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EASA Module 3 study materials
EASA Module 3 study resources

EASA Module 3: AC Theory, Resistive/Capacitive/Inductive Circuits, Transformers, Filters, AC Generators and AC Motors

EASA Module 3 · Work through your exam, one topic at a time.

All guide sections

AC Theory, Resistive/Capacitive/Inductive Circuits, Transformers, Filters, AC Generators and AC Motors

AC Theory

The sine wave

AC varies sinusoidally: v = V_p sin(2πft). Period T = 1/f; frequency in hertz. The peak value is the amplitude; peak-to-peak is twice that. The average of a full sine is zero, but the average of a rectified sine is 0.637 V_p. The RMS value is 0.707 V_p and represents the DC value giving the same heating: V_rms = V_p/√2. Form factor = rms/average = 1.11; peak (crest) factor = peak/rms = 1.414.

Phase and phasors

Phase angle describes the time offset between waveforms; one cycle is 360° or 2π radians. Phasors (rotating vectors) represent magnitude and phase and allow AC quantities to be added. In a pure resistance, voltage and current are in phase; a capacitor makes current lead voltage by 90°, an inductor makes current lag by 90°.

Reactance and impedance

X_L = 2πfL rises with frequency; X_C = 1/(2πfC) falls with frequency. Impedance combines R and X as vectors: Z = √(R² + X²) with φ = arctan(X/R).

Traps

  • A 115 V supply is RMS; its peak is about 163 V.
  • Frequency depends only on the source, not on the load.
  • Average power in a pure reactance is zero, yet reactive power still flows.
  • ωt is in radians - do not mix degrees and radians in calculations.

Worked example

A 50 Hz supply with 325 V peak: V_rms = 325 x 0.707 ≈ 230 V and T = 1/50 = 20 ms. A 100 mH inductor has X_L = 2π x 50 x 0.1 ≈ 31.4 Ω.

Resistive, Capacitive and Inductive Circuits

Series behaviour

In a series RLC circuit the current is common and voltages add as phasors: Z = √(R² + (X_L − X_C)²), I = V/Z. If X_L > X_C the circuit is inductive and current lags; if X_C > X_L it is capacitive and current leads. At resonance X_L = X_C, Z = R is minimum, current is maximum, and the voltages across L and C can far exceed the supply (voltage magnification, Q = X_L/R). Resonant frequency f_r = 1/(2π√(LC)).

In a parallel RLC circuit at resonance the branch currents cancel, so line current is minimum and impedance is maximum - the opposite of series. Parallel resonant (tuned) circuits therefore work as rejector filters.

Power

Real power P = VI cos φ (watts); apparent power S = VI (volt-amperes); reactive power Q = VI sin φ (VAr). Power factor = cos φ = P/S. A low power factor means larger currents for the same useful power, hence power-factor correction capacitors in ground installations.

Traps

  • Series resonance gives minimum impedance and maximum current; parallel resonance gives maximum impedance and minimum current. Examiners swap these.
  • In a series circuit the largest voltage appears across the largest reactance, not necessarily across R.
  • Adding resistance reduces Q and broadens the resonance curve.

Worked example

R = 10 Ω, X_L = 30 Ω, X_C = 10 Ω. Net X = 20 Ω, Z = √(100 + 400) = 22.4 Ω, φ = arctan(2) ≈ 63° lagging. With 100 V applied, I = 100/22.4 ≈ 4.5 A.

Transformers

Principle

A transformer transfers energy between two coils linked by a common changing flux - mutual induction. It works only with AC (or changing DC); steady primary current induces nothing after the initial transient, a favourite exam trap.

Ideal relationships: V₁/V₂ = N₁/N₂ = I₂/I₁. Power in equals power out (V₁I₁ = V₂I₂) ignoring losses, and the frequency is unchanged. A step-up transformer raises voltage and lowers current.

Losses and construction

Copper loss is I²R in the windings; core loss is hysteresis (reduced by soft magnetic material) plus eddy currents (reduced by laminations or ferrite). Efficiency = output/input, best near full load. In core-type and shell-type construction, concentric windings place the LV winding nearest the core. Large units may be oil cooled with a conservator; dry-type and resin-cast units are common in aircraft.

