EASA Module 3 cheat sheet

Atom structure: protons (positive) and neutrons (neutral) in the nucleus, electrons (negative) in shells around it.

Electron charge = -1.602 x 10^-19 C; the proton carries the same magnitude of positive charge.

Shell n holds a maximum of 2n^2 electrons; shells are labelled K, L, M, N outwards from the nucleus.

Valence (outermost) shell electrons decide electrical behaviour: 1-3 valence electrons conductor, 4 semiconductor, 5-8 insulator.

Free electrons drift from negative to positive under an EMF; conventional current is drawn from positive to negative.

An ion is an atom that has gained or lost electrons; removing an electron requires its binding energy.

Good conductors: silver, copper, gold, aluminium. Good insulators: rubber, glass, mica, PTFE, dry air.

Energy is absorbed or emitted in discrete quanta when an electron moves between shells.

Coulomb's law: F = kQ1Q2/r^2 with k = 9 x 10^9 N m^2/C^2; like charges repel, unlike attract.

Static charge sits on the outer surface of a conductor; the field inside a closed conducting shell is zero (Faraday cage).

Uniform field between parallel plates: E = V/d, in volts per metre.

Field at distance r from a point charge: E = kQ/r^2.

Charging mechanisms: friction (triboelectric), direct contact/conduction, and induction without contact.

Charge leaks away faster in humid air; dry air encourages static build-up.

Aircraft protection: bonding of components, grounding during refuelling, static dischargers on wing and tail trailing edges.

Capacitance of an isolated sphere: C = 4 x pi x epsilon0 x r.

V = W/Q: one volt is one joule per coulomb.

I = Q/t: one ampere is one coulomb per second.

R = V/I in ohms; conductance G = 1/R in siemens.

P = VI = I^2R = V^2/R.

Energy W = Pt (joules = watts x seconds); 1 kWh = 3.6 MJ.

EMF is the open-circuit source voltage; potential difference is the drop developed across a load.

Efficiency = useful output / total input x 100 per cent.

Charge transferred Q = It.

Six production methods: friction, pressure (piezoelectric), heat (thermoelectric), light (photovoltaic), chemical, and electromagnetic induction.

Faraday's law: induced EMF e = -N dPhi/dt.

Lenz's law: the induced current opposes the change that produced it.

Conductor moving through a field: e = Blv sin(theta).

Thermocouple: two dissimilar metals joined at both ends give an EMF proportional to the temperature difference (Seebeck effect).

Piezoelectric: pressure on a quartz crystal produces an EMF; used in accelerometers and igniters.

Photovoltaic cell: light releases electron-hole pairs in silicon, giving about 0.5 V per cell.

Primary cells cannot be recharged; secondary cells can.

Lead-acid: 2.0-2.1 V per cell nominal, dilute sulphuric acid electrolyte, vents hydrogen when charging.

Nickel-cadmium: 1.2 V per cell nominal, alkaline electrolyte, prone to memory effect.

Lithium-ion: 3.6-3.7 V per cell nominal, high energy density, risk of thermal runaway.

Carbon-zinc dry cell: 1.5 V per cell; alkaline-manganese gives the same voltage with longer life.

Capacity in ampere-hours: a 40 Ah battery delivers 4 A for 10 h at the C/10 rate.

Terminal voltage: V = E - Ir, where r is the internal resistance.

Cells in series add EMF; cells in parallel keep the same EMF and share the current.

A short circuit is limited only by internal resistance and wiring, so batteries must never be shorted.

Series: R total = R1 + R2 + ...; current is common; voltages add.

Parallel: 1/R total = 1/R1 + 1/R2 + ...; voltage is common; currents add.

Voltage divider: Vx = Vs x Rx / R total.

Current divider (two resistors): I1 = It x R2/(R1 + R2).

KCL: algebraic sum of currents at a node is zero. KVL: sum of EMFs equals sum of potential differences round a loop.

Thevenin: Vth is the open-circuit voltage; Rth is the resistance seen with sources replaced by their internal resistance.

Maximum power transfer to a load when R load = R source; efficiency is then 50 per cent.

Superposition applies to linear circuits: solve one source at a time, then add the results.

R = rho x L / A: resistance rises with length and resistivity, falls as cross-sectional area increases.

Metals have a positive temperature coefficient; carbon, semiconductors and electrolytes have a negative one.

R = R0(1 + alpha x deltaT).

Colour code: black 0, brown 1, red 2, orange 3, yellow 4, green 5, blue 6, violet 7, grey 8, white 9; gold +/-5 per cent, silver +/-10 per cent.

A potentiometer is a three-terminal voltage divider; a rheostat is a two-terminal variable series resistance.

Dissipated power P = I^2R; the resistor power rating must exceed this value.

Preferred values follow the E12, E24 and E96 series for 10, 5 and 1 per cent tolerances.

A fuse protects the wiring, not the load; its rating must lie below the cable current rating.

C = Q/V; one farad is one coulomb per volt.

Parallel-plate capacitor: C = epsilon0 x epsilonr x A / d, with epsilon0 = 8.85 x 10^-12 F/m.

Capacitors in parallel add; in series the reciprocals add.

Energy stored W = 0.5 x C x V^2.

Capacitor voltage cannot change instantaneously; in a pure capacitor current leads voltage by 90 degrees.

Time constant tau = RC; after one tau the capacitor reaches 63.2 per cent of final voltage.

Capacitive reactance XC = 1/(2 x pi x f x C); it falls as frequency rises.

