mod 3 final

7/30/2019 mod 3 Final

1/212

EASA PART 66Course Notes

Faculty of Transport Engineering Technologies

School of Aeronautical Engineering

Electrical FundamentalsModule 3

7/30/2019 mod 3 Final

2/212

Amendment and Annual Review Record

AmendmentNo

Incorporatedby

Date AnnualReview

Completed by Date

2011

2012

2013

2014

2015

2016

2017

2018

20192020

2021

2022

2023

2024

2025

2026

2027

2028

20292030

2031

7/30/2019 mod 3 Final

3/212


2

3.1

ELECTRON THEORY __________________________________ 3

3.2 STATIC ELECTRICITY AND CONDUCTION _________________ 103.3 ELECTRICAL TERMINOLOGY___________________________ 113.4 GENERATION OF ELECTRICITY _________________________ 163.5 DC SOURCES OF ELECTRICITY _________________________ 203.6 DC CIRCUITS _______________________________________ 343.7 RESISTANCE AND RESISTORS _________________________ 383.8 POWER ___________________________________________ 623.9 CAPACITANCE AND CAPACITORS ______________________ 663.10 MAGNETISM ______________________________________ 803.11 INDUCTANCE AND INDUCTORS ________________________ 983.12 DC MOTOR AND GENERATOR THEORY _________________ 1123.13 AC THEORY _______________________________________ 1433.14 RESISTIVE, CAPACITIVE AND INDUCTIVE CIRCUITS _______ 1533.15 TRANSFORMERS __________________________________ 1773.16 Filters ___________________________________________ 1913.17 AC GENERATORS __________________________________ 1963.18 AC MOTORS ______________________________________ 204

7/30/2019 mod 3 Final

4/212


3

3.1 ELECTRON THEORY

Matter

Matter is defined as anything that occupies space andmay be classified in a number of ways.

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.

Chemical Classification

From a chemical view we again have three divisions:

Elements: An element is a substance which cannotby any known chemical process be splitinto two or more chemically simpler

substances. Eg: Hydrogen, Oxygen,Copper, Iron, Aluminium, carbon.

Compounds: A compound is a substance whichcontains two or moreelementschemically joined together. Eg: Water

Hydrogen and Oxygen, Salt (Sodiumand Chlorine), Sulphuric Acid(Hydrogen, Oxygen and Sulphur).

Mixtures: A mixture consists of elements or

compounds which are broughttogether by a physical process. Eg:

Salt and Sand, Earth and sawdust,Carbon and Iron Filings.

However, material may also be classified according tothe particles it contains; this is the atomic view ofmatter. This view gives us a better understanding of

electrical and electronic phenomena and is the view weshall concentrate upon.

7/30/2019 mod 3 Final

5/212


4

Molecules

Let us take a piece of matter, for example, a drop ofwater 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. Theresulting smaller and smaller droplets will soon become

invisible to the naked eye, but it is known what happensif the process could be carried far enough; a point would

eventually be reached where the particles of water areof such a size that further sub-division would split them

into the hydrogen and oxygen of which they arecomposed. These last minute particles of water areknown as molecules and are the smallest particles ofwater which can exist alone and still behave chemicallyas water. Every material is built-up from molecules andthere are as many different molecules as there are

different substances in existence.

Molecules: The molecule of an element or compound isthe smallest particle of it which can normally exist

separately. It consists of one or more atoms, of thesame or different types joined together.

Atoms: If a water molecule could be magnifiedsufficiently it would be seen to consist of three smaller

particles closely bound together. These three

particles are ATOMS, two of hydrogen and one ofoxygen.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 therefore92 types of naturally occurring atoms.

Every molecule consists of atoms. Molecules of

elements contain atoms of the same types, for examplethe hydrogen molecule consists of two atoms of

hydrogen joined together, the oxygen molecule consistsof two atoms of oxygen joined together, but themolecules of compound contain different atoms joined

together.

7/30/2019 mod 3 Final

6/212


5

Most molecules contain more than one atom but some

elements can exist as single atoms. In such a case theatom is also the molecule. For example the Heliumatom is also the Helium molecule.

An atom is the smallest indivisible particle of an elementwhich can take part in a chemical change.

The Structure of an Atom

The Nucleus and Electrons: Atoms themselves arealso composed of even smaller particles. Let us take an

atom of hydrogen as an example. A hydrogen atom isvery small indeed (about 10 10 in diameter), but if itcould be magnified sufficiently it would be seen toconsist of a core or nucleus with a particle called anelectron 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 atomis electrically neutral and the electrical attraction keepsthe electron circling the nucleus. Atoms of other

elements have more than one electron travelling aroundthe nucleus, the nucleus containing sufficient positivecharges to balance the number of electrons.

Protons and Neutrons: The particles in the nucleus

each carrying a positive charge are called protons. Inaddition to the protons the nucleus usually contains

electrically neutral particles called neutrons. Neutronshave the same mass as protons whereas electrons are

very much smaller only1

1836of the mass of a proton.

The Fundamental Particles

Although other atomic particles are known, the threefundamental ones are:

Protons: The proton has unit mass and carries a unitpositive charge.

Neutron: The neutron has unit mass but no electricalcharge.

7/30/2019 mod 3 Final

7/212


6

Electron: The electron has only

1

1836 unit of mass butit carries a unit negative charge. Thus although we have92 types of naturally occurring atoms, they are all built-up from different numbers of these three fundamental

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

below.

Particle function

Protons: The number of protons in an atom determinesthe kind of material:

E.g. Hydrogen 1 protonHelium 2 protons

Lithium 3 protonsBeryllium 4 protons

Copper 29 protonsUranium 92 protons

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

Neutrons: The neutron simply adds to the weight of thenucleus and hence the atom. There is no simple rule fordetermining the number of neutrons in any atom. In

fact atoms of the same kind can contain differentnumbers of neutrons. For example chlorine may contain

18 20 neutrons in its nucleus.

The atoms are chemically indistinguishable and arecalled isotopes. The weight of an atom is due to theprotons and neutrons (the electrons are negligible in

weight), thus the atomic weight is virtually equal to thesum of the protons and the neutrons.

7/30/2019 mod 3 Final

8/212


7

Electrons: The electron orbits define the size or volume

occupied by the atom. The electrons travel in orbitswhich are many times the diameter of the nucleus andhence the space occupied by an atom is virtually empty!

The electrical properties of the atom are determined byhow tightly the electrons are bound by electricalattraction to the nucleus.

Ions

A neutral atom contains an equal number of positive

charges (protons) and negative charges (electrons).Atoms however do not always exist in the neutral formand it is possible for atoms to gain and lose electrons.An atom (or possibly a group of atoms) which loses anelectron has lost one of its negative charges and istherefore left with an excess of one positive charge; it is

called a positive ion. An atom that gains an electron hasan excess of negative charge and is called a negative

ion.