Current transformers step current down for measurement and must never be open-circuited on the secondary while energised - dangerous voltages appear. An autotransformer uses one tapped winding: cheaper and lighter, but there is no isolation.

Traps

  • The turns ratio is the voltage ratio; the current ratio is its inverse.
  • Transformers do not change frequency or (ideally) power.
  • Dot convention shows polarity: dots at the same end mean in-phase outputs.
  • An open-circuited CT secondary is a hazard, not a no-load condition.

Worked example

400 primary turns and 40 secondary turns on 230 V: V₂ = 230 x 40/400 = 23 V. If the secondary supplies 4 A, primary current ≈ 4 x 40/400 = 0.4 A.

Filters

Filter basics

A filter passes some frequencies and attenuates others. Passive filters use R, L and C; active filters add amplifiers. The cut-off frequency (corner) is where the output falls to 70.7% of the pass-band level, i.e. −3 dB.

RC filters

Low-pass: resistor in series, capacitor to earth - high frequencies are shunted away, so the circuit smooths and removes noise. High-pass: capacitor in series, resistor to earth - DC and low frequencies are blocked. For a first-order RC filter, f_c = 1/(2πRC). Above cut-off a low-pass filter falls at 20 dB per decade (6 dB per octave); each extra order adds another 20 dB/decade.

A band-pass filter combines high-pass and low-pass sections (or a resonant LC network); a band-stop/notch filter rejects a narrow band, such as one interference frequency.

Decibels

Voltage gain in dB = 20 log₁₀(V_out/V_in). −3 dB ≈ 0.707; −20 dB = one tenth; +6 dB ≈ double voltage. For power use 10 log₁₀(P_out/P_in).

Aircraft relevance

Filters suppress EMI on radio and data lines, smooth rectifier output in transformer-rectifier units (ripple reduction) and shape signals in avionics. LC low-pass filters are common on generator outputs.

Traps

  • Cut-off is at −3 dB (0.707), not at half voltage.
  • Increasing R or C lowers the cut-off frequency of an RC filter.
  • A series capacitor passes high frequencies and blocks DC - that is a high-pass, not a low-pass.
  • Slopes are quoted in dB/decade unless stated otherwise.

Worked example

R = 10 kΩ and C = 10 nF: f_c = 1/(2π x 10⁴ x 10⁻⁸) ≈ 1592 Hz, so a 1.6 kHz low-pass filter.

AC Generators and AC Motors

AC generators

An alternator has a rotating field and a stationary armature, so heavy current is taken from fixed windings and only small excitation current passes through slip rings. Three-phase windings displaced by 120° give smoother power; outputs are star or delta connected and rectified where DC is needed (transformer-rectifier units). Frequency is set by poles and speed: f = pn/120, with p poles and n in rpm. A 400 Hz aircraft system running at 12 000 rpm needs a 4-pole machine.

Voltage is held by an automatic voltage regulator controlling field current. A constant-speed drive (CSD) or integrated drive keeps generator speed constant so frequency stays at 400 Hz despite engine speed changes.

AC motors

Synchronous machines run exactly at synchronous speed. Induction motors run slightly slower; the difference is slip: s = (n_s − n_r)/n_s. Slip is essential - with no slip there is no rotor emf, no rotor current and no torque. Typical full-load slip is 2-5%. Starting methods include direct-on-line, star-delta and soft starting. Single-phase motors need a split-phase or capacitor-start winding to create a rotating field.

Traps

  • Frequency depends on poles and speed only - not on load.
  • Induction motors cannot run at synchronous speed; synchronous motors can.
  • A rotating field from a single-phase supply requires phase splitting.
  • Alternator frequency changes only if the prime mover speed changes.

Worked example

A 4-pole induction motor on 50 Hz has n_s = 120 x 50/4 = 1500 rpm. Running at 1440 rpm, slip = 60/1500 = 4%.