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 A symbol ρ (Rho) and is measured in ohm meters (check this from ρ = R ) and

λ

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 ρ at 0°C are:

8.2

• Silver

1.5 x 10-8 Ω - m

• Copper

1.6 x 10-8 Ω - m

• Manganin

41 x 10-8 Ω - m

• Carbon

7000 x 10-8 Ω - m

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.


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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 given by; R =

Rt - Ro Ro

this resistance change has been brought about by a temperature change t equal to t -to (to being 0º). Hence the change in resistance, caused by a 1ºC change in temperature is; R Rt - Ro Rt - Ro = = because t = 1 and to = 0 T Rot Ro (t - to) 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 temperature change. and may be represented graphically as shown below. The graph is reasonably linear for many materials over a moderate temperature range (0º - 200ºC). The units are ºC because the ohms cancel out in the calculation. Materials whose resistance increases with increasing temperature have a positive temperature co-efficient of resistance. Materials whose resistance decreases with increasing temperature have a negative temperature co-efficient of resistance. Some materials have very small temperature co-efficients of resistance and are used where it is important that the resistance does not change with temperature. Examples are Manganin and Eureka.


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8.4 RESISTORS The electrical component used to introduce resistance into a circuit is called a resistor. Resistors can be fixed or variable. Symbols used in circuit diagrams are shown below:

Resistor Type

Old Symbol

New Symbol

Fixed resistor Fixed resistor with fixed tapping point Variable resistor Resistor with pre-set adjustment Voltage divider (potentiometer) Pre-set potentiometer

The physical size of a resistor does not give any clue to the resistance value of the component. This value must be marked on individual components. Two codes are currently used to indicate resistor values: a Colour Code and a Letter and Digit Code. 8.4.1 FIXED RESISTORS

Fixed resistors may be:

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

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


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8.4.2 COLOUR CODES

The current method of colour code marking of resistors is the Band System. Close to one end of the resistor are four coloured bands (there may appear to be only three, in this case the forth band is ‘no colour’ – see diagram below). They are known as bands 1 – 4. Bands 1 and 2 give the first two numbers of the resistor value, band 3 gives the multiplication factor, i.e. the number of zeros, the fourth band gives the tolerance, which indicates how close the actual value may be to the stated value. Colour

First band (or body) First figure

Second band (or tip) Second figure

Third band (or spot) Multiply by

Fourth band Tolerance

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 temperature changes. These are called ‘high stability’ resistors and this is shown by a fifth band coloured ‘pink’.


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

Red is 2

Second band

Yellow is 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 wider than 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 resistance depends on the tolerance of the resistors being used. An example of resistor Preferred 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 value cover the complete range; eg.

2.2KΩ + 10% = 1.98KΩ to 2.42KΩ 2.7KΩ + 10% = 2.43KΩ to 2.97KΩ


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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, MΩ) and the tolerance as shown below. Multiplying Factor

Tolerance %

X1

R (resistor)

Ω

0.1

B

5

J

X103

K

KΩ

0.25

C

10

K

X106

M

MΩ

0.5

D

20

M

X109

G

GΩ

1.0

F

30

N

X101

T

TΩ

2

G

2

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

470R

is

470Ω

4K7

is

4·7KΩ

R47

is

0·47Ω

4R7

is

4·7Ω

The tolerance letter is added on the end. eg.

1M5 B

is

1·5MΩ + 0.1%

2K2 N

is

2·2KΩ + 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 at which 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 the more current it can carry.


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8.4.6 POTENTIOMETERS

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

8.4.7 RHEOSTATS

Variable resistors can be made to vary either current or voltage. A variable resistor arranged to control current is called a ‘Rheostat’ and controls the current by 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 them does not vary linearly as the applied voltage is varied. These elements are known as non-linear resistors or non-linear conductors. Transistors, diodes and voltage dependent resistors all fall into this group. The current through a voltage dependent resistor increases at a progressively rapid rate as the voltage across it increases, such a device is used for protecting circuits against voltage surges or as a voltage stabiliser. 8.5 THERMISTORS Insulators and semi-conductors behave in a different way when the temperature increases, because their resistivity decreases. That is: the resistance of an insulator and of a semi-conductor decreases with temperature increase, (their resistance-temperature coefficient is negative!). This feature can be used to advantage as the following example shows.


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One example of this effect occurs in a thermistor, which is a t hermally sensitive resistor whose resistance alters with temperature; a negative temperature coefficient (n.t.c.) thermistor is one whose resistance reduces with increase in temperature. A thermistor is used in the cooling-water temperature-measuring circuit of a car or lorry; it is inserted in the cooling water and connected in series with the battery and temperature gauge. As the water temperature rises, the resistance of the n.t.c. thermistor falls and allows more current to f low through the temperature gauge; this causes the gauge to indicate variations in water temperature.


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RESISTORS IN DC CIRCUITS

9.1

RESISTORS IN SERIES

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

When a current flows through a resistor (or a component having resistance) there is a potential difference between its ends. Thus where two or more resistors are connected in series the potential difference between the extreme ends is the sum of the individual potential differences.