Electrical materials

Materials which allow an electric current to flow easilyare known as conductors and those which prevent the

flow of an appreciable current are known as insulators.Conductors and insulators are used in electrical circuitsto provide paths for and to control the flow of, electric

current. Practically all normal materials are either goodconductors or good insulators. There are, however, a

few materials which fall between these two categoriesand these are called semiconductors. Semiconductors

will be studied in detail when we begin the electronicsphase of the course.The best electrical conductor is silver, but for mostpurposes its high cost is prohibitive so copper is thestandard conductor material. Aluminium is analternative, but it is not such a good conductor. Brass,

which is harder than copper, is commonly used forterminals, switches etc. Tungsten and nickel are used in

the construction of lamps and thermionic valves.

Electron distribution

The atoms of a solid have electrons rotating in orbits

around the positive nucleus. This is true of gases and

7/30/2019 mod 3 Final

9/212


8

liquids as well. These orbiting electrons exist in energy

shells or levels.To calculate the maximum No of electrons that can existin a shell the formula 2n2can be used, where 'n' is the

shell number.

The potential energy (energy of position) increases with

distance out from the nucleus. The outermost occupiedenergy level is called the valence shell. This is a higher

energy level than the energy levels of electrons in theother 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 electriccurrent. Furthermore, the valence electrons are theones that go into chemical reactions, or combinations,

with other atoms.

When an outside influence such as an electronic field or

addition of heat is applied a valence electron mayacquire sufficient energy to jump through a forbidden

(energy) gap and on into the conductor band where it isfree of any influence of the positive nucleus and

becomes a carrier of electricity, ready to take the placeof another electron that has just left its own atom, in thesame manner.

Ionisation

If the amount of external energy is large enough thevalence electron can gain sufficient kinetic energy

(energy of movement) to be removed completely fromits atomic orbit and may not be replaced by another

accelerated electron. This process is known asionisation, since an atom which now contains one moreproton than can be neutralised by the remaining

electrons is a positive ion. Gas-filled devices such asNeon tubes make use of this process. In a solid where

7/30/2019 mod 3 Final

10/212


9

atoms are close together, simple ionisation does not

occur as with individual items.

Energy levels

The energy levels, measured in electron volts in whichorbiting electrons exist comply with a law of physics

which states that energy can be given to electrons onlyin discrete amounts (quanta) which means that there

are energy values that an electron cannot acquire. Fromthis 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 topof the valence band and the bottom of the conductionband determine the electrical conducting properties ofmaterials.

Conductors

Elements with 1 or 2 electrons in their outer orbitsreadily transfer them from atom to atom, because there

is an overlap between the valence and conductionbands. Silver and copper elements are good conductors.

Insulators

Elements with 6 to 8 valence electrons cannot haveelectrons-in the conduction bands because the forbidden

gap is to large. Sulphur and rubber elements areinsulators.

Semi-conductors

The elements Germanium and Silicon have fourelectrons in their valence shells. In conductivity they lie

between good conductors and good insulators, ie; theyare semi-conductors.

7/30/2019 mod 3 Final

11/212


10

3.2 STATIC ELECTRICITY ANDCONDUCTION

If electrons are removed from one material and placedon another or if they are moved from one region of amaterial to another we have a separation of charge. Thematerial or area receiving electrons becomes negativelycharged and the material or region having lost electrons,

positively charged. If these accumulations of chargeremain stationary after their transfer then the build up

of charge is referred to as static electricity.

Fundamental Law of Electrostatics

It is observed that if negatively charged bodies aremade to approach each other there is a force of

repulsion between them and similarly with two positivelycharged bodies. If however a positively charged body is

brought close to a negatively charged body they attracteach other. Hence:

Like Charges Repel, Unlike Charges Attract.

Unit Of Charge

The charge on an electron is very small, therefore amore practical unit of charge called a Coulomb, has been

chosen:

One Coulomb = 6.29 x 1018electrons

7/30/2019 mod 3 Final

12/212


11

3.3 ELECTRICAL TERMINOLOGYVoltage

Voltage is the electrical equivalent of mechanicalpotential. If a person drops a rock from the first storeyof a building, the velocity it will reach when dropped willbe fairly small. However, if the rock is dropped from thetwentieth floor, it will have reached a much greater

velocity on reaching the ground. On the twentieth floorthe rock had much more potential energy.

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

Potential

If one coulomb of electrons is added to a body and onejoule of work has been done, then the body will acquire

of potential of 1 volt. If the electrons had beenremoved, then the body would have acquired a potentialof +1 volt. The unit of potential is the volt.

Potential Difference

When charges move from one point to another, it is notthe actual values of potential at those points which are

Important, but the potential different (pd) through whichthe charge has travelled. Just as lifting weight in thegymnasium, the height above sea level is not important,

but the distance between the gym floor and the heightof ones body. In cases where an actual level of

potential is required, the zero of potential is taken asEarth and whenever the potential at a point is given, it

means the difference in potential between the point andthe earths surface.If one coulomb of electricity requires one joule of workto move it between two points, then there is a potentialdifference of 1 volt between themIf a current flows round a circuit, then a potential

difference must exist between any two points in thatcircuit and each point in the circuit must be at a different

potential. However because there is very littleopposition to current flow in conducting wires, very little

potential difference is required to push the current alongthe wires and it is normally assumed to be zero.Whenever the opposition to current flow is not

negligible, then a potential different exists across thatcomponent to push the electrons through the device.

7/30/2019 mod 3 Final

13/212


12

The converse is also true, if no current is flowing, then

no potential difference exists. The larger the potentialdifference the larger the current.

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) useschemical energy to maintain the potential difference.

Another device used for this purpose is the generator,which uses electro-mechanical energy to maintain thepotential difference. The potential difference across theterminals of the source (cell, battery or generator) whenit 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 acurrent flowing, the potential difference across the

terminals of the source is always less than the emf andis referred to as the terminal voltage.

Current

The SI unit of current is the ampere (A). Although it isknown that electric current is a flow of electrons, this

flow cannot be measured directly.

Movement Of Charge

Although electric current is referred to as the flow of

electrons through a conductor, it should be noted thatmore exactly, any movement of electric charge

constitutes an electric current. Thus, passage ofelectricity may occur through a:

Conductor such as metal, due to the movement ofthe loosely held outer electrons of the atoms.

Vacuum or gas, due to the movement of electrons.

Gas, due to the movement of the ionised gasmolecules.

Liquid, due to the ionisation of certain molecules,

particularly those of acids and salts in solution (e.g.Electrolytes).

7/30/2019 mod 3 Final

14/212


13

The ampere may be defined in terms of the mechanical

units of force and length, a more helpful picture is thatof moving electrons. When a current of one ampere isflowing in a conductor, one coulomb (6.29 x 1018

electrons) of charge passes any point in the conductorevery second.

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

The Coulomb and the Ampere

Since:

One coulomb = 6.29 x 1018electrons

One ampere = a rate of flow of 6.29 x 1018electronsper second,

Then one ampere = one coulomb per second

Conventional FlowAn applied emf causes directional flow. Usingconventional flow the charge carriers are considered to

be positive, that is they leave the positive terminal of asupply and return to the negative terminal.This form of flow was decided upon before anybody

knew exactly what current flow was, however it is stillwidely used in Britain and will be assumed throughout

the course, unless stated otherwise.

