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C h a p t e r

5Electrical fundamentals

5.1 Introduction

In todays world, electricity is something thatwe all take for granted. So, before we get started,it is worth thinking about what electricity meansto you and, more importantly, how it affectsyour life.

Think, for a moment, about where and howelectricity is used in your home, car, workplaceor college. You will quickly conclude that elec-tricity is a means of providing heat, light, motionand sound. You should also conclude that elec-tricity is invisible we only know that it is thereby looking at what it does!

Now let us turn to the world of aircraft andflight. Although it may not be obvious at firstsight, it is fair to say that an aircraft just couldnot fly without electricity. Not only is electric-ity used to provide a means of ignition for the

engines, but it also supplies the lighting andinstruments within an aircraft as well as thenavigational aids and radio equipment essentialfor safe flight in a modern aircraft. Electricityis used to heat windows, pump fuel, operatebrakes, open and shut valves, and to controlnumerous other systems within the aircraft. Infact, aircraft that use modern fly-by-wire con-trols could not even get off the ground without

Table 5.1

Unit Abbreviation Symbol Notes

Ampere A I Unit of electric current (a current of 1 A flows in a conductorwhen a charge of 1 C is transported in a time interval of 1 s)

Coulomb C Q Unit of electric charge or quantity of electricity (a fundamental unit)Farad F C Unit of capacitance (a capacitor has a capacitance of 1 F when a charge

of 1 C results in a potential difference (p.d.) of 1 V across its plates)Henry H L Unit of inductance (an inductor has an inductance of 1 H when an

applied current changing uniformly at a rate of 1 A/s produces ap.d. of 1 V across its terminals)

Hertz Hz f Unit of frequency (a signal has a frequency of 1 Hz if one completecycle occurs in a time interval of 1 s)

(continued)

the electrical systems and supplies that makethem work!

In this chapter we will explain electricity interms of electric charge, current, voltage andresistance. We will begin by introducing youto some important concepts, including the Bohrmodel of the atom and the fundamental natureof electric charge and conduction in solids, liq-uids and gases. Next we will look briefly at static

electricity before moving on to explain some ofthe terminology that we use with electric circuitsand measurements. We also describe some of themost common types of electrical and electroniccomponent including resistors, capacitors,inductors, transformers, generators and motors.

5.1.1 Electrical units and symbols

You will find that a number of units and symbolsare commonly encountered in electrical circuits

so let us get started by introducing some of them.In fact, it is important to get to know these unitsand also to be able to recognize their abbre-viations and symbols before you actually needto use them. Later we will explain how theseunits work in much greater detail but for nowwe will simply list them (Table 5.1) so that atleast you can begin to get to know somethingabout them.

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312 Aircraft engineering principles

Table 5.1 (continued)

Unit Abbreviation Symbol Notes

Joule J W, J Unit of energy (a fundamental unit)Ohm R Unit of resistance (a fundamental unit)Second s t Unit of time (a fundamental unit)

Siemen S G Unit of conductance (the reciprocal of resistance)Tesla T B Unit of magnetic flux density (a flux density of 1 T is producedwhen a flux of 1 Wb is present over an area of 1 m2)

Volt V V, E Unit of electric potential (we sometimes refer to this as electromotiveforce (e.m.f.) or p.d.

Watt W P Unit of power (equal to 1 J of energy consumed in a time of 1 s)Weber Wb Unit of magnetic flux (a fundamental unit)

Key point

Symbols used for electrical and other quantities

are normally shown in italic font whilst units areshown in normal (non-italic) font. Thus V and Iare symbols whilst V and A are units.

5.1.2 Multiples and sub-multiples

Unfortunately, because the numbers can be verylarge or very small, many of the electrical unitscan be cumbersome for everyday use. For exam-ple, the voltage present at the antenna inputof a very high frequency (VHF) radio could beas little as 0.0000015 V. At the same time, theresistance present in an amplifier stage couldbe as high as 10,000,000! Clearly we needto make life a little easier. We can do this byusing a standard range of multiples and sub-multiples. These use a prefix letter in order toadd a multiplier to the quoted value, as follows:

Prefix Abbrev. Multiplier

Tera T 1012

(=1,000,000,000,000)Giga G 109 (=1,000,000,000)Mega M 106 (=1,000,000)Kilo k 103 (=1000)(None) (None) 100 (=1)Centi c 102 (=0.01)Milli m 103 (=0.001)Micro 106 (=0.000,001)Nano n 109 (=0.000,000,001)Pico p 1012 (=0.000,000,000,001)

Example 5.1

An indicator lamp requires a current of 0.15 A.Express this in mA.