Hence E = V1 + V2 + V3 But from Ohm’s Law V = IR Therefore E = IRTOTAL So

V1 = IR1

Thus IRTOTAL

V2 = IR2

V3 = IR3

= IR1 + IR2 + IR3 = I (R1 + R2 + R3)

So RTOTAL

= R1 + R2 + R3


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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 the circuit 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 potential rise 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


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9.1.2 VOLTAGE DIVISION

In a series circuit Ohm’s law applies for each component. However, since the current is common to all components we have: 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 of the resistance values. It should also be noted, that for any given applied voltage we may derive any smaller voltages we wish by inserting resistors of the appropriate values in series. The following example shows how voltages of 8V, 4V and 24V can be derived from a 36V supply. RTOTAL = 12 + 6 + 36 = 54Ω

∴ 54Ω ≡ 36V and 1Ω ≡ 36/54V ∴ 12Ω = 36/54 × 12 = 8V across AB and 6Ω = 36/54 × 6 = 4V across BC and 36Ω = 36/54 × 36 = 24V across CD 9.1.3 THE POTENTIAL DIVIDER

A device which employs voltage division and which is commonly used in electrical and electronic circuits is the potential divider. Here two or more resistors are used to divide a given input voltage to achieve a specified output voltage. See diagram. The potential divider is also known as a voltage divider or scaling circuit. Note that if current is drawn from the output then the effective resistance of the circuit changes and the output voltage v OUT changes.


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9.1.4 VOLTAGES RELATIVE TO EARTH

It is very common in electrical circuits to have an earth connection. This earth connection has no effect on potential differences across components, however it does 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. Potential differences between earth and the negative terminal of the supply result in negative voltages and potential differences between earth and the positive terminal result in positive voltages. It should be noted that due to static build up on the airframe, the earth connection (airframe) of an airborne aircraft is unlikely to be at zero potential with respect to the ground

You should also note that earth connections, for example to the chassis of an equipment or the airframe of an aircraft, are often used as the current return lead in an electrical circuit. 9.2

INTERNAL RESISTANCE

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

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


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• Generators. Internal resistance is mainly the resistance of the wires which form the internal windings.

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

• When the source forces electrons around a closed circuit they must pass through the internal resistance of the source, thus causing a drop in voltage within the source itself, i.e. the source has to do work to push current through itself. This loss of potential or ‘voltage drop’ may be referred to as lost volts, since they are not available in the external circuit, thus the terminal voltage is less than the emf by the value of the lost volts when current 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 the external circuit is open, no current flows and the terminal voltage is equal to t he emf. OPEN CIRCUIT

TERMINAL VOLTAGE = EMF

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


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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.

V1 = V2 = V3 = V

and

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

From Ohm’s law

= I =

V

=

Therefore and

R TOTAL 1

R TOTAL

=

V R V1 V 2 + R1 R2

1 1 + R1 R2

+

+

V3 R3

=

V V + R1 R2

+

V R3

1 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 the equivalent resistance 1 and therefore needs inverting to find RTOTAL. RTOTAL


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

1 1 1 1 + + R1 R2 R3

=

+ ......

1 Rn

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 R TOTAL

Therefore

R TOTAL

=

1 1 + R1 R2

=

=

R1 × R2 R1 + R2

=

R2 + R1 R1× R2

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 R TOTAL Therefore

=

1 R

RTOTAL =

+

1 R

+

1 R

+

1 R

=

4 R

R 4

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. R TOTAL

=

R The total number of resistors connected in parallel


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9.3.3 EFFECTIVE VALUE OF RESISTORS IN PARALLEL

If a second resistor is connected in parallel with a first, the voltage across the second is equal to the voltage across the first. The first resistor still draws the same current and the second now also draws current. Thus the total current drawn from the supply has increased and therefore the effective resistance (RTOTAL) has decreased. Since the supply of current is now greater than either individually would draw, the effective resistance of the two is less than the resistance of either individually. This is generally true and for any number of parallel resistors the effective resistor (RTOTAL) is less than the value of any single resistor in the parallel combination. An important point to note here is that the supply current has increased and unless the supply wiring can cope with it, it may be 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 resistance provided that the voltage remains constant. In a parallel network the voltage across each component is the same, therefore the current through each component is inversely proportional to its resistance. Simply stated, this means that 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 currents flowing towards the junction is equal to the sum of the currents flowing away from it. 10A

2A

9A 7A

8A

• Current flowing towards junction = 2 + 7 + 9 = 18A • Current flowing away from junction = 10 + 8 = 18A


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RESISTORS IN SERIES / PARALLEL COMBINATIONS

In the previous units we have used Ohm’s law to solve combinations of resistors in series or in parallel. It is possible to solve combinations of resistors in both serial and parallel by Ohm’s law provided sufficient information is given. However in 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 physical appearances can be deceptive. When components are mounted they are usually done so in a manner as to reduce the space they occupy to a minimum. Care must be taken to decide whether they are mounted in series or parallel or in a combination 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 of resistors 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 known or be capable of determination. Where resistors appear in both series and parallel they may be reduced to a single effective resistance using a step-by-step sequence as follows.

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


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• Replace any simple parallel groups by single equivalent resistors 1 R

=

1 R1

+

1 R2

+----

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

• Replace any simple parallel groups.


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• Determine the single equivalent resistance.

At this point the total circuit current (Is) may be found if Vs is given, or Vs found if Is is given. Having determined Vs or Is, as appropriate, the current in any branch and the voltage drop across any resistor can be found by working backwards through the sequence in the first paragraph of this section, applying Ohm’s law at each stage. 9.5

THE EFFECTS OF OPEN CIRCUITS

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


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In a circuit with parallel paths, an open circuit path will cause an increase in the circuit resistance and a reduction in the circuit current. The change in current flow will 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 is generally considered to have a low resistance. If a short circuit is placed across a resistor, the current will flow through the short circuit rather than through the resistor. Short circuits across series or parallel connected resistors will result in a decrease in the circuit resistance and an increase in the current drawn from the supply. Short circuits may result in the fuse blowing, the circuit breaker tripping or the circuit burning out if no protection devices are fitted. If the definition of a short circuit is taken to be 'an unwanted current path', then high 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 parallel resistors called a Wheatstone Bridge. 10.1 CONSTRUCTION The Wheatstone Bridge circuit and other similar variants were widely used in test equipment to determine the value of an unknown resistor by comparison with other resistors whose values are accurately known.