Electron Flow

It is now known that current flow is a movement ofnegatively charged particles i.e. electrons. Electronsflow 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.

7/30/2019 mod 3 Final

15/212


14

Resistance

An electric current is a flow of free electrons through aconductor. 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. Tosimplify matters it is usual to ignore the second factorand 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, andallows a large current to flow. Conversely a poorconductor has a high resistance, i.e. few free electronsand allows only a small current to flow for the sameapplied 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.

Factors Affecting Resistance

The four factors that affect the resistance of a wireconductor are:

Material (). Some materials conduct better thanothers.

Length (l). Resistance is directly proportional to

length thus if the length is doubled (other factorsremaining constant), resistance is doubled.

Cross Sectional Area (A). Resistance is inversely

proportional to A. Thus if the cross sectional areais doubled, resistance is halved.

Temperature. Temperature affects the number offree electrons and hence resistance.

Units of resistance

Resistance is measured in ohms, symbol (omega).

The resistance of a piece of material is one ohm if a

potential difference of one volt applied across it causes acurrent of one ampere to flow.

7/30/2019 mod 3 Final

16/212


15

Conductance and conductivity

Also, the conductance (G) of a material is the reciprocalof its resistance and is:

The conductivity of a material is the reciprocal of itsresistively. It is given the Greek symbol (sigma) and

has the units Siemens per metre (S/m).

Thus at 0 C copper has a conductivity of;

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

INTENTIONALLY LEFT BLANK

7/30/2019 mod 3 Final

17/212


16

3.4 GENERATION 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. Whatis needed is some form of external energy that willseparate the electrons from their nuclei. In this way, theexternal energy that is applied will give rise to electrical

energy.

There are six sources of external energy that arecapable of separating the electrons from their nuclei;these are friction, pressure, magnetism, heat, light andchemical action.

By Friction

Static electricity that is the separation and build-up ofcharge is an everyday phenomenon that is often causedby friction the physical stripping of electrons from one

body and depositing on another. Early examples inscience were the rubbing of a glass rod (which loseselectrons 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 fur (becomes positively charged).

Everyday examples are:

Combing the hair (dry). The comb attracts theindividual hairs and the hairs repel each other andstand on end.

Removing a shirt (especially nylon). The shirtcrackles and sparks may be seen, the shirt is also

attracted to the body.

The receiving of electric shock from cars (alsoaircraft) when touching them on the outside. Here

the charge has been produced by the friction of airpassing around the vehicle.

The rapid collection of dust by records. The dust is

attracted by the charge built up on the recordproduced by friction of handling and playing.

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

Although not used to produce electricity for any aircraftsystems, static electricity is generated by friction as the

aircraft moves through the air and will therefore beconsidered at various points throughout the course.

7/30/2019 mod 3 Final

18/212


17

By Pressure

Certain crystals and semiconductors produce an emfbetween two opposite faces when the mechanical

pressure on them is either increased or decreased (thepolarity of the emf is reversed when the pressurechanges from an increase to a decrease). This emf is

known as the piezoelectric emf.

This effect is used in a number of devices includingsemi-conductor strain gauges and vibration sensors. As

the mechanical pressure on the crystal is altered, avarying voltage which is related to the pressure isproduced by the crystal.

The voltage can be as small as a fraction of a volt or aslarge as several thousand volts depending on the crystal

material and the pressure.

Aircraft systems employing the piezoelectric effectgenerally only produce very small emfs, the very high

voltages produced by materials such as Lead ZirconateTitanate are used in ignition systems for gas ovens andgas fires.

By Magnetism

Magnetism itself is not used as the direct source ofexternal energy. In a manner which will be studied in

great detail later in the course, large amounts ofelectrical energy are produced by machines calledgenerators.

Energy is used to drive the generator, which when it

turns, makes use of the properties of magnetism toproduce the external energy necessary to break the

electrons away from their nuclei and so make it possiblefor electric current to flow.

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 ofthe metals more easily than they can leave the other

metal. This is because of the difference in what isknown as the work function of the two metals.

7/30/2019 mod 3 Final

19/212


18

Since electrons leave one metal and are gained by the

other, a potential difference exists between the twometals; thus the emf is known as the contact potentialor contact emf.

If two metals, say copper and iron, are joined at twopoints 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 inthe loop of wire. However, Thomas Johann Seebeck

(1770 1831) discovered that if the two junctions arekept at different temperatures, there is a drift of

electrons around the circuit, that is to say, current flows.The magnitude of the voltage produced by this methodis small only a few millivolts per degree centigrade

but it is sufficient to be measured.

The current flow is proportional to the difference in

temperature between the hot junction and the coldjunction.

Each junction is known as a thermocouple and if anumber of thermocouples are connected in series so thatalternate junctions are hot and the other junctions are

cold, the total emf is increased; this arrangement isknown as a thermopile.

On aircraft, thermocouples are used for temperature

measurement and will be examined in more detail at alater date.

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 ofthe earliest types being the selenium photovoltaic cell in

which a layer of selenium is deposited on iron and anylight falling on the selenium produces an emf betweenthe selenium and the iron.

7/30/2019 mod 3 Final

20/212


19

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 isp-type 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 1 m thick) through which lightcan pass without significant loss of energy. When thelight reaches the junction of the two regions it causeselectrons and holes to be released, to give the electro-

voltaic potential between the two regions.

A better understanding of this action will be obtainedlater in the course when semi-conductor materials anddevices are studied.

By Chemical Action

The final method of producing electricity is by chemicalaction. It is the particular kind of chemical action that

takes place in electric cells and batteries which is putto practical use in the production of electricity.


7/30/2019 mod 3 Final

21/212


20

3.5 DC SOURCES OF ELECTRICITY

To study electrical principles further we require a source

of emf. Although an emf can be produced by any of thesix methods discussed above, large amounts of useablepower can only be produced chemically or bygeneration. Generation requires a more in depth studyof magnetism and therefore cells and batteries will bestudied first.

On an aircraft the battery may be used for engine

starting, but far more importantly, the battery is thesource of emergency power when the generator fails.Although aircraft battery systems and servicing will bestudied at a later date, battery principles and batteryconstruction will be studied now and will not be

repeated.

Principles

A Cell is a portable device which converts chemical

energy into electrical energy. A group of interconnectedcells is known as a battery. Cells operate on a principleof the exchange of charges between dissimilar metals.

Cell & Battery Symbols

The circuit symbols for cells and batteries are shownbelow. To identify the polarity of the terminals, a long

thin line is used to represent the positive terminal and ashort thick line the negative terminal. Sometimes theterminal voltage is indicated.

Construction & Chemical Action

In cells, an electrolyte separates two charge collecting

materials called electrodes, to which externalconnections are made. The electrolyte pushes electrons

onto one of the plates and takes them off the other. Thisaction results in an excess of electrons, or a negative

charge, on one plate and a loss of electrons, or apositive charge, on the other plate.

