3.1 — Electron Theory

Electron theory explains the fundamental nature of electricity by examining atomic structure and the behaviour of electrons. This section lays the groundwork for understanding how electrical current flows and why different materials conduct electricity to different degrees — essential knowledge for every aircraft maintenance engineer working with electrical systems.

Structure of Matter

All matter is composed of atoms, the smallest particles of an element that retain its chemical identity. Each atom consists of a central nucleus containing positively charged protons and (except in ordinary hydrogen) electrically neutral neutrons, surrounded by orbiting negatively charged electrons.

Particle	Location	Charge	Relative Mass
Proton	Nucleus	Positive (+1)	1
Neutron	Nucleus	Neutral (0)	1
Electron	Shells (orbits)	Negative (−1)	≈ 1/1836

In a neutral atom the number of electrons equals the number of protons, so the overall charge is zero. The atomic number (Z) equals the number of protons and defines the element. The mass number (A) is the total of protons plus neutrons.

Electron Shells and Energy Levels

Electrons occupy discrete energy levels called shells, labelled K, L, M, N outward from the nucleus. Each shell has a maximum capacity:

Shell	Number (n)	Max Electrons
K	1	2
L	2	8
M	3	18
N	4	32

The outermost shell is called the valence shell, and the electrons in it are valence electrons. These determine the electrical and chemical properties of the element.

Charge, Mass and Scale

The charge on a proton and the charge on an electron are exactly equal in size and opposite in sign. That size is the elementary charge, and no smaller quantity of free charge exists anywhere in nature — charge comes only in whole multiples of it. A proton carries \( +1.602 \times 10^{-19} \) C; an electron carries \( -1.602 \times 10^{-19} \) C. The minus sign is part of the value and should never be dropped: it is the reason adding electrons to a body makes it more negative rather than more positive.

The masses are nothing like as balanced as the charges. A proton has a mass of about \( 1.673 \times 10^{-27} \) kg and a neutron is marginally heavier still, while an electron is only about \( 9.11 \times 10^{-31} \) kg — some 1,836 times lighter. Two consequences follow directly. Almost the whole mass of an atom is concentrated in its nucleus, so the mass number counts nucleons and ignores electrons altogether. And because electrons weigh so little, an atom that gains or loses a few of them changes its electrical charge dramatically while its mass barely alters at all.

The nucleus is also extraordinarily small compared with the atom that surrounds it: of the order of \( 10^{-15} \) m across against roughly \( 10^{-10} \) m for the whole atom, so its diameter is around one hundred-thousandth of the atom's. An atom is therefore mostly empty space, and what one atom presents to its neighbours is not its nucleus but the outer edge of its electron cloud. This is why every chemical property and every electrical property of a material is settled by the outermost electrons, and why nothing an aircraft engineer does to a wire ever touches its nuclei.

What holds the structure together is the electrostatic attraction between the positive nucleus and the negative electrons. That force obeys an inverse-square law, so an electron twice as far out is attracted only a quarter as strongly; on top of that, the inner shells of electrons partly screen the nuclear charge from the outer ones. Both effects point the same way: the further out a shell lies, the more weakly its electrons are held. Everything in this note about conductors, insulators and ionisation is a consequence of that one statement.

Neutrons, Isotopes and the Hydrogen Exception

Because the mass number counts protons plus neutrons and the atomic number counts protons alone, the number of neutrons in any nucleus is simply the difference between them. A copper-63 atom has \( 63 - 29 = 34 \) neutrons alongside its 29 protons, and if it is electrically neutral it also has 29 orbiting electrons. An aluminium-27 atom has \( 27 - 13 = 14 \) neutrons and 13 electrons.

Atoms of the same element can carry different numbers of neutrons; these variants are called isotopes. They share an atomic number, so they are chemically and electrically identical — conduction depends entirely on electrons, and isotopes differ only in nuclear mass. The one case worth memorising is the lightest atom of all: ordinary hydrogen consists of a single proton with a single electron orbiting it and no neutron at all. This is why the correct statement is that neutrons are found in the nucleus of most atoms rather than all of them.

How the Shells Actually Fill

The \( 2n^2 \) rule gives the maximum capacity of a shell, not the order in which electrons are added. In a neutral atom in its normal, lowest-energy state the outermost shell never holds more than eight electrons, no matter how large its capacity. So filling proceeds K, then L, then M up to eight — and at that point the next electron starts the N shell rather than continuing to fill M toward its capacity of 18.