The normal arrangement in a W heatstone bridge used for resistance measurement is for two resistors, usually R1 and R2, to be fixed and of known value and R4 to be an accurate variable resistor adjusted by means of a calibrated dial. The resistor R3 is then the unknown whose value is to be measured. 10.2 CALCULATING UNKNOWN RESISTANCES The current through the galvanometer (G) – a very sensitive ammeter, is reduced to zero by adjusting R4. The bridge is then said to be balanced. When the bridge is balanced, the voltage at A is equal to the voltage at B and no current flows between A and B. Hence

VR1

=

VR2

therefore I1 × R1

=

I2 × R2 ------------- (1) (by Ohm’s law)

Also

=

VR4

=

I2 × R4 ------------- (2)

VR3

therefore I1 × R3


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Dividing (1) by (2)

R2

=

R1 × R 4 R3

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 is required 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 unknown resistor, it is far easier to use an Ohmmeter. The Wheatstone bridge is however extremely useful for measuring and displaying remote indications. On aircraft, Wheatstone bridge circuits are used for the measurement and display of temperatures, pressures, positions and quantities. In each case, the item being measured varies the value of resistor R3, causing a voltage imbalance that produces a current flow through the galvanometer. The amount of current through the galvanometer, and the amount of pointer deflection depend upon the potential difference across the bridge, which in turn depends upon the change in resistance of R3. The galvanometer can therefore be calibrated to give the appropriate 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 two points which are at different electrical potentials.

• The SI unit of work is the ‘joule’. One joule of work is done when a charge of one coulomb moves through a potential difference of one volt. Electrical Work (joule) = Charge (coulomb)

× Potential Difference (volt)

× V joules

Work = Q

• 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 equal to the work done. The units of energy and work are the same, that is joules and the same equation is used for both. Energy = Work = VIt joules The energy a body contains may be determined by calculating the electrical work done on the body to give it that energy. Conversely, the work that a body could do if it used up all its energy may be determined by calculating how much energy it 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 other form. This is stated in the Law of Conservation of Energy - energy can neither be 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 of conversion of energy by an electrical system.

∴ Power (watts) = Work done (joules) Time taken seconds

= VIt t

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

× I

Therefore

P = V

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 watts R 11.4 POWER RATINGS Electrical equipment can only stand a certain amount of heat production without damage and the safe power which a piece of equipment can consume without damage is its ‘power rating’ or ‘wattage rating’. Each component is given a wattage 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 a given time; a 100w lamp gives more light than a 60w lamp. The rating 6V 12W on a lamp means that if is connected to a 6V supply, its resistance is such that it develops 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 is increased more power is developed and the component may be damaged.

• A fluorescent tube of 12W rating produces more light than a 12W filament bulb because the tube produces much less heat and is therefore more efficient.


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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 we must always keep below the stated value. To keep below the stated power value, there are maximum permissible values of voltage and current, which may be calculated as follows: Maximum Current P = I2R

= Therefore I =

P R

and this is the maximum current to avoid damage to the resistor.

Maximum Voltage P = V2 R Therefore V = resistor.

√P × √R and this is the maximum voltage to avoid damage to the

11.4.2 SIZE AND POWER RATING

The surface area and therefore the size of a component determines the rate at which heat is dissipated from the component to its surroundings. Generally therefore the larger a component, the higher its power rating. Carbon resistors of the same resistance value are commonly available in ratings between ¼W and 2W. When higher wattage is required wire-wound resistors may 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 of power as a Watt second. The joule however is a very small unit and it is therefore of ten more convenient to measure energy used in kilowatt hours where: 1kWh

=

1000 watt hours

=

1000 × 3600 watt seconds or joules

=

3 600 000 J


or

3.6 MJ

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11.5 MAXIMUM POWER TRANSFER Every source of EMF has internal resistance. If it is required to develop the maximum possible amount of power in an external load, then the load resistance must be equal in value to the internal resistance of the source. This may be shown by calculating the power developed in RLoad for different values of RLoad.

This illustrates that maximum power is developed in the load when RLoad equals RInternal. Matching is very important in electronic circuits which usually have a fairly high source resistance. A typical example is the ‘matching’ of a loudspeaker to an audio amplifier. Note however that:

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

• Batteries, generators and other power supply systems are not operated under maximum power transfer conditions, since to do so would result in the same amount of power being dissipated in the source as was supplied to the load, which is wasteful of energy. Thus power systems are designed to have 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 electric flux. The ease with which this change takes place is a measure of the capacitance of the circuit. In d.c. circuits, capacitance is only effective when the voltage is switched on and off, but in a.c. circuits where the voltage varies continuously, the effect of capacitance is continuous. A device used specifically to introduce capacitance into a circuit is known as a capacitor (sometimes called a condenser). 12.1 CHARGING A BODY A conductor is given a positive charge when electrons are forcibly removed from the 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 negative charge. The use of force means that energy has been expended by the source of d.c. and this energy is stored in an electric field. An electric field is represented by lines of flux whose direction is the direction of force which would be experienced by a free positive charge placed in the field. Lines of electric flux behave in an analogous manner to lines of magnetic flux. As the charge on a body increases, it repels further charge with greater force until eventually the repelling force equals the charging force and the conductor is fully charged. The charge on a fully charged body may be changed by changing the voltage supplying the charging force, but the conductor will oppose this charge due to the charge it already possesses. Any conductor will hold a charge, the magnitude of the charge depends upon the magnitude of the voltage applied, but for a single conductor, even a large voltage produces 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 or dielectric (which could be air) and we apply a voltage across them, electrons are removed from one plate and applied to the other and each becomes charged. The charge held by the combination may be very large because of the concentration of the electric field between the plates. This represents a basic capacitor.