7/30/2019 mod 3 Final

22/212


21

Electrolytes are chemical solutions manufactured toallow the generation and free movement of both types ofions, and are normally acid or alkaline pastes or liquids.The action of the electrolyte in carrying electrons from

one plate to the other is actually a chemical reactionbetween the electrolyte and the two plates. This action

changes chemical energy into electrical charges on thecell plates and terminals.

With nothing connected to the cell terminals, theelectrons would be pushed onto the negative plate until

there was no more room. At the same time theelectrolyte 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 themovement of electrons would cease.

If a wire were connected between the negative andpositive terminals of the cell, electrons on the negativeterminal would leave the terminal and travel through the

wire to the positive terminal. The electrolyte wouldcarry more electrons across from the positive plate to

the negative plate. Whilst the electrolyte is carryingelectrons you would see the negative plate being used

up and you would see bubbles of gas at the positiveplate.

Primary & Secondary Cells

In a primary cell, current will continue to flow until

chemical action had dissolved the negative plate into theelectrolyte, 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 reversingthe chemical action is referred to as charging and entails

passing a current through the cell in the oppositedirection to the discharge current.

7/30/2019 mod 3 Final

23/212


22

Cell Emf

The size of a cell has no bearing on the emf that it willproduce, the generated emf being determined solely by

the materials used in its construction. Another point tonote is that the potential difference, or voltagemeasured across the terminals of a cell, is not the same

as the emf generated by the cell. The terminal voltage ofa cell depends on the:

Internal resistance of the cell.

Size of the discharge current.Charge state of the cell.

As a general rule, whenever a cell is providing current,

the terminal voltage will be less than the cell emf. Thedifference between the cell emf and its terminal voltageis directly proportional to the discharge current.

All sources of electricity have internal resistance whichaffects the terminal voltage; this will be examined inmore detail later in the notes.

Cell Capacity

The amount of electrical energy that a cell can providefrom 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 fromthe 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 forNickel Cadmium cells, with 10 hr or 20 hr rates beingused for Lead Acid cells.

A cell quoted at 40A-h at the 10 hr rate will provide 4Amps 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 dischargecurrent of 80 amps for approximately 20 minutes, not30 minutes as may be expected by calculation. Similarly,

it will be able to supply a discharge current of 20 ampsfor longer than the expected 2 hrs.

7/30/2019 mod 3 Final

24/212


23

The capacity of a cell is also affected by its age, the

older a cell, the lower its capacity; therefore the onlyway of determining actual capacity is to measure it.

Interconnection of Cells

Cells may be connected in series, parallel or any

combination of the two in order to form a battery. Whencells are connected to form a battery they should be of

similar construction, and have the same terminalvoltage, internal resistance and capacity.

Series Connection.

When connected in series:The battery voltage is the total of theindividual cell voltages.

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

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

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 paralleltotal of the cell resistances.

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

These rules can also be applied when connecting

batteries together in series, parallel or any combinationof the two.

7/30/2019 mod 3 Final

25/212


24

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 theAnode (positive plates) is Lead Peroxide (Pb02) and inthe Cathode (negative plates) and the, Spongy Lead

(Pb). The electrolyte is dilute sulphuric acid (2H2SO4).

Conventional Construction

There are two forms of Lead Acid battery construction,conventional and solid block, often referred to as aVarley type battery.

In the conventional battery the plates consist of leadgrids into which the active materials are pressed. The

positive and negative plates are then interleaved andconnected to a lug that forms both a mechanical support

and the terminal.

Cells are generally constructed with an additionalnegative 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.

The plate arrangement is then inserted into a composite

material container which is fitted with a lid. The inside ofthe container is ribbed to provide additional support forthe plates, which are raised clear of the bottom of the

container to prevent shorting by any sediment thatforms.

7/30/2019 mod 3 Final

26/212


25

To provide further support for the plates and to ensure

they cannot touch separators are fitted, these wereoriginally cedar wood but modern batteries use micro-porous plastic materials.

Each cell is fitted with a special non spill valve thatallows gasses to escape, but prevents the spillage of

electrolyte, this valve can be removed for checking andadjusting the electrolyte level.

The electrolyte used is sulphuric acid diluted with pure

distilled water, the specific gravity of the electrolyteused is determined by the manufacturer, however, it isgenerally lower than 1300.

Solid block type construction

In the solid block type battery the electrolyte iscompletely 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, thisgives better absorption and an enhanced electrochemicalactivity.

The support given to the plates means practically nodistortion 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 isstronger, less susceptible to vibration damage and has a

higher capacity to weight ratio than its conventionalcounterpart.

7/30/2019 mod 3 Final

27/212


26

Chemical action

When the lead acid battery is delivering current, thesulphuric acid breaks up into Hydrogen ions (H2) that

carry a positive charge and Sulphate ions (SO4) thatcarry a negative charge. The SO4 ions combine with thelead (Pb) plate and form lead sulphate (PbSO4). At the

same time they give up their negative charge, thuscreating an excess of electrons on the negative plate.

The H2 ions go to the positive plate and combine withthe oxygen of the lead peroxide (PbO2) forming water

(H2O), during this process they take electrons from thepositive plate. The lead of the lead peroxide combineswith some of the SO4 ions to form lead sulphate on thepositive plate.

The result of this action is a deficiency of electrons on

the positive plate and an excess of electrons on thenegative plate.

When a circuit is connected to the battery, electrons flow

from the negative plate to the positive plate. Thisprocess will continue until both plates are coated withlead 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 batteryin a reverse direction. The SO4 ions are driven back into

solution in the electrolyte, where they combine with theH2 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 isdischarged, and returned to the electrolyte as it is

charged, a test of the specific gravity of the electrolyte

7/30/2019 mod 3 Final

28/212


27

will give a good indication of the state of charge of the

battery.

Charge and Discharge Characteristics

During discharge the plates are converted into leadsulphate, the water content of the electrolyte increases,

the internal resistance of the cell increases and theterminal voltage decreases.

By passing a current through the battery in the opposite

direction these effects are reversed. The plates areconverted back to their original form, the water contentof the electrolyte decreases, the internal resistancedecreases and the terminal voltage increases. Theprocess of recharging takes approximately 8 to 10hours.

During most of the charge and discharge cycle the

battery terminal voltage remains constant at 1.95V, ittherefore gives no indication as to the batterys 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 batterys

state of charge.

Voltage & Specific Gravity Characteristics

The voltage and specific gravity figures for a lead acidbattery are:

Fully charged and still connected to the chargingboard 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 theabove discharged values.

7/30/2019 mod 3 Final

29/212


28

Common Lead Acid Battery Faults

Careful treatment of lead acid batteries preventsdamage 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 randomgreyish 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 continuallyundercharging the battery or by discharging below1.8 Volts or 1150 SG and if severe there is no cure.However, if mild, it can sometimes be cured bygiving the battery a long low charge.

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 chargeand discharge currents being imposed on thebattery 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 the bottom of the cell.Sedimentation may result in shorting of the platesand complete loss of capacity, slight shedding is

normal in a well maintained battery.