Solution

To convert A to mA, we apply a multiplier of

103

or 1000. Thus to convert 0.15 A to mA wemultiply 0.15 by 1000 as follows:

0.15 A = 0.15 1000 = 150mA

Key point

Multiplying by 1000 is equivalent to moving thedecimal point three places to the right whilstdividing by 1000 is equivalent to moving thedecimal point three places to the left. Similarly,multiplying by 1,000,000 is equivalent to movingthe decimal point six places to the right whilst

dividing by 1,000,000 is equivalent to moving thedecimal point six places to the left.

Example 5.2

An insulation tester produces a voltage of2750 V. Express this in kV.

Solution

To convert V to kV we apply a multiplier of

103 or 0.001. Thus we can convert 2750 V tokV as follows:

2750 V = 2750 0.001 = 2.75kVHere, multiplying by 0.001 is equivalent tomoving the decimal point three places to the left.

Example 5.3

A capacitor has a value of 27,000 pF. Expressthis in F.

Solution

There are 1,000,000 pF in 1F. Thus, to expressthe value in 27,000 pF inF we need to multiply

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Electrical fundamentals 313

by 0.000,001. The easiest way of doing thisis simply to move the decimal point six placesto the left. Hence 27,000 pF is equivalent to0.027F (note that we have had to introduce anextra zero before 2 and after the decimal point).

Test your understanding 5.1

1. State the units for electric current.

2. State the units for frequency.

3. State the symbol used for capacitance.

4. State the symbol used for conductance.

5. A pulse has a duration of 0.0075s. Express this

time in ms.

6. A generator produces a voltage of 440V. Express

this in kV.

7. A signal has a frequency of 15.62 MHz. Express this

in kHz.

8. A current of 570A flows in a resistor. Express this

current in mA.

9. A capacitor has a value of 0.22 F. Express this capac-

itance in nF.

10. A resistor has a value of 470 k. Express this resistance

in M.

5.2 Electron theory

Syllabus

Structure and distribution of electrical chargeswithin atoms, molecules, ions and compounds;Molecular structure of conductors, semiconduc-tors and insulators.

Knowledge level key

1

A

1

B1

1

B2

To understand what electricity is we need to takea look inside the atoms that make up all formsof matter. Since we cannot actually do this witha real atom we will have to use a model. Fortu-nately, understanding how this model works isnot too difficult just remember that what weare talking about is very, very small!

5.2.1 Atomic structure

As you already know, all matter is made up ofatoms or groups of atoms (molecules) bondedtogether in a particular way. In order to under-stand something about the nature of electrical

Figure 5.1 The Bohr model of the atom.

charge we need to consider a simple model ofthe atom. This model known as the Bohr model(see Figure 5.1) shows a single atom consistingof a central nucleus with orbiting electrons.

Within the nucleus there are protons whichare positively charged and neutrons which, astheir name implies, are electrical neutral andhave no charge. Orbiting the nucleus are elec-trons that have a negative charge, equal in mag-nitude (size) to the charge on the proton. Theseelectrons are approximately 2000 times lighterthan the protons and neutrons in the nucleus.

In a stable atom the number of protons andelectrons are equal, so that overall, the atomis neutral and has no charge. However, if we

rub two particular materials together, electronsmay be transferred from one to another. Thisalters the stability of the atom, leaving it with anet positive or negative charge. When an atomwithin a material looses electrons it becomespositively charged and is known as a positiveion, when an atom gains an electron it has asurplus negative charge and so is known as anegative ion. These differences in charge cancause electrostatic effects. For example, comb-

ing your hair with a nylon comb may result ina difference in charge between your hair andthe rest of your body, resulting in your hairstanding on end when your hand or some otherdifferently charged body is brought close to it.