Potassium shows this clearly. With 19 electrons it fills as 2, 8, 8, 1: the M shell stops at eight and the nineteenth electron opens the N shell. Potassium therefore has a single, remote, weakly held valence electron and behaves as a strongly conducting metal, even though its M shell holds only eight of the eighteen electrons it could take. Copper, with 29 electrons, fills as 2, 8, 18, 1 — here the M shell does reach 18, and the lone N-shell electron is the one valence electron that makes copper the conductor of choice for aircraft wiring.

Element	Atomic number (Z)	Electrons per shell (K, L, M, N)	Valence electrons	Bulk electrical behaviour
Hydrogen	1	1	1	Insulating gas; bonds as \( \text{H}_2 \)
Helium	2	2	2 (K shell full)	Inert insulating gas; forms no bonds
Oxygen	8	2, 6	6	Insulating gas; bonds as \( \text{O}_2 \)
Aluminium	13	2, 8, 3	3	Conductor (power feeders, busbars)
Silicon	14	2, 8, 4	4	Semiconductor
Chlorine	17	2, 8, 7	7	Non-conductor; readily gains one electron
Copper	29	2, 8, 18, 1	1	Excellent conductor
Germanium	32	2, 8, 18, 4	4	Semiconductor

Read down the valence column and much of what follows in this note is already visible: among the solid elements, one to three valence electrons gives a metal, four gives a semiconductor, and a full or nearly full outer shell — most often seven or eight valence electrons — gives an insulator. Aluminium is worth noting particularly, because it is a genuine conductor carrying three valence electrons — the boundary is not at one or two. The two gases at the head of the table are a useful reminder that the rule describes how electrons are bound in the bulk material rather than in the isolated atom: hydrogen's single electron is not free to wander, because in \( \text{H}_2 \) it is tied up in a shared pair, and helium's shell is complete already.

Energy Levels, Excitation and Ionisation

Calling the shells "energy levels" is more than a label. An electron may occupy an allowed level but never the space between two of them, so it cannot drift outward gradually; it must absorb a specific quantum of energy that exactly matches the step and jump. An electron pushed to a higher shell this way is said to be excited, and it falls back after a short time, releasing the same energy again — often as light, which is exactly how a gas-discharge lamp works. Supply more energy still and the electron leaves the atom's influence altogether. That is ionisation, and it is the point at which an electron becomes available to carry current.

Two other familiar light sources are worth placing against that one. A light-emitting diode works on the same principle one step removed: the electron drops across the forbidden gap of a semiconductor rather than between the shells of an isolated atom, and the size of that gap fixes the colour. An incandescent filament does not work this way at all. It emits because it is a solid heated until it glows, and a hot solid radiates a continuous thermal spectrum — which is why a filament reddens as it is dimmed and why its light contains no spectral lines, while a gas-discharge lamp shows the sharp lines of its own atoms' energy steps. That fits what the band model later in this note says about solids: pack atoms together into a metal and their outer levels merge into continuous bands, leaving no discrete shell steps to jump between.

Energies this small are quoted in electron-volts rather than joules. One electron-volt is the energy gained by one electron moving through a potential difference of one volt, which numerically is the elementary charge expressed in joules.

Keep this unit in mind: the band-gap figures quoted later for semiconductors and insulators are in electron-volts, and they only become meaningful once they can be compared with the energy actually available inside a material at working temperature.

Molecules, Compounds and Chemical Bonding

Isolated atoms are rare. Almost every material an engineer meets is atoms joined to other atoms, and the way they are joined decides where the charge sits and whether any of it is free to move. Bonding is therefore not a chemistry digression — it is the direct explanation of why copper conducts, why PVC does not, and why dry salt insulates while salt water does not.

Elements, Compounds and Mixtures

• Element — a substance built from one kind of atom only, identified by its atomic number. Copper, aluminium, silicon and oxygen are elements.
• Compound — two or more different elements chemically bonded in a fixed proportion. The compound's properties bear no relation to those of its ingredients: sodium is a metal that reacts violently with water and chlorine is a poisonous gas, yet sodium chloride is common salt.
• Mixture — substances present together but not chemically bonded, in any proportion, and separable by physical means. Air is a mixture of gases; brass is a mixture (an alloy) of copper and zinc.