7/30/2019 mod 3 Final

30/212


29

Nickel Cadmium Batteries

Construction

The plates of a nickel cadmium battery are made bysintering a nickel plated steel screen with nickel carbonylpowder. 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 toconvert 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 arethen 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 is

inserted into its container, which is sealed and pressuretested.

The separator used is normally a triple layer type, onelayer 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 duringovercharge, from passing to the negative plates where itwill combine with the cadmium, reducing the cell voltage

and producing heat.

7/30/2019 mod 3 Final

31/212


30

The electrolyte, a solution of potassium hydroxide and

distilled water, with a SG of between 1240 and 1300, isthen injected into the cell under a vacuum. Fitted to thetop 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

metal case that incorporates 2 venting outlets, carryinghandles, a quick release connector and a lid. Each cell is

separated from its neighbour by its moulded plastic caseand electrically connected by nickel plated steel links

between the terminals.

Chemical Action

As the battery discharges, hydroxide ions (OH) from theelectrolyte combine with the cadmium in the negative

plates and release electrons to the plate. The cadmiumis converted to cadmium hydroxide during the process.At the same time, hydroxide ions from the nickel

hydroxide positive plates go into the electrolyte carryingextra electrons with them. Thus electrons are removed

from the positive plate and delivered to the negativeplate during discharge.

The composition of the electrolyte remains a solution ofpotassium hydroxide because hydroxide ions are addedto the electrolyte as quickly as they are removed. Forthis reason the specific gravity of the electrolyte remainsessentially 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 arecaused to leave the negative plate and enter theelectrolyte. Thus the cadmium hydroxide of the negative

plate is converted back to metallic cadmium. Hydroxideions from the electrolyte recombine with the nickel

7/30/2019 mod 3 Final

32/212


31

hydroxide of the positive plates, and the active material

is brought to a higher state of oxidation. This processcontinues until all the active material of the plates havebeen converted.

If charging is continued, the battery will be inovercharge, and the water in the electrolyte will be

decomposed by electrolysis. Hydrogen will be releasedat the negative plates and oxygen at the positive plates.

This combination of gases is highly explosive.

Charge and Discharge Characteristics

During charging and discharging the electrolyte acts onlyas an ionised conductor, transporting electrons from oneplate to the other, its specific gravity remaining

constant.

On discharge the terminal voltage initially falls rapidlyand then remains constant for most of the discharge

cycle, dropping rapidly again when the battery is nearlyfully discharged.

When charged, the terminal voltage initially rises rapidlyand 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, hydrogenbeing released at the negative plates, oxygen at thepositive plates, this combination of gases is explosive.

Prolonged gassing should be avoided as it reduces thewater content of the electrolyte and causes overheating

of the battery, a slight amount of gassing, however, isnecessary to ensure charging is complete.

The terminal voltage remains constant for most of the

batteries life and the specific gravity of the electrolyteremains unchanged, the only way of determining thestate of charge of the battery therefore, is to carry out afull charge followed by a capacity test.

During discharge the plates absorb electrolyte to such an

extent that the level may disappear from view. As thebattery is charged, the electrolyte is forced back out of

the plates, a point to note when topping up the cells.

7/30/2019 mod 3 Final

33/212


32

Advantages & Disadvantages

A Nickel Cadmium battery has the following advantagesover a Lead Acid battery:

They have a longer life

The terminal voltage remains almost constantduring the discharge cycle

They can be charged and discharged at much highercurrents without causing cell damage

They can be discharged to a very low voltagewithout 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 cellare required to produce a battery.

They are more susceptible to thermal runaway.

Thermal Runaway

Batteries loose 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 quickly

enough its temperature will start to increase. As thebattery temperature increases the internal resistance

decreases causing the circuit current to increase. Thisincrease in current leads to an increase in chemical

activity within the battery, this generates more heat andthe cycle repeats.

Nickel Cadmium batteries are very susceptible tothermal runaway which can result in the battery boiling,or even being totally destroyed.

Small Alkaline Cells

Hermetically sealed Ni-Cad cells are produced in the

same size and shape as their primary counterparts. Theyare small, portable and maintenance free, but have theadded advantage of being rechargeable.

7/30/2019 mod 3 Final

34/212


33

The plates are constructed in a similar manner to the

larger Ni-Cad cells, the separator being a thin porousmaterial. The electrolyte is fully absorbed by the platesand 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 andelectrolyte 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 thecells further but damage will occur if allowed to go below1 volt.

Charging should be carried out using a constant currentat the 10 hour rate, total charge taking approximately14 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.


7/30/2019 mod 3 Final

35/212


34

3.6 DC CIRCUITS

So far you have been introduced to the concepts of

electric current (as a movement of free electronsthrough a conducting material), to voltage (or potential)and potential difference and to the resistance to currentflow by any conducting material. The relationship whichexists between these quantities was discovered by aphysicist called Georg Simon Ohm (1789-1854) and is

now referred to as Ohms Law.

This is the most fundamental law of electricity andelectronics. Ohms law statesFor a fixed metalconductor, the temperature and other conditionsremaining constant, the current through it isproportional to the potential difference between its

ends.Mathematically this is expressed as:

Thus the ratio:

And this ratio is called the resistance of

the conductor.

Hence we may write:

Where:V = the potential difference in VoltsI = the current in Amperes

R = the resistance in Ohms

Transposition of Ohms Law

By transposition it is seen that Ohms law may bewritten in three forms:

thus resistance may be calculated if Vand I are known.

thus current may be calculated if V and R

are known.

thus voltage may be calculated if I and Rare known.

7/30/2019 mod 3 Final

36/212


35

The Ohms Law Triangle

One simple way of memorising Ohmslaw is the Ohmslaw triangle see below.

By covering up the unknown quantity, the relationshipbetween the remaining two is directly observed. Youmay check this against the equations in the above sub-chapter. This is not necessary if you are able toremember one form of the equation and derive the othertwo directly by transposition.

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 onthe 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 studiedin some depth later in this course, because the principlebehind their operation is the same as the principle

employed in many aircraft instruments.

Modern meters are referred to as a 'digital meters' or

'Digital Multi-meters' more commonly abbreviated toDMM's. Digital meters are cheaper and, arguably, more

reliable and more robust and generally considered moreaccurate than their analogue counterparts.

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

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.

V

I R

7/30/2019 mod 3 Final

37/212


36

Voltmeters

Voltmeters are used to measure emf's and morecommonly potential differences. The two probes of the

meter are therefore connected in parallel to the twopoints between which the potential difference isrequired.

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

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

If it is required to measure a potential between anypoint on the circuit and ground or Earth, the red lead is

connected to the point and the black lead is connected

to ground or Earth.

Ammeters

Ammeters are used to measure current flowing in thecircuit; as such they need to be inserted in series with

the circuit under test so that the current to be measuredflows through the meter. This means the circuit must bebroken.

To connect an ammeter, the power must beswitched off. The circuit is broken at the point wherethe current is to be measured; the meter is then

inserted into the circuit ensuring that the pola5ity iscorrect for conventional current flow.

Once the meter is connected, circuit power may berestored and the measurement taken.

To disconnect the meter, the circuit power mustagain be switched off. Once the meter is removed

from the circuit, the circuit must be reconnected.