The number of electrons occupying a givenorbit within an atom is predictable and is basedon the position of the element within the peri-odic table. The electrons in all atoms sit in aparticular position (shell) dependent on their

energy level. Each of these shells within the atomis filled by electrons from the nucleus outwards,as shown in Figure 5.2. The first, inner most,of these shells can have up to two electrons; the

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second shell can have up to eight and the thirdup to 18.

5.2.2 Conductors and insulators

A material which has many free electrons avail-

able to act as charge carriers and thus allowscurrent to flow freely is known as a conduc-tor. Examples of good conductors include alu-minium, copper, gold and iron. Figure 5.2shows a material with one outer electron thatcan become easily detached from the parentatom. It requires a small amount of externalenergy to overcome the attraction of the nucleus.Sources of such energy may include heat, lightor electrostatic fields. The atom once detached

Figure 5.2 A material with a loosely bound electronin its outer shell.

Figure 5.3 Free electrons and the application of anexternal force: (a) electrons in random motion and(b) current flow.

from the atom is able to move freely around thestructure of the material and is called a free elec-tron. It is these free electrons that become thecharge carriers, within a material. Materials thathave large numbers of free electrons make goodconductors of electrical energy and heat.

In a material containing free electrons theirdirection of motion is random, as shown inFigure 5.3(a), but if an external force is appliedthat causes the free electrons to move in a uni-form manner (Figure 5.3(b)) an electric currentis said to flow.

Metals are the best conductors, since theyhave a very large number of free electrons avail-able to act as charge carriers. Materials that donot conduct charge are called insulators, theirelectrons are tightly bound to the nuclei of theiratoms. Examples of insulators include plastics,glass, rubber and ceramic materials.

The effects of electric current flow can bedetected by the presence of one or more of thefollowing effects: light, heat, magnetism, chem-ical, pressure and friction. For example, if apiezoelectric crystal is subject to an electricalcurrent it can change its shape and exert pres-sure. Heat is another, more obvious effect from

electric heating elements.

Key point

Metals, like copper and silver, are good conduc-tors of electricity and they readily support the flowof current. Plastics, rubber and ceramic materi-als are insulators and do not support the flow ofcurrent.

5.2.3 Semiconductors

Some materials combine some of the electricalcharacteristics of conductors with those of insu-lators. They are known as semiconductors. Inthese materials there may be a number of freeelectrons sufficient to allow a small current toflow. It is possible to add foreign atoms (calledimpurity atoms) to the semiconductor materialthat modify the properties of the semiconductor.Varying combinations of these additional atomsare used to produce various electrical devices,

such as diodes and transistors. Common typesof semiconductor materials are silicon, germa-nium, selenium and gallium.

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Key point

Semiconductors are pure insulating materialswith a small amount of an impurity elementpresent. Typical examples are silicon andgermanium.

5.2.4 Temperature effects

As stated earlier, all materials offer some resis-tance to current flow. In conductors the free elec-trons, rather than passing unobstructed throughthe material, collide with the relatively large andsolid nuclei of the atoms. As the temperatureincreases, the nuclei vibrate more energeticallyfurther obstructing the path of the free electrons,

causing more frequent collisions. The result isthat the resistance of conductors increases withtemperature.

Due to the nature of the bonding in insulators,there are no free electrons, except that whenthermal energy increases as a result of a temper-ature increase, a few outer electrons manage tobreak free from their fixed positions and act ascharge carriers. The result is that the resistanceof insulators decreases as temperature increases.

Semiconductors behave in a similar mannerto insulators. At absolute zero (273C) boththe types of material act as perfect insulators.However, unlike the insulator, as temperatureincreases in a semiconductor large numbers ofelectrons break free to act as charge carriers.

Figure 5.4 Variation of resistance with temperaturefor various materials.

Therefore, as temperature increases, the resis-tance of a semiconductor decreases rapidly.