A molecule is the smallest particle of a substance that can exist on its own and still show that substance's chemical properties. It is built from two or more atoms bonded together, which makes it larger than an atom and vastly larger than an electron. Where those atoms are all the same kind the result is a molecule of an element — oxygen travels as \( \text{O}_2 \), nitrogen as \( \text{N}_2 \), hydrogen as \( \text{H}_2 \). Where they are of different kinds the result is a molecule of a compound, such as water \( \text{H}_2\text{O} \) or carbon dioxide \( \text{CO}_2 \). The unit built from two or more different types of atom is therefore a molecule of a compound, and that distinction is a favourite of examiners.

One refinement is worth knowing because it explains the ionic case below. Discrete molecules genuinely exist only where atoms are bonded covalently. Ionic compounds and metals are continuous lattices with no individual molecules in them, so their smallest repeating unit is properly called a formula unit. In Part-66 examinations, however, the expected answer for the smallest part of a compound or substance remains the molecule.

Why Atoms Bond at All

Bonding is driven entirely by the valence shell. A full outer shell — two electrons for the K shell, eight for any shell beyond it — is the stable, low-energy arrangement, which is why the noble gases such as helium neither bond nor conduct. Every other atom reaches that arrangement in one of three ways: by giving valence electrons away, by taking them, or by sharing them. Which of the three routes it takes is exactly what determines the material's electrical character.

Covalent Bonding – Electrons Shared

Two atoms that are both short of a full shell can each contribute electrons to a shared pair which then counts toward both shells at once. An oxygen atom has six valence electrons and needs two more; two oxygen atoms therefore share two pairs between them, so each atom sees an effective eight. That double bond is what holds an oxygen molecule together, and note precisely what is shared: electrons. Protons and neutrons are locked in their nuclei by the nuclear force and are never exchanged in any chemical or electrical process.

The consequence for charge distribution is that nothing is transferred and nothing is set loose. The shared pairs sit in fixed positions between the two nuclei, every electron is accounted for, and there are no spare carriers. A wholly covalent solid is therefore an insulator until something breaks a bond. Diamond is the extreme illustration: every carbon atom shares four pairs with four neighbours, the whole lattice is tied up, and the energy step needed to release an electron is above five electron-volts. It is also the standing exception to the valence-counting rule set out earlier: a solid element with four valence electrons that is an insulator rather than a semiconductor, because counting valence electrons only predicts the class, while the size of the gap decides it. Silicon uses the same four-neighbour arrangement, but its energy step is smaller by a factor of about five — and that single difference is the whole distinction between an insulator and a semiconductor.

Ionic Bonding – Electrons Transferred

Where one atom has very few valence electrons and the other is only just short of a full shell, sharing is not the cheapest route — outright transfer is. Sodium fills as 2, 8, 1; shedding its single outer electron leaves the stable 2, 8 arrangement behind. Chlorine fills as 2, 8, 7 and completes itself by accepting exactly one. So sodium hands its valence electron to chlorine, and neither particle is neutral any more: the sodium is left with 11 protons and 10 electrons, the chlorine with 17 protons and 18 electrons. The bond is nothing more than the electrostatic attraction between those two opposite charges.

Here the charge really is separated, and it is locked into a rigid three-dimensional lattice of alternating positive and negative sites. There are no free electrons anywhere in that lattice, and the ions themselves cannot move, so a dry ionic solid is an insulator. Melt it, or dissolve it in water, and the lattice releases its ions; now the charged particles themselves are mobile and the material conducts readily. This is conduction by ion transport rather than by electron transport, and it is the second of the two ways charge moves through matter.

Metallic Bonding – Electrons Delocalised

Metals take a third route. Their valence electrons are not paired off with one particular neighbour but surrendered to the lattice as a whole, so what remains is a regular array of positive ion cores immersed in a cloud of electrons that belong to no single atom. The bond is the mutual attraction between those fixed positive cores and that mobile negative cloud, which is why it holds the metal together perfectly well even though the electrons themselves are wandering.