Thus, a capacitor is a device which opposes voltage change in a circuit through its capacity to store electrical energy (or charge) in the form of an electric field.

12.3 CAPACITANCE If we increase the voltage between the plates, the charge increases, but the ratio of charge to voltage remains the same. This ratio gives the capacitance (C) of the capacitor. Charge = A constant called capacitance Voltage When the charge (Q) is in coulombs and the voltage (V) in volts, then the capacitance (C) is in farads (F). C=

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

A capacitor has a capacitance of one Farad when a charging current of one ampere, flowing for one second, causes a change of voltage of one volt between its plates. The Farad is a huge unit and smaller units are used in practice. 1 microfarad (µF) = 10-6 farad 1 picofarad (pF) = 10-12 farad


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12.4 FACTORS AFFECTING CAPACITANCE The factors which affect the capacitance of a parallel-plate capacitor are:

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

• Distance between the plates (d). The capacitance increases as the distance between the plates decreases, since the electric f ield then becomes more concentrated.

• Material between the plates. This introduces a constant called the absolute permittivity (ε). The constant ε is actually the product of two constants, the permittivity of space (εo) which has a value of 8·85 x 10-12 Fm-1 and the relative permittivity (εr ), which is basically a multiplication factor (no units) that indicates how many more times the material is able to concentrate the electric flux compared with space. For example, if waxed paper is inserted between the plates instead of air, the ability to concentrate a flux (the permittivity) is multiplied by approximately 3, therefore the relative permittivity (εr ) of waxed paper is approximately 3. We may summarise this in equation form as: C=

ε A 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 (ε) – farads per metre (Fm-1). In the case of multi-plate capacitors, capacitance is calculated using the formula: C=

(n - 1) ε A d

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


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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

12.6 CAPACITOR CONSTRUCTION 12.6.1 FIXED CAPACITORS

Fixed capacitors usually consist of sheets of metal foil between which is sandwiched the dielectric, or alternatively the m etal, such as aluminium, is deposited onto both sides of the dielectric. The characteristics and quality of the capacitor depends mainly on the dielectric, which may be paper, chemically impregnated paper, plastics mica or ceramic. 12.6.2 VARIABLE CAPACITORS

Variable capacitors are usually meter plates with air as the dielectric. The variation 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 formed directly on the metal plates. High values of capacitance can be achieved here with small physical size. Most electrolytic capacitors must be connected into circuit with the correct polarity or damage (possibly including explosion) may result. 12.6.4 SAFE WORKING VOLTAGE

The safe working voltage is the maximum d.c. voltage that can safely be applied to a capacitor without causing the dielectric to break down. When breakdown occurs, the electric field is strong enough to ‘tear’ electrons free from their orbits. A current then flows with the production of a large amount of heat. The dielectric is commonly burned through rendering the capacitor unserviceable. Issue 1 - 30 August 2001

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Higher voltage require thicker dielectrics, but this reduces capacitance. Thus, a given value of capacitance requires a larger capacitor (greater plate area ‘a’) for greater 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 be made 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 the negative terminal of the cell to the right hand plate of C3, and one electron moves from the left hand plate of C1 to the positive terminal of the cell, one electron will move between C1 and C2 and between C2 and C3. Thus, the total charge moved is one electron and the charge on each capacitor is one electron. Thus: QTOTAL

= Q1 = Q2 = Q3

but

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

V

also V Therefore

Hence

= Q C Q = CTOTAL

Q + Q + Q C1 C2 C3

1 = 1 + 1 + 1 C C1 C2 C3

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


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13.2 CAPACITORS IN PARALLEL

Three capacitors are connected in parallel. If on closing the switch S a current I flows 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 = C V

Therefore C = C1 + C2 + C3 Thus, we may replace capacitors in parallel by a single capacitor whose value is given 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 process of finding the total capacitance is basically the same as that used to find the total resistance of a resistor network. It must of course be noted, that the f ormulae used for capacitors in series and parallel are different from those used for resistors connected the same way. Where capacitors appear in both series and parallel, they may be reduced to a single 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 the reverse sense) and so preventing further current flow. However, in any real circuit, 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 and shown as a single value R.