By producing special alloys, such as eurekaand manganin that combine the effects of insu-lators and conductors, it is possible to produce amaterial where the resistance remains constantwith increase in temperature. Figure 5.4 showshow the resistance of insulators, semiconductorsand conductors change with temperature.


1. In a stable neutral atom the number of _______ and

_______ are equal and there is no overall charge.

2. When an atom within a material losses electrons

it becomes ________ charged and is known as a

______________.

3. When an atom gains an electron it has a surplus_________ charge and so known as a _______

_______.

4. The electrical properties of a material are determined

by the number of ______________ present.

5. Materials that do not conduct electric charge are called

_______.

6. Name two materials that act as good electrical

conductors.

7. Name two materials that act as good electrical

insulators.

8. Name two semiconductor materials.9. Explain briefly how the resistance of a metallic conduc-

tor varies with temperature.

10. Explain briefly how the resistance of an insulator varies

with temperature.

5.3 Static electricity and conduction

Syllabus

Static electricity and distribution of electro-static charges; Electrostatic laws of attractionand repulsion; Units of charge, Coulombs law;Conduction of electricity in solids, liquids, gasesand a vacuum.

Knowledge level key

1

A

2

B1

2

B2

Electric charge is all around us. Indeed, many

of the everyday items that we use in the homeand at work rely for their operation on the exis-tence of electric charge and the ability to make

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that charge do something useful. Electric chargeis also present in the natural world and anyonewho has experienced an electric storm cannotfail to have been awed by its effects. In thissection we begin by explaining what electriccharge is and how it can be used to produceconduction in solids, liquids and gases.

5.3.1 Static electricity

We have already found that, if a conductor hasa deficit of electrons, it will exhibit a net positivecharge. On the other hand, if it has a surplus ofelectrons, it will exhibit a net negative charge.An imbalance in charge can be produced byfriction (removing or depositing electrons using

materials, such as silk and fur, respectively)or induction (by attracting or repelling elec-trons using a second body which is, respectively,positively or negatively charged).

5.3.2 Force between charges

Consider two small charged bodies of negligibleweight are suspended as shown in Figure 5.5.If the two bodies have charges with the samepolarity (i.e. either both positively or bothnegatively charged) the two bodies will moveapart, indicating that a force of repulsion existsbetween them. On the other hand, if the charges

Figure 5.5 Force between charged bodies:(a) charges with same polarity and (b) charges withopposite polarity.

on the two bodies are unlike (i.e. one positivelycharged and one negatively charged), the twobodies will move together indicating that a forceof attraction exists between them. From this wecan conclude that like charges repel and unlikecharges attract.

Key point

Charges with the same polarity repel one anotherwhilst charges with opposite polarity will attractone another.

5.3.3 Coulombs law

Coulombs law states that if charged bodies existat two points, the force of attraction (if thecharges are of opposite charge) or repulsion (ifof like charge) will be proportional to the prod-uct of the magnitude of the charges divided bythe square of their distance apart. Thus:

F= kQ1Q2d2

where Q1 and Q2 are the charges present at thetwo points (in C), d the distance separating thetwo points (in m), F the force (in N) and k is a

constant depending upon the medium in whichthe charges exist.

In vacuum or free space

k = 140

where 0 is the permittivity of free space(8.854 1012 C/Nm2).

Combining the two previous equations gives:

F=

Q1Q2

40d2

or

F= Q1Q24 8.854 1012 d2 N

If this formula looks complex there are only acouple of things that you need to remember.The denominator simply consists of a constant(4 8.854 1012) multiplied by the squareof the distance, d. Thus we can re-write theformula as:

F Q1Q2d2

where the symbol denotes proportionality.

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5.3.4 Electric fields

The force exerted on a charged particle is a man-ifestation of the existence of an electric field. Theelectric field defines the direction and magnitudeof a force on a charged object. The field itself is

invisible to the human eye but can be drawn byconstructing lines which indicate the motion of afree positive charge within the field; the numberof field lines in a particular region being used toindicate the relative strength of the field at thepoint in question.

Figures 5.6 and 5.7 show the electric fieldsbetween isolated unlike and like charges whilst

Figure 5.6 Electric field between two isolatedunlike charges.