Three practical consequences follow, and all three matter on an aircraft. First, the charge carriers are already free before any voltage is applied, so conduction needs no bond to be broken and works at any temperature. Second, the bond has no preferred direction, so planes of ions can slide past one another without it being destroyed — that is why copper can be drawn into wire, bent around a former and crimped without fracturing, while an ionic or covalent solid of the same size would shatter. Third, the same mobile electrons that carry current also carry heat, so good electrical conductors are also good thermal conductors, and a heavy feeder can act as a heat path into the equipment at either end of it.

Polar Molecules and Dipoles

When a covalent bond joins two different elements, the shared pair is rarely shared fairly. The atom with the stronger pull on electrons keeps the pair closer to itself, so although the molecule remains neutral overall, one end of it carries a small negative charge and the other an equal small positive charge. A molecule with this permanent internal charge separation is a polar molecule, and the separated pair of charges is an electric dipole. Water is the standard example: its bent shape prevents the two bond dipoles from cancelling, leaving the oxygen end negative and the hydrogen end positive.

Three electrical consequences follow. Polar molecules can pull an ionic lattice apart, each ion being surrounded by water molecules turning their opposite ends toward it — that is precisely how water dissolves salt and manufactures an electrolyte out of two insulators. Polar insulating materials also absorb moisture more readily than non-polar ones, so their insulation resistance falls when damp and recovers when dried. And although an applied electric field cannot free electrons inside an insulator at any strength short of breakdown, it can rotate the dipoles and distort the electron clouds, storing energy in that displacement; the effect is called polarisation, and it is why placing a dielectric between two plates lets them hold more charge at the same voltage. Under alternating voltage those dipoles have to reverse every cycle, and the internal friction of doing so appears as heat in the insulation, growing as the frequency rises.

The fluoropolymers used for aircraft wire insulation are chosen partly on this basis. Their molecules are highly symmetric, so the individual bond dipoles cancel and the net molecular dipole is close to zero. The results are a low dielectric constant, very low dielectric loss and little moisture uptake — exactly what is wanted where wiring runs alongside sensitive signal lines, coaxial feeders and high-frequency equipment.

Where the Charge Actually Sits

The syllabus asks for the structure and distribution of electrical charge in atoms, molecules, ions and compounds. Collecting the cases above gives the complete answer, and the final column is the one that decides whether the material can carry a current.

Structure	Positive charge	Negative charge	Net charge	Mobile carriers
Neutral atom	Protons, concentrated in the tiny nucleus	Electrons, spread through the shells	Zero	None until an electron is freed
Molecule of an element, e.g. \( \text{O}_2 \)	Nuclei, symmetrically placed	Shared pairs, symmetrically placed	Zero	None
Polar molecule of a compound, e.g. \( \text{H}_2\text{O} \)	Hydrogen end slightly positive	Oxygen end slightly negative	Zero overall, but separated inside the molecule	None; the dipole can only rotate
Ion	Protons, unchanged in the nucleus	Electrons, now too few or too many to balance them	Positive if electrons were lost, negative if they were gained	The whole ion, wherever it is free to move
Ionic compound, solid	Positive ion sites in the lattice	Negative ion sites in the lattice	Zero	None — the lattice is rigid
Ionic compound, molten or dissolved	Free positive ions	Free negative ions	Zero	Both, drifting in opposite directions
Metal	Fixed positive ion cores	Delocalised electron cloud	Zero	Electrons, throughout the material

Ions and Ionisation

An atom is electrically neutral only while its electron count exactly matches its proton count. Disturb that balance by adding or removing one or more electrons and the atom is left with a net charge. A charged atom is called an ion, and the process of creating one is ionisation.

• Positive ion (cation) — the atom has lost one or more electrons. Protons now outnumber electrons, so the surplus positive charge of the nucleus is no longer cancelled and the net charge is positive.
• Negative ion (anion) — the atom has gained one or more electrons. Electrons now outnumber protons and the net charge is negative.

Note carefully what does not change. The protons stay locked in the nucleus throughout; ordinary ionisation moves electrons and nothing else. An ionised copper atom is still copper, because its atomic number is untouched — only its charge has altered. Removing a proton would change the element itself, but that is a nuclear process and has nothing to do with electricity.

Ionisation Energy

The ionisation energy of an atom is the energy needed to strip away its most loosely held electron. That electron is always in the outermost shell, where the nuclear attraction has been weakened both by distance and by the screening effect of the inner shells, so it is by far the cheapest one to remove. Across any row of the periodic table the ionisation energy rises as the valence shell fills: an atom with one or two valence electrons parts with them easily, while one with a full or nearly full outer shell holds on tightly and will not release an electron under ordinary conditions at all.