With S1 closed and S2 open, the capacitor will charge up. Note that Kirchhoff’s second law always applies, 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: IINIT

=

VR R

=

E I

• As C charges, the potential difference across it (VC) increases, opposing the applied 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 and

dVc dt

dI are progressively decreasing as time increases. dt

13.4.2 TIME CONSTANT

It is found that the time taken to charge up the capacitor depends on the product of capacitance and resistance. This product is called the ‘time constant’ of the circuit 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

= Iinitial × TC (but Iinitial =

Therefore CE/ Hence

=

E ) R

so

CE =

E × TC R

/ E × TC R

Time Constant TC = CR

13.4.3 DISCHARGING A CAPACITOR

On opening S1 and closing S2 (after the capacitor is fully charged), the capacitor discharges, 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 CR seconds and takes 5CR seconds to fall to zero (0.368 is sometimes taken as 1/3 in 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. circuit containing a capacitor (until the capacitor is fully charged), the current is eventually reduced to zero. Thus, a capacitor inserted in a d.c. circuit prevents current 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 leaving the other plate. 2. Alternating current always appears to pass through a capacitor. The degree of opposition to a.c. current flow is determined by a variety of factors which will be studied later in a.c. circuits. The study of capacitors in a.c. circuits will also 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 capacitor were to go open circuit then it would be unable to charge and there would be absolutely no current flow. If this occurred in a parallel combination, the total capacitance of the circuit would decrease, in a series combination the capacitors would be ineffective because of the lack of current flow. When a capacitor is short circuited it is unable to charge, if one capacitor in a parallel combination is short circuited it will prevent the other paralleled capacitors from 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 detail as there uses in various circuits are studied. 13.6 SAFETY & TESTING A charged capacitor can store a large amount of energy which it releases on discharge. It is therefore important to ensure that capacitors, especially large ones, are discharged before you attempt to touch them. Particular care is required when servicing faulty high voltage equipment. A capacitor can be tested using an ohmmeter. When connected across a capacitor, the ohmmeter's battery charges the capacitor. The charging of the capacitor is indicated by a changing value of resistance, from zero to infinity as the capacitor charges. If the charging process is too quick to see, a resistor can be 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 in order 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 circuit can 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 the output (across C). If Cr<>T, the circuit is an integrating circuit, since the output waveform is that of the integral of the square wave, that is the area underneath it. This is shown in the lower diagram. If the positions of the resistor and capacitor are reversed and the voltage across the 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 is applied to the input. Shown in the top diagram. If CR<

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


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14 MAGNETISM Everyone has seen and handled a magnet in the form of a straight or horseshoeshaped bar of steel or steel-alloy. The magnet was originally a piece of steel before it was magnetised. A material called magnetite is a naturally occurring magnet (also called lodestone) which was used at sea for primitive navigation. A magnet is easily recognised by its ability to attract pieces or iron and steel; and if suspended freely on a piece of string, will swing to align with the earth’s own magnetic field. 14.1 MAGNETIC THEORIES 14.1.1 MOLECULAR THEORY

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

• All materials contain molecules with magnetic properties. • In unmagnetised substances, these molecules are arranged in a random manner and no external magnetic effect is produced.

• When the material is being magnetised, we are aligning the molecules. The number aligned increases, as we further magnetise the specimen and when all are aligned no further increase in magnetisation is possible and the specimen is said to be magnetically saturated.

• In theory all substances could be magnetised, but in practice it is impossible to align the molecules of most substances. 14.1.2 DOMAIN THEORY

In domain theory it is assumed that magnetic materials are composed of tiny individual magnets called domains, a single domain is very small - about 1012 atoms. Considering each atom - orbital electrons not only orbit the nucleus but spin axially on their own axis. In non magnetic materials the same number of electrons spin clockwise as anti-clockwise. In magnetic materials more electrons spin one way than the other way The unbalanced spin creates twists called magnetic moments. Issue 1 - 30 August 2001

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In unmagnetised state the moments of the electrons are in the same direction in a single domain, but the domains produce random pockets of magnetism. As the magnetic material becomes magnetised the domains become partially aligned. 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 appear to be concentrated are called the magnetic poles.

The pole (when freely suspended) which points towards t he earth’s geographic north pole is called the North Seeking Pole ‘N’ (or north pole for short) and that which points to the south geographic pole, the South Seeking Pole ‘S’ (or south pole). It is observed that two north poles repel each other and likewise with two south poles; however a north pole and a south pole will attract each other. This is summarised 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 observe repulsion. Attraction simply means that the specimen is magnetic but it may not be 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 ‘magnetic field’. The magnetic field is three-dimensional and it may be shown visually by drawing imaginary lines called ‘lines of magnetic flux’.


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14.2.3 LINES OF FLUX

A line of flux is a line indicating the direction in which a free north pole would travel, if placed in the field at that point. Alternatively it is the direction in which the north pole of a compass needle would point. The direction which would be taken is indicated on the lines of flux by arrow heads. Therefore lines of flux emanate from north poles and re-enter at south poles, see diagram below.

14.2.3.1

Properties of Lines of Flux

To make the imaginary lines of flux describe the behaviour of the magnetic field we must give them appropriate properties. Thus lines of flux have the following properties:

• 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 magnet from the south to north).

• They never cross each other (a compass placed at a given point can only point 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 the pattern shown in the diagram below. If the Earth were completely symmetrical, the north and south magnetic poles would coincide with the axis of the Earth. The magnetic poles are, in fact, separated from the true poles by about 1000 Miles, the north magnetic pole being in the area 70 - 75 degrees North and roughly 95 degrees West. Since the North pole of a magnet is really a North seeking pole and similarly the South pole is really a South seeking pole it follows that at the Earth's North pole there must be a south seeking magnet and similarly at the Earth's South pole there must be a North seeking magnet. Unfortunately before the significance of the Earth's magnetism was realised, navigators had dropped the word "seeking" leaving the embarrassing statement that there is a magnetic south pole at the North pole and a magnetic North pole at the South pole. This problem is overcome by defining the North seeking pole as the Red Pole and 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 m agnetic properties. This group can be further subdivided into hard and soft magnetic materials. Above certain temperatures ferromagnetic materials behave as paramagnetic materials.