Figure 5.7 Electric field between two isolated likecharges.

Figure 5.8 shows the field which exists betweenthe two charged parallel metal plates (note thefringingwhich occurs at the edges of the plates).

5.3.5 Electric field strength

The strength of an electric field (E) is pro-portional to the applied p.d. and inverselyproportional to the distance between the twoconductors (see Figure 5.9). The electric fieldstrength is given by:

E = Vd

Figure 5.8 Electric field between two chargedparallel metal plates.

Figure 5.9 Electric field strength.

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where E is the electric field strength (in V/m), Vis the applied p.d. (in V) and d is the distance(in m).

Example 5.4

Two charged particles are separated by a dis-tance of 25 mm. Calculate the force betweenthe two charges if one has a positive charge of0.25C and the other has a negative charge of0.4C. What will the relative direction of theforce be?

Solution

Now F= Q1Q24 8.854 1012 d2

where Q1 =0.25C= 0.25 106 C, Q2 =0.4C=0.4 106 C, and d= 2.5mm=2.5 103 m, thus:

F= 0.25 106 0.4 106

4 8.854 1012 (2.5 103)2

= 0.1 1012

4 8.854 1012 6.25 106

or

F= 0.14 8.854 6.25 106

= 0.1695.39 106 = 1.438 10

2

Hence F=

1.438

102 N=

143.8 N

Example 5.5

Two charged particles have the same positivecharge and are separated by a distance of 10 mm.If the force between them is 0.1 N, determine thecharge present.

Solution

Now F= Q1Q24 8.854 1012 d2

where F=0.1 N, d=0.01 m and Q1 =Q2 =Q,thus:

0.1 = QQ4 8.854 1012 (0.01)2

Re-arranging the formula to make Q the subjectgives:

Q2 = 0.1 4 8.854 1012 (0.01)2

or

Q =

0.1 4 8.854 1012 (0.01)2

= 4

8.854

1017

=

111.263 1017 =

11.1263 1016

thus

Q =

11.1263

1016 = 3.336 108 C= 0.03336C

Example 5.6

Two parallel conductors are separated by a dis-tance of 25 mm. Determine the electric fieldstrength if they are fed from a 600V directcurrent (DC) supply.

Solution

The electric field strength will be given by:

E=

V

d

where V= 600 V and d= 25mm=0.025 m,thus:

E = 6000.025

= 24,000 V/m = 24kV/m

Example 5.7

The field strength between the two parallel

plates in a cathode ray tube is 18 kV/m. If theplates are separated by a distance of 21 mm,determine the p.d. that exists between the plates.

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Solution

The electric field strength will be given by:

E = Vd

Re-arranging this formula to make Vthe subjectgives:

V= E dNow E=18 kV/m=18,000 V/m and d=21mm= 0.021 m, thus:

V= 18,000 0.021 = 378V

5.3.6 Conduction of electricity in

solids, liquids, gases and a vacuumIn order to conduct an electric current a materialmust contain charged particles. In solids (suchas copper, lead, aluminium and carbon) it is thenegatively charged electrons that are in motion.In liquids and gases, the current is carried by thepart of a molecule that has acquired an electriccharge. These are called ions and they can pos-sess either a positive or a negative charge. Exam-ples include hydrogen ions (H+), copper ions

(Cu++) and hydroxyl ions (OH). It is worthnoting that pure distilled water contains noions and is thus a poor conductor of electricitywhereas salt water contains ions and is thereforea relatively good conductor of electricity.

Finally, you might be surprised to learn thatan electric current can pass through a vacuum. Itdoes this in the form of a stream of electrons lib-erated from a hot metal surface that can be madeto travel from a point that has a negative poten-

tial (known as a cathode) towards another pointwhich has a high positive potential (known asan anode). This is the principle of the cathoderay tube that you find in your television set orcomputer display!

Key point

Current flow in liquids and gases is made possi-ble by means of positively or negatively chargedmolecules called ions. In a vacuum, current flow

is made possible by means of a moving stream ofnegatively charged electrons, as in the cathoderay tube.