That ordering is the same ordering as electrical conductivity, and it is not a coincidence — both are measuring how firmly the outer electrons are bound. "Few valence electrons", "low ionisation energy" and "good conductor" are three descriptions of a single physical property. Watch the wording carefully, though, because one phrase carries two meanings. A deficiency of electrons in the outer shell is exactly this property, and it describes a material of low resistance. A deficiency of electrons in the atom as a whole is something quite different: it means the atom has been ionised and now carries a positive charge, and resistance is a property of a material rather than of a single ion.

How Atoms Are Ionised in Practice

Anything that can deliver the ionisation energy to an outer electron will free it. Five mechanisms account for essentially everything an engineer meets.

Mechanism	What happens	Where it is met on an aircraft
Heat	Thermal agitation of the lattice or the gas shakes electrons free	Thermionic emission from a heated cathode; rising leakage through hot-zone insulation
Electric field	The field itself pulls electrons out of their bonds	Dielectric breakdown, arcing across a contaminated connector, corona on high-voltage leads
Radiation	Photons or energetic particles knock electrons out of atoms	Cosmic and solar particles ionising air and depositing charge in avionic semiconductors at altitude; ultraviolet ageing of exposed insulation
Friction or contact separation	Electrons are transferred from one surface to the other as they part	Precipitation static in flight, refuelling hazards, electrostatic discharge damage to line-replaceable units
Chemical action	A reaction drives electrons onto one electrode and removes them from the other	Every battery cell

In every one of these, charge is never created — it is only separated. If one body ends up with a surplus of electrons, some other body has an exactly equal deficit, and the two together still total zero. That is the conservation of charge, and it is why a static problem on an aircraft is always a question of where the charge went rather than where it came from.

Conduction by Ions

In a metal only electrons move; the positive ion cores are pinned in the lattice and go nowhere. In a liquid or a gas the picture changes completely, because whole ions are free to travel, and carriers of both signs move at the same time in opposite directions. Positive ions migrate toward the cathode and are called cations; negative ions migrate toward the anode and are called anions — that migration is precisely what the two names mean. In an electrolysis cell driven by an external supply, the cathode is the electrode connected to the negative side and the anode the one connected to the positive side, so there the cations travel toward the negative electrode and the anions toward the positive electrode. Because the two sets of carriers have opposite charges as well as opposite directions of travel, both movements carry charge the same way round the circuit and the contributions add rather than cancel.

A battery is the everyday case. The external circuit carries electrons through the aircraft wiring while the electrolyte carries ions between the plates, and only the two together make a complete circuit. The same ion movement drives electroplating, anodising and electrolytic corrosion.

Ionisation of Air

Dry air is an excellent insulator, but only up to a threshold — and it is a comparatively low one, because air breaks down at roughly 3 kV per millimetre, well below the figure for any of the solid insulating materials used on an aircraft. Raise the electric field high enough and it strips electrons from air molecules directly; each freed electron is then accelerated by that same field, collides with further molecules and frees more electrons still. The process feeds itself, which is why breakdown is sudden rather than gradual: the air converts from insulator to conductor almost instantly and the result is an arc.

Several familiar requirements follow from this. Creepage and clearance distances exist to keep the field below the threshold. Contamination and moisture lower the threshold, so a dirty or damp connector arcs at a voltage a clean dry one holds comfortably — which is why cleanliness is an electrical requirement and not merely a cosmetic one. Sharp points concentrate the field and start ionising first, producing corona. And an airframe flying through precipitation accumulates charge which will eventually leave from its extremities.

Static dischargers, the small wicks fitted at trailing edges and wing tips, exist to control that departure. Each provides a deliberately high-resistance path terminating in fine points where the field is intense, so the accumulated charge bleeds away continuously and quietly as a controlled corona. Without them the charge builds until it jumps as a spark across the structure, and the broadband noise from those sparks floods the radio and navigation receivers.

Valence and Free Electrons

When a valence electron gains enough energy, it can break free from its parent atom and move through the material. Such electrons are called free electrons. The ease with which this happens determines whether a material is a conductor, semiconductor, or insulator.