7/30/2019 mod 3 Final

38/212


37

Ohmmeters

The use of ohmmeters is somewhat more involved. Mostimportantly when measuring resistance the circuit

power must be switched off, power is derived fromwithin the instrument.

Secondly, great care must be taken to ensure there areno parallel paths that would affect the measurement.

This is generally best confirmed by removing thecomponent or device, or by disconnecting one end of it

from the circuit concerned. Thirdly, it is essential thatan analogue meter is zeroed before it is used.

To measure resistance, the meter is simply connectedacross 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).When making resistance measurement, care must betaken to ensure the correct

7/30/2019 mod 3 Final

39/212


38

3.7 RESISTANCE AND RESISTORS

Resistivity

The factors affecting the resistance of a conductor of agiven material at constant temperature are related bythe expression:

The constant depends on whether the material itself is agood or a poor conductor; this constant is called

resistivity of the material.

Resistivity has thesymbol (Rho) and is measured in Ohm meters andis defined as the resistance between the ends of a pieceof material one metre long which has a cross sectional

area of one square metres (i.e. between the faces of a

one metre cube).

Typical values of at 0 C are:

Silver 1.5 x 10-8 - m

Copper 1.6 x 10-8 - m

Manganin 41 x 10-8 - m

Carbon 7000 x 10-8 - m

Changes of Resistance with Temperature

The resistance of all materials changes, with changes intemperature. The resistance of all pure metal increases

with temperature whereas the resistance of electrolytes,insulators, carbon and semi-conductors decreases withincreasing temperatures.

If it is assumed that the resistance change is inproportion to the temperature change, then the ratioprovides an indication of the material behaviour. It is

necessary however, to relate the change of resistance toits initial value. A large value resistor will change itsvalue more than a small value resistor for the sametemperature change.

7/30/2019 mod 3 Final

40/212


39

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

and at same other temperature (t) the resistance is Rtthe change of resistance is Rt - Ro.But the change of resistance is per unit value of the

original resistance is given by:

This resistance change has been brought about by atemperature change t equal to t - to (to being 0).

Hence the change in resistance, caused by a 1C changein temperature is:

This ratio is called the temperature co-efficient ofresistance.

Temperature Co-efficient of Resistance

The temperature co-efficient of resistance is defined as:The Fractional change in resistance, from 0C, perdegree temperature change and may be representedgraphically as shown below.

The graph is reasonably linear for many materials over amoderate temperature range (0 - 200C).The units are C because the ohms cancel out in thecalculation.

Materials whose resistance increases with increasingtemperature have a positive temperature co-efficient

of resistance.

7/30/2019 mod 3 Final

41/212


40

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 isimportant that the resistance does not change withtemperature. Examples are Manganin and Eureka.

Resistors

The electrical component used to introduce resistanceinto a circuit is called a resistor. Resistors can be fixed

or variable. Symbols used in circuit diagrams are shownbelow:The physical size of a resistor does not give any clue to

the resistance value of the component. This value mustbe marked on individual components. Two codes are

currently used to indicate resistor values: a Colour Codeand a Letter and Digit Code.

Fixed resistors

Fixed resistors may be:

Wire wound: Special resistance wire is wound onto a

former. The wire wound resistor can dissipate heateasily and is therefore used when larger currents are

expected (the larger the current the greater the heatproduced). These resistors are usually larger than other

types; The student should note that size does notindicate resistance value, but depends upon the heat tobe dissipated.

Resistor Type Old Symbol New Symbol

Fixed resistor

Fixed resistor with fixedtapping point

Variable resistor

Resistor with pre-setadjustment

Voltage divider

(potentiometer)

Pre-set potentiometer

7/30/2019 mod 3 Final

42/212


41

Carbon Composition, Metal Oxide and Metal

Film: Resistors made from carbon composition orfrom metal films and oxides are usually small.They are therefore used where the currents are

kept small.

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 theforth 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 themultiplication factor, i.e. the number of zeros, the fourthband gives the tolerance, which indicates how close the

actual value may be to the stated value.

Certain resistors remain very close to their stated value,

despite temperature changes. These are called highstability resistors and this is shown by a fifth band

coloured pink.

Colour First band

(or body)First

figure

Second

band(or tip)

Second

figure

Third band

(or spot)Multiply by

Fourth

bandTolerance

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%

7/30/2019 mod 3 Final

43/212


42

High value resistors

High value resistors may have three significant figures.

If the colour code is used here, the first three bandsrepresent figures, the fourth band is the multiplier andthe fifth band is the tolerance.

For example, a resistor of value 249,000 + 1% wouldbe coded as shown below:

First band Red is 2

Second band Yellow is 4Third band White is 9

Fourth band Orange is 3 zerosFifth band Brown

Tolerance + 1%

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

Preferred values and tolerances

In practical electrical circuits the precise value for aresistor is not usually critical. It is more economic toproduce large tolerance resistors than low tolerance

ones. The number of resistor values required to cover a

given range of resistance depends on the tolerance ofthe resistors being used. An example of resistorPreferred Values for 10% is given in the table below.

Note that the upper and lower tolerance resistance limitsof each preferred value cover the complete range:

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

2.7K + 10% = 2.43K to 2.97K3.3K + 10% = 2.98K to 3.63K

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

7/30/2019 mod 3 Final

44/212


43

7/30/2019 mod 3 Final

45/212


44

7/30/2019 mod 3 Final

46/212


45

7/30/2019 mod 3 Final

47/212


46

Letter & Digit Codes

In this code the numbers are printed on the body of theresistor to indicate its value. In addition, letters areused to indicate the multiplying factor (eg, M ) and the

tolerance as shown below.

Multiplying Factor Tolerance %

X1 R (resistor) 0.1 B 5 J

X103 K K 0.25 C 10 KX106 M M 0.5 D 20 MX109 G G 1.0 F 30 N

X1012

T T 2 G

The position of the multiplying letter is also used toindicate the decimal point position

eg 470R is 470

4K7 is 4.7

R47 is 0.47

4R7 is 4.7

The tolerance letter is added on the end.

eg 1M5 B is 1.5M + 0.1%

2K2 N is 2.2K + 30%

Other markings may also be used in the code torepresent date of manufacture. They are placed after

the value and tolerance markings.

Power Rating

Resistors are rated according to their resistance valueand 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 thewattage rating the more current it can carry.

7/30/2019 mod 3 Final

48/212


47

Potentiometers

A variable resistor arranged so asto control voltage in a circuit iscalled a Potentiometer andcontrols 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.

Rheostats

Variable resistors can be made tovary either current or voltage. A

variable resistor arranged tocontrol current is called a

Rheostat and controls thecurrent by varying the resistance in the circuit.

Voltage Dependent Resistors

Some components do not obey Ohms law, in that the

current flow through them does not vary linearly as the

applied voltage is varied. These elements are known asnon-linear resistors or non-linear conductors.Transistors, diodes and voltage dependent resistors allfall into this group.

The current through a voltage dependent resistorincreases at a progressively rapid rate as the voltage

across it increases; such a device is used for protectingcircuits against voltage surges or as a voltage stabiliser.