1. If a body has a shortage of electrons it will exhibit a

___________ charge.

2. Isolated charges having the same polarity will

___________ one another.

3. List the factors that determine the force that exists

between two charges.

4. Two charges are separated by a distance of 1 mm. If the

distance increases to 2 mm whilst the charges remain

unchanged, by how much will the force between them

change?

5. Two plates are separated by a distance of 100 mm. If

the p.d. between the plates is 200V where what will the

electric field strength be?

6. The electric field between two parallel plates is 2 kV/m.

If the plates are separated by a distance of 4 mm,

determine the p.d. between the plates.

7. Two charged particles have the same positive chargeand are separated by a distance of 2 mm. If the force

between them is 0.4 N, determine the charge present.

8. In liquids and gases electric current is carried by

___________.

9. An electric current can be made to pass through a vac-

uum by means of a stream of ___________ charged

___________.

10. Explain why salt water conducts electricity whilst pure

distilled water does not.

5.4 Electrical terminology

Syllabus

The following terms, their units and factorsaffecting them; p.d., e.m.f., voltage, current,resistance, conductance, charge, conventionalcurrent flow and electron flow.

Knowledge level key

1

A

2

B1

2

B2

This section will introduce you to some of theterminology that we use in electric circuits. Inaddition to the syllabus topics listed above wehave also included two other important terms,power and energy.

5.4.1 ChargeAll electrons and protons have an electro-static charge, its value is so small that a more

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convenient unit of charge is needed for prac-tical use, which we call the coulomb. Onecoulomb C is the total charge Q of 6.211018electrons. Thus a single electron has a charge of1.61 1019 C.

5.4.2 Current

Current, I, is defined as the rate of flow of chargeand its unit is the ampere, A. One ampere isequal to one coulomb per second, or:

One ampere of current, I= Qt

where t is time in seconds.So, for example, if a steady current of 3 A

flows for 2 min, then the amount of chargetransferred will be:

Q = I t= 3 A 120s = 360C

Key point

Current is the rate of flow of charge. Thus, if morecharge moves in a given time, more current willbe flowing. If no charge moves then no current isflowing.

5.4.3 Conventional current and

electron flow

In Section 5.2.2 we described electric current interms of the organized movement of electronsin a metal conductor. Owing to their nega-tive charge, electrons will flow from a negativepotential to a more positive potential (recall thatlike-charges attract and unlike-charges repel).

However, when we indicate the direction of cur-rent in a circuit we show it as moving from apoint that has the greatest positive potential toa point that has the most negative potential. Wecall this conventional current and, although itmay seem to be odd, you just need to rememberthat it flows in the opposite direction to that ofthe motion of electrons!

Key point

Electrons move from negative to positive whilstconventional current is assumed to flow frompositive to negative.

5.4.4 Potential difference (voltage)

The force that creates the flow of current (orrate of flow of charge carriers) in a circuit isknown as the e.m.f. and it is measured in volts(V). The p.d. is the voltage difference or voltage

drop between two points.One volt is the p.d. between two points if onejoule of energy is required to move one coulombof charge between them. Hence:

V= WQ

where W is the energy and Q is the charge, asbefore. Energy is defined later in Section 5.4.8.

5.4.5 ResistanceAll materials at normal temperatures oppose themovement of electric charge through them, thisopposition to the flow of the charge carriers isknown as the resistance R of the material. Thisresistance is due to collisions between the chargecarriers (electrons) and the atoms of the mate-rial. The unit of resistance is the ohm, withsymbol .

Note that 1 V is the e.m.f. required to move

6.21 1018 electrons (1 C) through a resistanceof 1 in 1 s. Hence:

V=

Q

t

R

where Q is the charge, t is the time and R is theresistance.

Re-arranging this equation to make R thesubject gives:

R = V tQ

We shall be looking at the important relation-ship between voltage, V, current, I and resis-tance, R, later on in Sections 5.7.1 and 5.7.2.

5.4.6 Conductance

Conductance is the inverse of resistance. In otherwords, as the resistance of a conductor increases

its conductance reduces, and vice versa. A mate-rial that has a low value of conductance will notconduct electricity as well as a material that has a

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