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Hard Iron

Hard magnetic materials are more difficult to magnetise but retain most of their magnetism 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 of the 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 PARAMAGNETIC MATERIALS MATERIALS

Most materials fall into this group. These materials can only be magnetised with a great amount of effort, usually resulting in their destruction. If magnetised the material only exhibits small magnetic properties. Examples – Wood / Glass /Air / Water / Aluminium 14.4.3 DIAMAGNETIC DIAMAGNETIC MATERIALS MATERIALS

This is a small group of materials that actually oppose a magnetising force. If placed in a magnetic field they will decreases its strength. If suspended in a magnetic field, they will swing to adopt a position at 90 degrees to the lines of flux. 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 is determined 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 a permanent magnet or magnets. Backward and forward movement of the steel should be avoided and magnets should follow the assumed lines of force when stroking the steel. Issue 1 - 30 August 2001

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Magnets with same polarity at either end can be produced using the double stroke 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 have consequent poles.

14.5.2 INDUCTION

The property of magnetism may be induced in a piece of material that does not normally have that characteristic. If a piece of soft iron is placed in the magnetic field of a permanent magnet, the soft iron will assume the properties of a magnet and become magnetised. This action is called magnetic induction. It occurs because the lines of flux tend to flow through 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 up with the lines of force, their north poles pointing in the direction in which the lines of force are travelling through the iron. The end at which the lines of flux enter the soft 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 will concentrate the lines of flux f lux and become magnetised. Issue 1 - 30 August 2001

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14.5.3 USE OF ELECTRICAL ELECTRICAL CURRENT CURRENT

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

Oersted found that a wire carrying an electric current produces a magnetic field around the wire for as long as current continues continues to flow. The direction of the magnetic field depends depends upon the direction direction of the current. The field is symmetrical symmetrical around the wire and is represented by lines of flux drawn as concentric circles around the wire. By convention current flowing into a diagram is represented by a cross, current flowing out of the diagram by a dot. One can liken this t o the view obtained from a dart 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 the magnetic field using Maxwell’s Corkscrew rule, usually abbreviated to the Corkscrew Rule (or sometimes the right hand screw rule).


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The Corkscrew Rule states; if a corkscrew is turned so that it moves in the direction 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 in the same direction, the wires experience a force of attraction. If the currents flow in opposite directions, the wires experience a force of repulsion, see diagram below. The force between two such conductors forms the basis for the definition of the unit of current - the ampere.


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15 ELECTROMAGNETISM

If a straight wire carrying a current is formed into a circular loop, the magnetic field is as shown. The field may be deduced by taking elements of the loop and looking at the field around each part of the loop. 15.1 PRODUCTION OF A BAR MAGNET If a length of wire is bent into a series of loops, it forms a solenoid. The direction of the magnetic field around any small part of it can be obtained by using the corkscrew rule. If the fields for a series of such loops are combined, the result will 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 conventional current flow. We can find out which end of the coil is acting as the north pole and which 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 a coil. The coil is gripped by the right hand with the f ingers pointing along the conductors in the direction of conventional current flow, when the thumb is then extended, 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 an electromotive force. In the same way, in a magnetic circuit, a flux is established due to the existence of a magnetomotive force. The mmf is produced by the current flowing in the coil and its value is the product of the current and the number 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 in amperes. 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 given the symbol H. The magnetising force is a measure of the intensity of the magnetic effects at any given point in the magnetic field. Magnetising Force (H) =


Magnetomotive Force Length of magnet

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

• The length of a solenoid ‘l’, is the length along its axis and not the length of wire from which the solenoid is made. It will therefore be seen that a solenoid having 10 turns per metre carrying a current of 6A (10 × 6 = 60 ampere/metre) will produce the same strength of magnetic field as one of 12 turns per metre carrying 5A (12 × 5 = 60 ampere/metre). 15.2.3 FLUX & FLUX DENSITY

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

Φ A

Teslas

The unit of flux density is actually Webers per m2, so: 1 Tesla =

1 Weber m2

15.2.4 PERMEABILITY

When an mmf produces a magnetising force H, a certain flux density B is established. Ratio

B is termed 'the permeability of the material'. H

Permeability is an indication of the ability of the flux to permeate the material. If the material in which the flux is established is a vacuum, or f ree space, then the ratio is called ‘the permeability of free space' and given the symbol µo. This value 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 flux density will increase. The number of times by which the flux density increases is called the ‘relative permeability of the material’ denoted by the symbol µr . This is not a constant but varies with different material. i.e. steel = 800. Issue 1 - 30 August 2001

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The product of µo and µr is called the ‘absolute permeability’ and is denoted by the symbol µ. For all materials

B = H

µ = µo x µr

15.2.5 RELUCTANCE

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

mmf = I.N and H =

and

mmf = H × length (2)

using equations (1) and (2) above B = H

Therefore

(from flux density B = ) A

IN length

therefore H x length = IN

But

Φ

Φ = B × A Webers (1)

Φ mmf

=

BxA H x length

µo x µr Φ mmf

=

A

µo x µr x length

And reluctance (S) =

mmf

Φ

The units of reluctance are

=

length µo x µr x A

Ampere Turns Weber

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.


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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.