Thermistors

Insulators and semi-conductors behave in a differentway when the temperature is increased this is because

their resistivity decreases (their temperature coefficientof resistance is negative).

One example of this effect occurs in a thermistor. Athermistor is a thermally sensitive resistor whoseresistance alters with temperature; a negative

temperature coefficient (n.t.c.) thermistor is one whoseresistance reduces with increase in temperature. Athermistor 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

7/30/2019 mod 3 Final

49/212


48

and temperature gauge. As the water temperaturerises, the resistance of the n.t.c. thermistor resistancefalls and allows more current to flow through thetemperature gauge; this causes the gauge to indicatevariations in water temperature.

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 thecomponents (including the power supply). See diagrambelow.

When a current flows through a resistor (or a componenthaving resistance) there is a potential difference

between its ends. Thus where two or more resistors areconnected in series the potential difference between the

extreme ends is the sum of the individual potentialdifferences.

Hence E = V1 + V2 + V3

But from Ohms Law V = IR therefore E = IRTOTAL

So V1 = IR1 V2 = IR2 V3 = IR3

Thus IRTOTAL= IR1 + IR2 + IR3

= I (R1 + R2 + R3)

So RTOTAL = R1 + R2 + R3

7/30/2019 mod 3 Final

50/212


49

Kirchhoffs Second Law

This law states that in any closed circuit the sum of allthe potential differences (voltage drops) is equal to thetotal applied voltage in that circuit.Thus the potential difference across R2is given by:

VR2 = 9 7 = 2V

Example of Kirchhoffs Second Law

There are four possible routes around the circuit shownand whichever one is taken, Kirchhoffs law is true.

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

Route MPQSNM 3+710=0Route MPRSNM 4+610=0

Route MPQRSNM 3+1 + 6 10=0Route MPRQSNM 41+70=0

It should also be noted that within the resistor network:

Route PRQP 4 1 3 = 0Route PQRP 3 + 1 4 = 0Route RSQR 6 7 + 1 =0Route RQSR -1 + 7 6 = 0

7/30/2019 mod 3 Final

51/212


50

Voltage Division

In a series circuit Ohms law applies for eachcomponent. However, since the current is common toall 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 eachresistor can be calculated from the

ratio of the resistance values.It should also be noted, that for anygiven applied voltage we may deriveany smaller voltages we wish byinserting resistors of the appropriatevalues in series. The following example

shows how voltages of 8V, 4V and 24Vcan be derived from a 36V supply.

RTOTAL = 12 + 6 + 36 = 54

54 36V and 1 36/54V

12 = 36/54 12 = 8V across AB

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

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

The Potential Divider

A device which employs voltagedivision and which is commonly used

in electrical and electronic circuits isthe potential divider. Here two ormore resistors are used to divide agiven input voltage to achieve aspecified output voltage. Seediagram.

The potential divider is also known asa voltage divider or scaling circuit.

Note that if current is drawn from the output then theeffective resistance of the circuit changes and the output

voltage vOUT changes.

7/30/2019 mod 3 Final

52/212


51

Voltages Relative to Earth

It is very common in electrical circuits to have an earthconnection. This earth connection has no effect onpotential differences across components; however itdoes affect the values of the potentials or voltages atpoints in the circuit.

The earth is a reference point and considered to be atzero volts. Potential differences between earth and thenegative terminal of the supply result in negativevoltages and potential differences between earth and the

positive terminal result in positive voltages. It should benoted that due to static build up on the airframe, theearth connection (airframe) of an airborne aircraft isunlikely to be at zero potential with respect to theground.

You should also note that earth connections, for exampleto the chassis of equipment or the airframe of anaircraft, are often used as the current return lead in an

electrical circuit.

7/30/2019 mod 3 Final

53/212


52

Internal Resistance

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

Cells (and batteries): The internal resistance ismainly due to the resistance of the electrolyte. This

varies considerably with temperature andconcentration of the electrolyte.

Generators. Internal resistance is mainly theresistance of the wires which form the internalwindings.

Electronic Power Supplies. Here the internal

resistance is due to the resistance of componentswithin the power supply.

When the source forces electrons around a closed circuitthey must pass through the internal resistance of thesource, thus causing a drop in voltage within the sourceitself, i.e. the source has to do work to push currentthrough it.

This loss of potential or voltage drop may be referred toas lost volts, since they are not available in the external

circuit, thus the terminal voltage is less than the emf bythe value of the lost volts when current is drawn from

the supply.

Loss of potential only occurs when current flows fromthe source. If therefore the external circuit is open, no

current flows and the terminal voltage is equal to theemf.

OPENCIRCUIT TERMINAL VOLTAGE = EMF

The Size of the lost voltage is determined by theinternal resistance and the current flowing (Ir).

CLOSEDCIRCUIT

TERMINAL VOLTAGE = EMF LOST VOLTS

7/30/2019 mod 3 Final

54/212


53

For a given emf the larger the external resistance, thesmaller the current and the smaller the lost volts. Thusif the internal resistance is much smaller than theexternal resistance the lost volts is very small and theterminal voltage is almost equal to the source emf.

Resistors in Parallel

Components are said to be in

parallel when they are

connected in such a way as toprovide alternative paths forcurrent 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

Ohms law applies to each component connected in

parallel.

In the diagram below:

Vtotal= V1 = V2 = V3 and Itotal= I1 + I2 + I3

(By Kirchhoffs first law)

From Ohms law:

and

7/30/2019 mod 3 Final

55/212


54

Hence the three resistors shown above may be replacedby a single resistor of value RTOTAL which may becomputed using the above equation.Note that the most usual error which occurs when usingthis equation is to forget that the calculation on the righthand side of the equation gives the reciprocal of theequivalent resistance and therefore needs inverting to

find RTOTAL.

To avoid this possible error the equation may be

remembered in the form:

Having found RTOTALit is now possible to use Ohms lawto calculate either V or I, providing one of the two is

known. Knowing V (= V1 = V2 = V3 etc) it is nowpossible to find the current values through the branches

I1, I2, I3 etc (provided of course that R1, R2, R3 etc areknown).

As a check, the total resistance of any parallel

combination of resistors should always be less than thevalue of the lowest resistor in the network.

Two resistors in parallel

When we have only two resistors in parallel then thegeneral equation may still be used. However a simplerformula can be derived.Using the general equation we obtain:

Therefore

Equal resistors connected in parallel

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

7/30/2019 mod 3 Final

56/212


55

Therefore:

When any numbers of equal value resistors are

connected in parallel, the effective resistance (Total) is

equal to the value of one resistor divided by the number

of resistors.

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 voltageacross the first. The first resistor still draws the samecurrent and the second now also draws current. Thusthe total current drawn from the supply has increased

and therefore the effective resistance (RTOTAL) hasdecreased. Since the supply of current is now greater

than either individually would draw, the effectiveresistance of the two is less than the resistance of eitherindividually. This is generally true and for any number

of parallel resistors the effective resistor (RTOTAL) is lessthan the value of any single resistor in the parallelcombination. An important point to note here is that thesupply current has increased and unless the supplywiring can cope with it, it may be damaged (e.g. beginsto melt).