The energy band model explains this:

• Valence band — the energy range occupied by valence electrons bound to atoms.
• Conduction band — the energy range where electrons are free to move and carry current.
• Band gap (forbidden gap) — the energy difference between the valence and conduction bands.

Why Bands Exist at All

A single isolated atom has sharp, well-separated energy levels — the shells of the previous sections. Pack atoms together into a solid at a density of the order of \( 10^{28} \) per cubic metre and every atom's outer levels are disturbed by all of its neighbours. No two electrons in the assembly may occupy the same state, so each original level is forced to split into an enormous number of very slightly different ones. Crowded that closely, they stop behaving as separate levels and act instead as a continuous band of allowed energies. Between two such bands lies a span of energies that no electron in the solid is permitted to have, and that span is the forbidden gap.

Why the Gap Decides Everything

An electron can only contribute to a current if there is an empty state close by for it to move into. This is the deeper reason behind the familiar three-way division of materials, and it goes further than counting valence electrons:

• In a metal the valence and conduction bands overlap, so empty states sit immediately above the occupied ones. Even a vanishingly small applied field produces a net drift, no bond has to be broken first, and conduction happens at any temperature.
• In a semiconductor or an insulator the valence band is completely full. A full band can carry no current at all, however strong the field, because there is simply nowhere for an electron to move to. Current becomes possible only when an electron is lifted right across the gap into the empty conduction band above it.

So the question that sorts materials is not how large the gap is in isolation, but how large it is compared with the energy actually available. At room temperature the characteristic thermal energy in a material is only about 0.026 eV.

Set that against the gaps. Silicon's is about 1.1 eV, roughly forty times the thermal energy available, so only the small fraction of electrons in the high-energy tail of the distribution ever manage the jump — but the fraction is not zero, which is why a semiconductor conducts a little. An insulator's gap is above 5 eV, roughly two hundred times the thermal energy available, and the fraction able to cross is smaller again by many orders of magnitude — effectively none. One number, compared against one other number, sorts every material into its class.

Electrons and Holes

When a bond does break, two carriers appear rather than one: the electron that escaped, and the vacancy it left behind. That vacancy, called a hole, is not merely an absence. A valence electron in a neighbouring bond can hop sideways into it, which fills the original vacancy but opens a new one where the neighbour came from. The vacancy therefore travels through the lattice in the opposite direction to the hopping electrons, and for circuit purposes it behaves exactly like a mobile particle carrying one positive elementary charge.

Under an applied field the free electrons and the holes drift in opposite directions, but because their charges are also opposite, both contribute current the same way round the circuit. Holes drift along the electric field, in the same sense as conventional current; free electrons drift against it.

How Many Free Electrons Are There?

The numbers are worth carrying, because they show that the difference between a conductor and a semiconductor is one of quantity on a staggering scale rather than one of kind. A monovalent metal such as copper contributes about one free electron per atom, which works out at \( 8.5 \times 10^{28} \) per cubic metre; a trivalent metal such as aluminium contributes three, giving roughly \( 1.8 \times 10^{29} \) per cubic metre, about twice copper's figure. Either way the count is of the order of \( 10^{28} \) to \( 10^{29} \) free electrons per cubic metre, and that population is present whether or not any voltage is applied. Pure silicon at room temperature manages of the order of \( 10^{16} \) per cubic metre. Between the two lies a factor of some twelve to thirteen orders of magnitude. It is that difference in the number of carriers, rather than any difference in how freely an individual carrier moves, that accounts for the enormous gap between copper's resistivity and silicon's. Within the metals themselves the balance is different: having more carriers does not by itself make the better conductor, and aluminium's resistivity is still higher than copper's, because conductivity depends on how far a carrier drifts between collisions as well as on how many carriers there are, and aluminium's electrons are scattered more heavily. Note 3.7, Resistance/Resistor, works that comparison through.

It also explains why doping is so effective. A donor or acceptor atom introduces an energy level lying only a few hundredths of an electron-volt from the nearest band, which is comparable with the thermal energy already available at room temperature. Its carrier therefore does not have to cross the full gap and is released essentially every time, so an impurity of a few atoms in a million can multiply the carrier population by orders of magnitude and set the material's conductivity deliberately and precisely.

How Fast Do Free Electrons Actually Move?