S TOTAL

=

S1 × S 2 S1 + S 2

For more than two parallel paths:

1 S TOTAL

=

1 S1

+

1 S2

+

1 1 ..... + S3 Sn

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 only be obtained using a piece of material that has never been magnetised before. Once the material has been magnetised and the curve obtained, the production of 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 it is found that the magnetic property of different specimens of the same material vary considerably. The fact that permeability varies for a given material may also be seen from the shape of the curve, if the permeability was a constant, the graph of B against H would be a straight line. 15.4 HYSTERESIS LOOP A ferromagnetic material retains some magnetism after the magnetising force is removed. The BH curve (O to Q) will therefore only be followed once, on initial magnetisation. When a material is subjected to a changing magnetising force, the flux density is affected by its previous magnetic history. There is tendency for the magnetic conditions to lag behind the magnetising force that is producing them. This is known 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 and demagnetising the graph of B against H is as shown, this diagram is called a hysteresis loop.

O to Q - Initial magnetisation to saturation at point A Q to R - Magnetising force is reduced to zero. O to R or 0 to U

Represents remanence. Remanence is the flux density remaining in the material after the magnetising force is removed. It is sometimes called ‘retentivity’. If the material had not been taken to saturation then OR or OU would represent the remanent flux density.

R to S -

The magnetising force is reversed.

O to S or

Represents the magnetising force required to reduce the flux density to 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 the material to reach saturation in the opposite direction.

T to Q -

Reversal of magnetising force again eventually makes the material saturate in original direction.

The term residual magnetism is used to describe the useful flux remaining after the magnetising force has been removed for a considerable time. It is proportional to the coercivity of the material and is also called coercivity. This term should not be confused with remanence or remanent flux density. The area of the loop represents the energy loss during each magnetic cycle, or the power dissipated. It’s size is dependent upon the type of material and frequency 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 soft iron. 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 their relationships. 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

Reluctance

Ampere 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 magnetic screening. Air had high reluctance whilst soft iron has a low reluctance. Thus if the equipment to be screened is surrounded by soft iron, most of the flux will pass through the soft iron, rather than the air inside it, since lines of flux take the path of least reluctance.


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16 INDUCTION In 1831, a scientist called Michael Faraday discovered that an electric current was produced by the relative movement of a magnet and a coil, a phenomenon which 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 a meter, 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 is moved. 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). Note that energy is not being produced but simply converted from mechanical energy to 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 deflection obtained on the meter. This shows that the magnitude of the emf is proportional to the rate of relative movement.

• Repeating the experiment using a stronger magnet results in greater meter deflection for the same rates of movement. Hence the magnitude of the emf is proportional to the flux density.

• Reversal of the direction of motion produces meter deflecting in the opposite sense. The direction of the induced emf therefore depends on the direction of motion.

• Using the south pole of the magnet instead of the north results in meter deflections in the opposite sense, showing that the direction of the induced emf depends upon the direction of the magnetic field. Issue 1 - 30 August 2001

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• If more turns are used on the coil, meter deflection is greater and is proportional to the number of turns (N). 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. dΦ = change of flux dΦ α E Hence, where dt = time taken to change dt 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

αN

dΦ volts dt

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

= -N

dΦ volts dt

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


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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, in the manner of the coil and magnet experiment. Once again, lines of flux are being cut by a conductor and if the wire forms part of a closed circuit, a current will flow. The same effect is observed if the wire is stationary and the magnetic field moves. The direction of the induced emf may be determined by Fleming’s Right Hand Rule. The thumb, first finger and second finger of the right hand are held at right angles to 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 f ield (N to S). • Then the seCond finger points in the direction of conventional current flow and thus indicates the direction of the induced voltage. 16.2 SELF INDUCTANCE When current through a coil changes, the changing flux induces an emf that opposes 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

dI dt

Where L is the inductance in henries, and

dI the rate of change of current. dt

The minus indicates back emf.


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The unit of inductance is the henry and is based on the equation. If current changing at a rate of 1 amp a second induces an emf of 1 volt then the inductance is 1 henry. All circuits have inductance even a straight conductor, but if a straight piece of wire is formed into a coil the number of flux linkages increases and so does the inductance. A further increase in inductance is achieved by increasing the flux density. This depends on the area, the length of the coil and the permeability of material in which flux is established, Thus,

L N

N2 µo µr A = Henries l

= Number of Turns

µo µr = Absolute Permeability A

= Area in square metres

I

= Length of coil in metres (not wire)

length As reluctance (S) = µo x µr x A Also by transposition of E = -L × L = -E ×

l µo µr A = S

and

N2 L = S

dl dt

dt dl

16.3 MUTUAL INDUCTANCE If the changing flux in a coil links with the turns of a second coil, the two coils are said to be mutually coupled and mutual inductance exists between them. The unit of mutual inductance is Henry and is defined by: If the primary current, changing at a rate of 1 amp per second, induces a secondary voltage of 1v, then the mutual inductance is 1 henry. Thus:

Es = M ×

dlprimary dt


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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 = k L1 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 t he energy used in the circuit must go into the magnetic field. It can be shown that the 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 flowing through it in amps. 16.5.1 SPARK SUPPRESSION

If we consider a circuit with a large inductance, possibly one using a magnetic relay. At the instant the switch is opened, the current through the coil is changing at 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 electrical resistance and radiates energy which may cause interference, therefore sparks must be suppressed. Good design of switch contacts can help, but connecting a capacitor in parallel with the switch is the best method of eliminating sparking. When using a capacitor the energy released by the coil charges the capacitor instead of ionising air. When the switch is closed again the capacitor discharges.