Resistor size and current flow

Ohms law states that the current flowing is inversely

proportional to resistance provided that the voltageremains constant. In a parallel network the voltageacross each component is the same, therefore thecurrent through each component is inversely

proportional to its resistance. Simply stated, this meansthat the largest current always flows through the

smallest resistor and vice-versa. This is a simple checkthat may often be useful in numerical calculation.

7/30/2019 mod 3 Final

57/212


56

Kirchhoffs First Law

Kirchhoffs first law states that at any circuit junction,the sum of the currents flowing towards the junction isequal to the sum of the currents flowing away from it.

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

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

Resistors in series / parallel combinations

In the previous units we have used Ohms law to solvecombinations of resistors in series or in parallel. It is

possible to solve combinations of resistors in both serialand parallel by Ohms law provided sufficient informationis given. In some cases, however, solution is notpossible without the use ofKirchhoffs laws.

Physical arrangement of resistors

Before we look at some problems it is necessary to warnyou 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 aminimum. Care must be taken to decide whether they

are mounted in series or parallel or in a combination ofboth.

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

2A

7A

10A

9A

8A

7/30/2019 mod 3 Final

58/212


57

Solution of resistor networks using Ohms Lawonly

Many problems may be solved by combining series andparallel groups of resistors and applying Ohms law.

Remember that Ohms 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. Whereresistors 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 withinbranches

Replace any simple parallel groups by singleequivalent resistors

7/30/2019 mod 3 Final

59/212


58

Combine any simple series groupings

Replace any simple parallel groups.

Determine the single equivalent resistance.

At this point the total circuit current (Is) may befound ifVs is given, or Vs found ifIsis given.

Having determined Vsor Is, as appropriate, thecurrent in any branch and the voltage drop acrossany resistor can be found by working backwards

through the sequence in the first paragraph ofthis section, applying Ohms law at each stage.

7/30/2019 mod 3 Final

60/212


59

The effects of open circuits

An open circuit is essentially a break in the circuit. Anopen circuit in a series circuit will prevent the flow ofcurrent through the circuit. With no current flowing inthe circuit there can be no voltage drop across anyresistors and, therefore, the supply potential will be

measured at all points between the positive terminal andthe break.

In a circuit with parallel paths, an open circuit path willcause an increase in the circuit resistance and areduction in the circuit current. The change in currentflow will cause the voltages measured around the circuitto change.

The effects of short circuits

A short circuit is a path for current where a path shouldnot exist, the path is generally considered to have a lowresistance. If a short circuit is placed across a resistor,

the current will flow through the short circuit rather thanthrough the resistor.

Short circuits across series or parallel connectedresistors 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 noprotection devices are fitted.

7/30/2019 mod 3 Final

61/212


60

The Wheatstone bridge

You have already solved resistor networks using Ohmslaw and Kirchhoffs laws. In this unit we are going tolook at a special arrangement of series and parallelresistors called a Wheatstone bridge.

Construction

The Wheatstone bridge circuit and other similar variants

were widely used in test equipment to determine thevalue of an unknown resistor by comparison with otherresistors whose values are accurately known.The normal arrangement in a Wheatstone bridge used

for resistance measurement is for two resistors, usuallyR1 and R2, to be fixed and of known value and R4 to be

an accurate variable resistor adjusted by means of acalibrated dial. The resistor R3 is then the unknownwhose value is to be measured.

Calculating unknown resistances

The current through the galvanometer (G) a verysensitive 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 tothe voltage at B and no current flows between A and B.Hence:

Also:

Dividing (1). by (2). Then:

7/30/2019 mod 3 Final

62/212


61

In calculations it is possible for any of the four resistors

to be unknown. 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.

Uses on aircraft

Whilst the Wheatstone bridge may be used to determinethe value of an unknown resistor, it is far easier to use

an Ohmmeter.

The Wheatstone bridge is however extremely useful formeasuring and displaying remote indications.On aircraft, Wheatstone bridge circuits are used for themeasurement 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 producesa current flow through the galvanometer. The amountof current through the galvanometer, and therefore the

amount of pointer deflection, depends upon the potentialdifference across the bridge, which, in turn dependsupon the change in resistance of R3. The galvanometercan therefore be calibrated to give the appropriateindication.

7/30/2019 mod 3 Final

63/212


62

3.8 POWER

Electrical work

Electrical work is done if a quantity of charge(Coulombs) is moved between two points which are atdifferent electrical potentials.

The SI unit of work is the Joule. One Joule of work isdone when a charge of one Coulomb moves through a

potential difference of one Volt:

Since one Coulomb is one Ampere second

Electrical energy

Electrical energy is the ability of an electrical system todo work.

Energy is expended when work is done and the amountof energy used is equal to the work done. The units of

energy and work are the same, that is Joules and thesame equation is used for both:

The energy a body contains may be determined bycalculating the electrical work done on the body to giveit that energy. Conversely, the work that a body coulddo if it used up all its energy may be determined bycalculating 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.

No energy is actually destroyed, it is simply convertedinto some other form. This is stated in the Law ofConservation of Energy - energy can neither be created

nor destroyed but merely changed into other forms.

7/30/2019 mod 3 Final

64/212


63

Electrical power

Electrical power (symbol P) is the rate at which work isdone or the rate of conversion of energy by an electricalsystem.The SI unit of power is the Watt which is a rate of workof 1 Joule per second:

By substituting V = IR in the above formula, two otherexpressions for electrical power are obtained:

Power ratings

Electrical equipment can only stand a certain amount of

heat production without damage and the safe powerwhich a piece of equipment can consume withoutdamage is its power rating or wattage rating. Eachcomponent is given a wattage rating and if this isexceeded the component will overheat.

The more power consumed by a device the more heat orlight it produces in a given time:

A 100w lamp gives more light than a 60w lamp. Therating 6V 12W on a lamp means that if is connected to a6V supply, its resistance is such that it develops 12W ofpower and that it is intended to work at this rating.

Note: 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 lightthan a 12W filament bulb because the tube producesmuch less heat and is therefore more efficient.

Power ratings of resistors

This power rating has a different meaning from that of abulb. In this case we must always keep below thestated value.

To keep below the stated power value, there aremaximum permissible values of voltage and current,which may be calculated as follows:

7/30/2019 mod 3 Final

65/212


64

Maximum Current:

This is the maximum current to avoid damage to theresistor.

Maximum Voltage:

This is the maximum voltage to avoid damage to theresistor.

Size and power rating

The surface area and, therefore, the size of a componentis the determining factor of the rate at which heat isdissipated from the component to its surroundings.Generally larger components have a higher powerrating.

Carbon resistors of the same resistance value arecommonly available in ratings between W and 2W.

When higher wattage is required wire-wound resistorsmay be used, the normal range here is 1W to 200W.

The Kilowatt Hour

The unit of electrical energy is the Joule which may be

expressed in terms of power as a Watt second.

The Jou

mod 3 final

Documents