Two different speeds are involved here and confusing them is a classic error. Free electrons in a metal are already moving very fast at random, at speeds of the order of \( 10^{6} \) m/s, in every direction at once — and that motion transports no charge anywhere, because for every electron heading one way there is another heading back. Applying a field superimposes on that chaos a small average velocity along the field, called the drift velocity. The drift is what constitutes the current, and it is astonishingly slow.

Yet a lamp lights the instant the switch closes. The resolution is that what travels along the conductor at close to the speed of light is not the electrons but the electric field that pushes them. Every free electron along the entire length of the wire begins to drift almost simultaneously, and the electron that lights the lamp was already sitting in the filament before the switch was touched. Two practical points follow: a fault is felt everywhere in a circuit effectively at once, and the question "how fast does electricity travel?" is a question about field propagation, not about electron speed.

Which Way the Free Electrons Go

The direction follows from nothing more than repulsion and attraction. The negative terminal of a source is a region carrying a surplus of electrons, and like charges repel, so it pushes free electrons in the conductor away from itself. The positive terminal has an electron deficit, and unlike charges attract, so it pulls them toward itself. Work the concrete case: an electron sitting midway along a copper wire strapped across a battery feels a push from the crowded negative plate and a pull from the depleted positive plate, and both act in the same sense. Free electrons in the external circuit therefore drift away from the negative terminal and toward the positive one. The two naming conventions built on this physical fact are set out in the final section of this note.

What Slows Them Down

A free electron does not accelerate indefinitely under the field. It picks up energy, then collides with a vibrating lattice ion, an impurity atom or a defect in the crystal, and surrenders the energy it gained as heat. Repeated many times over, that gain-and-collide cycle produces a steady average drift rather than continuous acceleration, and the energy handed over at each collision is the ohmic heating found in every cable, joint and winding on the aircraft.

Resistance, at this level of explanation, simply is the rate at which drifting electrons are scattered. Stating it that way makes three otherwise separate facts obvious at once: resistance depends on temperature, because heat controls how violently the lattice vibrates; it depends on purity, because foreign atoms are extra scattering centres, which is why alloys have higher resistivity than the pure metals they are made from; and it depends on mechanical condition, because work-hardening, corrosion products and a poorly made crimp all add scattering exactly where the current is most concentrated.

Effect of Temperature on Conduction

Heating a material changes two things at once, and the two push in opposite directions. Which of them dominates is what decides whether a material's resistance goes up or down when it gets hot, and it is a different answer for each of the three classes of material.

• Scattering. A hotter lattice vibrates more violently, so a drifting electron collides more often and travels a shorter distance between collisions. Less drift results for the same applied field. Acting alone, this effect raises resistance.
• Carrier generation. A hotter material also has more thermal energy on hand, so more electrons can be lifted across the forbidden gap. More carriers means more current for the same applied field. Acting alone, this effect lowers resistance.

Metals: Scattering Wins

In a metal the carrier population is effectively already at its ceiling. Every atom has already surrendered its valence electron or electrons before any heat is applied, the bands overlap so nothing has to be lifted across a gap, and warming the metal cannot produce any meaningful number of additional carriers. Only the scattering effect is left in play, so a metal's resistance rises as it gets hotter. Metals are said to have a positive temperature coefficient of resistance.

The magnitude is easy to underestimate. Copper's temperature coefficient is roughly 0.0039 per degree Celsius referred to 20 °C, so a winding measuring 10 ohms at 20 °C rises to \( 10\,(1 + 0.0039 \times 50) = 11.95 \) ohms at 70 °C — nearly 20% more resistance from the same piece of wire. That is why a generator field or a motor winding checked cold reads noticeably lower than the same winding measured immediately after a run, and why a resistance figure quoted without a temperature is of limited use. Note 3.7, Resistance/Resistor, carries the temperature coefficient further, including the trap that the coefficient itself depends on the reference temperature it is quoted against.

There is a feedback loop hidden in this. A cable already warm from its load current has a higher resistance, so at the same current it dissipates more power, so it warms further, so its resistance rises again. The loop settles at a higher temperature than a naive calculation predicts, and it is one of the reasons wiring current ratings are de-rated for high ambient temperature and again for large bundles where the heat generated in the core of the bundle has no easy escape path.

Semiconductors: Carrier Generation Wins

In a semiconductor the carrier population at room temperature is minute, and it grows very steeply indeed with temperature, because the number of electrons able to cross the gap depends exponentially on it. That gain completely overwhelms the extra scattering, so a semiconductor's resistance falls as it gets hotter: a negative temperature coefficient.