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17 INDUCTORS Coils which are used for their opposition to current change in a circuit are known as inductors or chokes. 17.1 CONSTRUCTION Inductors with an air core have small inductance values and are used at high frequencies within radio tuning circuits, or as r.f. chokes to stop radio frequency currents taking certain paths in circuits. Coils for use at high frequency are made of 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. Iron increases the strength of the magnetic field several hundred times. Silicon steel and nickel iron are used at frequencies up to 20kHz. Iron cores are laminated. The laminations reduce the conversion of electrical energy to heat by making it difficult for currents in the coil to induce currents in the core. These induced currents are called ‘eddy currents’ because they flow in circles through the iron core. If the laminations are at right angles to the plane of the 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 a powder which has been coated with an insulator and pressed together. Ferrite cores consist of ferric oxide combined with other oxides such as nickel oxide and may also be used at high frequencies. Iron dust and ferrite cores increase the inductance of a coil considerably. For example, an air cored inductor of 1mH could be increased to 400mH by fitting a ferrite core. These cores also have a high resistance, thereby reducing eddy currents.


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17.2 INDUCTOR SYMBOLS Air Core:

old symbol

new symbol

Iron Core:

old symbol

new symbol

Iron Dust or Ferrite Core:

old symbol


new symbol

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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 more inductors may be connected in series. The total inductance then depends on the sum 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 self induced 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 the self 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 total inductance 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 coils located one inside the other. The outer coil (stator) is stationary whilst the inner coil (rotor) is capable of rotation through 180 degrees. The coils are mutually coupled and connected in series, in one position the rotor field aids the stator field, when the rotor is turned 180º the rotor field opposes the stator field. Then the 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: 1 1 1 1 = + + etc. LT L1 L2 L3 Issue 1 - 20 March 2001

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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  E  value I =  in zero time when the switch is closed.  R  In practice, there is no such thing as ‘pure’ resistance and it is normal t o find a circuit containing resistance resistance and inductance inductance in series. Also, there is no such such thing as pure inductance inductance since any any coil must have have some resistance. Therefore, the circuit to be considered will have inductance and resistance in series. An inductance opposes opposes any change in current by producing a back emf. 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 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 Kirchhoff’s second law applies.

By Kirchhoff’s second law E - Eb = VR (Eb = back emf) but

Eb = -L

and

VR = IR

hence

E = L

dl dt

dl - IR dt

Issue 1 - 20 March 2001

volts

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In the above equation, E, L and R are constant, therefore as I increases, dl (the slope of the graph graph at any point) point) must decrease. Dt The current therefore follows a curve whose gradient is continually decreasing and which is called an ‘exponential ‘exponential curve’.

18.3.2 TIME CONSTANT

It is impossible to decide exactly when the maximum point is reached on an exponential curve, curve, or when the curve has fallen to exactly zero. zero. To enable calculations to be performed a time constant is constant is used. The time constant gives an indication of the time taken for the current to rise to its maximum value or fall to zero. The time constant is defined as either:

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

• The time taken for the current to reach 0.632 of its maximum value (or 63.2%). The latter definition arises since it is found that after one time constant, the current has always always built up to 63.2% of its maximum value. value. The time constant constant for a series LR circuit is given by: Time Constant =

L seconds R

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


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Proof of Time Constant

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

E = L

dl + IR dt

Therefore E = L

But

dl and dt

dl E = dt L

dl at A is the slope of of the graph at A. dt

The slope of AB =

BC E = AC L

But if AC is the time constant and BC = E 1 × R Time Constant

Then

=

E R

E L

Therefore the Time Constant must equal

L R

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, because, at that instant in time the current in the coil 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 equal and opposite to the applied voltage. Therefore, with no potential difference across the circuit, no current can flow. This fact is quite simple to prove using the equation for the self induced emf in a coil and elements of t he ‘proof of time constant’ above: E = -L x

dI dt

The current starts from zero, zero, and would rise to its maximum value in 1 time constant if the initial rate of change could be maintained. The rate of change change of current is therefore therefore given by the gradient gradient of line AB. The BC IMAX - 0 gradient of AB = = . AC Time Constant


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VSupply , because when the current reaches its R maximum 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 across the resistor. IMAX can be calculated using

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 any change and tries to maintain the current flow. Instead the current decays exponentially to zero over a period of 5 time constants.

In the circuit shown, the resistor is kept in circuit, therefore the time constant calculated will be the same as when the switch was moved to position A. If a different 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 direction around the circuit, the polarity of the voltage across the inductor must be the reverse of what it was when the switch was moved to position A. ie +ve at the bottom 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 stored in the magnetic field. On short circuiting an inductor, the magnetic field collapses and the energy is returned to the circuit in t he form of an emf that tries to maintain the current flow. If the circuit is open-circuited rather than short-circuited by a resistor, as in the case of the circuit studied (moving the switch to B), then the collapsing flux will produce a large back-emf that may cause sparking across the switch contacts as they are opened. The sparks damage the contacts, produce heat, could ignite fuel vapour and transmit electromagnetic radiation which interferes with communication and navigation equipment. The large emf ’s can also cause electric shocks on what are considered safe, low voltage d.c. circuits.


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19 CIRCUIT SYMBOLS The following circuit symbols have been taken from a typical aircraft manual and are intended to be a small selection of what you will find being used in aircraft maintenance documentation. You will be expected to memorise common symbols, as without them you will be unable to negotiate the aircraft schematic diagrams and wiring diagram manuals. This applies irrespective of your intended trade. For manuals produced i.a.w. the ATA specification 100, a list of circuit symbols can be found in the WDM Chapter 20. For other aircraft no such list may exist and you will have to rely on memory.


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