Series capacitors share voltage inversely to capacitance, so the smaller capacitor takes the larger share.

Flux Phi in webers; flux density B = Phi/A in tesla (Wb/m^2).

Magnetomotive force = NI (ampere-turns); magnetising force H = NI/l in A/m.

Reluctance S = l/(mu0 x mur x A); magnetic Ohm's law: Phi = mmf/S.

mu0 = 4 x pi x 10^-7 H/m; mur is 1 for air and hundreds to thousands for ferromagnetic materials.

Ferromagnetic materials: iron, nickel, cobalt; above the Curie temperature ferromagnetism is lost.

Hysteresis loop area equals energy lost per cycle; soft iron suits cores, hard steel suits permanent magnets.

Field around a long straight conductor: B = mu0 x I/(2 x pi x r).

Field inside a solenoid: B = mu0 x mur x N x I / l.

L = N x Phi / I; one henry is one weber-turn per ampere.

Induced EMF e = -L di/dt; fast current changes give large back EMF and contact sparking.

Energy stored W = 0.5 x L x I^2.

Inductors in series add; in parallel the reciprocals add (no mutual coupling).

Inductor current cannot change instantaneously; in a pure inductor voltage leads current by 90 degrees.

Time constant tau = L/R; current reaches 63.2 per cent of final value after one tau.

Inductive reactance XL = 2 x pi x f x L; it rises with frequency.

L is proportional to mur x N^2 x A / l: permeability, turns squared and area raise inductance, length lowers it.

Force on a current-carrying conductor: F = BIl, direction from Fleming's left-hand rule.

Generated EMF in a moving conductor: e = Blv, direction from Fleming's right-hand rule.

Motor back EMF: Eb = V - IaRa, so armature current Ia = (V - Eb)/Ra.

Torque T = k x Phi x Ia; more flux or more armature current gives more torque.

The commutator reverses armature current every half cycle in a motor and rectifies armature EMF in a generator.

Shunt motor: nearly constant speed; field weakening raises speed.

Series motor: very high starting torque and must never run unloaded, as it overspeeds.

Speed control: armature voltage control below base speed, field weakening above base speed.

RMS = peak/1.414 = 0.707 x peak; peak = 1.414 x RMS for a sine wave.

Average value of a sine wave = 0.637 x peak; form factor 1.11; peak factor 1.414.

f = 1/T and angular frequency omega = 2 x pi x f.

P = VI cos(phi) real power in watts; Q = VI sin(phi) reactive power in var; S = VI apparent power in VA.

Star: line voltage = 1.732 x phase voltage, line current = phase current. Delta: line current = 1.732 x phase current, line voltage = phase voltage.

In a purely capacitive circuit current leads voltage by 90 degrees; in a purely inductive circuit it lags by 90 degrees.

Aircraft AC systems typically use 115 V at 400 Hz.

Three-phase power P = 1.732 x VL x IL x cos(phi).

Z = square root of (R^2 + (XL - XC)^2); tan(phi) = (XL - XC)/R.

Series resonance when XL = XC at f0 = 1/(2 x pi x square root of (LC)); Z is minimum (= R) and current is maximum.

Parallel resonance gives maximum impedance and minimum line current.

Q factor = XL/R = f0/bandwidth.

Below resonance the circuit is capacitive (current leads); above resonance it is inductive (current lags).

Power factor = cos(phi) = R/Z; improved by connecting capacitors in parallel with inductive loads.

Bandwidth = f2 - f1 = f0/Q.

At series resonance the voltages across L and C can reach Q times the supply voltage.

Ideal transformer: V1/V2 = N1/N2 = I2/I1.

EMF per turn = 4.44 x f x Phi max; total EMF E = 4.44 x f x N x Phi max.

Laminated core reduces eddy currents; soft iron gives low hysteresis loss.

Losses are copper (I^2R), eddy current and hysteresis; the no-load loss is essentially the iron loss.

Autotransformer uses one winding and gives no isolation; a variac is a variable autotransformer.

A current transformer secondary must never be open-circuited while the primary is energised; lethal voltage results.

Reflected impedance Z1 = (N1/N2)^2 x Z2.

Efficiency = output power / input power x 100 per cent; maximum when copper loss equals iron loss.

RC low-pass cut-off frequency fc = 1/(2 x pi x R x C); frequencies below fc pass.

RC high-pass takes the output across the resistor and passes frequencies above fc.

At cut-off the output is 0.707 of maximum (-3 dB) with 45 degrees of phase shift.

Attenuation in dB = 20 log10(Vout/Vin) for voltage; 10 log10 for power.

A capacitor blocks DC and passes high frequencies; an inductor passes DC and blocks high frequencies.

An LC low-pass filter in a power supply smooths rectifier ripple.

Band-pass bandwidth = f2 - f1; series LC is band-pass, parallel LC is band-stop.

Feedthrough capacitors provide EMI filtering at aircraft connector shells.

Alternator frequency f = p x N / 120, with p the number of poles and N the speed in rpm.

Brushless generator chain: pilot exciter, voltage regulator, main exciter, rotating rectifier, main generator field.

Synchronous speed Ns = 120f/p; a synchronous motor runs exactly at Ns.

Induction motor slip s = (Ns - N)/Ns, typically 2-5 per cent at full load.

Three-phase induction motors are self-starting; single-phase motors need a start winding or capacitor.

High-power AC generators use a rotating field with DC fed to the rotor through slip rings.

CSD or IDG keeps generator speed constant so the output stays at 400 Hz.

Synchronous motors are not self-starting and need damper windings to run up to speed.