This behaviour is exploited deliberately. A negative-temperature-coefficient thermistor is a semiconductor whose resistance drops predictably as it warms, which makes it useful both for temperature sensing and for limiting the inrush current to equipment at switch-on. A positive-temperature-coefficient device behaves the opposite way, its resistance climbing sharply once it self-heats past a threshold, which makes it a resettable overcurrent protector.

Insulators: The Same Mechanism, From a Much Larger Gap

An insulator is not a fundamentally different kind of material in this respect — it behaves like a semiconductor with a very large gap. The same thermal generation operates, so its resistance falls as it gets hotter, for exactly the same reason a semiconductor's does. Because the dependence is exponential rather than linear, the drop per degree is far steeper than the near-linear rise a metal shows: the maintenance rule of thumb is that insulation resistance roughly halves for every 10 °C rise, which is about seven per cent per degree Celsius, against the 0.39 per cent per degree by which copper's resistance climbs. Exponential changes compound as well, so between a cold-soaked airframe and the same insulation sitting at engine-bay temperature the accumulated reduction in insulation resistance can be very large indeed.

Two practical consequences follow directly from that, and both are routine maintenance concerns rather than theoretical curiosities.

• Insulation resistance readings only mean something alongside the conditions they were taken in. The same harness measured hot reads lower than it does cold, so comparing an as-found hot reading against a cold baseline can suggest a defect that is not there — or, worse, hide a real one behind a favourable cold measurement. Where a trend is being followed over time, readings are corrected to a common reference temperature before they are compared.
• The loop can run away here too. Leakage current flowing through warm insulation dissipates power inside the insulation itself, which raises its temperature, which lowers its resistance, which increases the leakage. Contamination, absorbed moisture or mechanical damage concentrates the process at one spot, and the resulting hot track carbonises into a permanently conducting path.

This is why insulation failures so often appear sudden while having been developing for a long time. The final event is the electric field tearing electrons free from a material that has already been quietly degraded by heat, damp and contamination — the breakdown described at the end of the next section is the last step of that sequence, not the whole of it.

Conductors, Semiconductors, and Insulators

Property	Conductor	Semiconductor	Insulator
Valence electrons	1–3	4	5–8 (or full shell)
Band gap	None (bands overlap)	Small (≈ 0.7–1.1 eV)	Large (> 5 eV)
Conductivity	Very high	Moderate (variable)	Extremely low
Free electrons	Abundant at room temp	Few at room temp; increases with temp	Almost none
Temp effect on resistance	Increases with temp	Decreases with temp	Decreases markedly (roughly halves per 10 °C rise)
Examples	Copper, aluminium, silver, gold	Silicon, germanium	Glass, rubber, PVC, mica, ceramic

Conductors in Detail

Good conductors have atoms with only 1 to 3 valence electrons loosely bound to the nucleus. In metals, these electrons form a "sea" of free electrons that can drift through the material when a voltage is applied. Copper has one valence electron and is the most commonly used conductor in aviation.

Semiconductors in Detail

Silicon and germanium have 4 valence electrons and form covalent bonds with neighbouring atoms. At absolute zero they behave as insulators, but at room temperature some bonds break, releasing electron-hole pairs. Their conductivity can be dramatically altered by doping — adding tiny amounts of impurity atoms:

• N-type — doped with a pentavalent element (e.g. phosphorus), providing extra free electrons.
• P-type — doped with a trivalent element (e.g. boron), creating "holes" (positive charge carriers).

Insulators in Detail

Insulators have a full or nearly full valence shell, so electrons are tightly bound and the band gap is very large. Virtually no free electrons are available for conduction. Insulators are essential for preventing unwanted current flow and protecting personnel from electric shock.

Conventional Flow vs. Electron Flow

There are two conventions for describing current direction:

Convention	Direction	Used By
Conventional flow	Positive (+) to negative (−)	Circuit diagrams, engineering standards, EASA exams
Electron flow	Negative (−) to positive (+)	Physics, understanding actual particle movement

In reality, electrons (the actual charge carriers in metals) flow from negative to positive. However, before the electron was discovered, current was defined as flowing from positive to negative. This conventional current direction is used in virtually all circuit analysis and is the standard in EASA Part 66 examinations.