Module 3: Electrical Fundamentals

Module 3: Electrical Fundamentals – EASA Part-66 B2

1. Module Overview

Module 3, "Electrical Fundamentals," forms the cornerstone of all aircraft electrical and electronic systems knowledge for the EASA Part-66 B2 licence. This module provides the essential theoretical foundation required to understand, troubleshoot, and maintain the complex electrical systems found on modern aircraft. The syllabus covers a broad spectrum of topics, ranging from basic atomic theory and DC circuit analysis to AC theory, semiconductor devices, and electrical protection systems.

The module is structured to build knowledge progressively, starting with fundamental concepts and advancing to more complex applications. For the B2 category, the knowledge levels required are predominantly Level 2 (general knowledge) and Level 3 (detailed theory), reflecting the depth of understanding needed for certifying staff working on avionic and electrical systems.

2. Key Concepts Explained in Detail

2.1 Electron Theory and Electrical Materials

Atomic Structure and Charge Carriers

All matter consists of atoms containing protons (positive charge), neutrons (neutral), and electrons (negative charge). In metallic conductors, the outermost electrons (valence electrons) are loosely bound and can move freely, forming a "sea of electrons." This free electron movement constitutes an electric current when a potential difference is applied.

Conductors, Insulators, and Semiconductors

• Conductors: Materials with low resistivity, typically metals. Copper (resistivity ≈ 1.72 × 10⁻⁸ Ω·m) and aluminium (≈ 2.82 × 10⁻⁸ Ω·m) are the primary conductors used in aircraft wiring. Silver has the lowest resistivity but is rarely used due to cost and weight considerations.
• Insulators: Materials with very high resistivity that prevent current flow. For high-temperature aircraft applications, PTFE (polytetrafluoroethylene) is preferred due to its excellent thermal stability (operating range up to 260°C) and superior dielectric properties. PVC (up to 105°C), rubber, and polyethylene have lower temperature ratings and are unsuitable for engine bay or high-heat areas.
• Semiconductors: Materials with resistivity between conductors and insulators. Silicon and germanium are the most common. Their conductivity can be modified through doping—the controlled addition of impurity atoms.

Semiconductor Doping

• N-type material: Created by doping silicon with pentavalent atoms (e.g., phosphorus, arsenic). These impurities have five valence electrons, leaving one free electron per dopant atom. The majority carriers are electrons.
• P-type material: Created by doping with trivalent atoms (e.g., boron, aluminium). These impurities have three valence electrons, creating "holes" (absence of electrons). The majority carriers are holes.

Important: In P-type material, holes move in the same direction as conventional current. This is because conventional current is defined as the flow of positive charge, and holes are positive charge carriers.

2.2 DC Circuit Theory

Ohm's Law and Power

Ohm's law states that the current (I) through a conductor between two points is directly proportional to the voltage (V) across the two points and inversely proportional to the resistance (R):

V = I × R

Where:

• V is measured in volts (V)
• I is measured in amperes (A)
• R is measured in ohms (Ω)

Electrical power (P) is measured in watts (W), defined as one joule per second:

P = V × I = I² × R = V² / R

Resistors and Colour Coding

Resistors are identified by a colour code system. The standard code uses four or five bands:

• First band: first digit
• Second band: second digit
• Third band: multiplier (power of 10)
• Fourth band: tolerance (gold = ±5%, silver = ±10%, no band = ±20%)

Colour values: Black = 0, Brown = 1, Red = 2, Orange = 3, Yellow = 4, Green = 5, Blue = 6, Violet = 7, Grey = 8, White = 9.

Examples:

• Brown, Black, Red, Gold = 10 × 100 = 1000 Ω ± 5% (1 kΩ)
• Red, Violet, Orange, Gold = 27 × 1000 = 27,000 Ω ± 5% (27 kΩ)

Series and Parallel Resistances

• Series: R_total = R₁ + R₂ + R₃ + ...
• Parallel: 1/R_total = 1/R₁ + 1/R₂ + 1/R₃ + ...

For two resistors in parallel, the simplified formula is: R_total = (R₁ × R₂) / (R₁ + R₂)

Internal Resistance and Terminal Voltage

Real voltage sources (batteries, generators) have internal resistance (r). When current flows, there is a voltage drop across this internal resistance:

V_terminal = EMF - (I × r)

Where EMF is the electromotive force (open-circuit voltage).

Example: A 24 V battery with internal resistance 0.5 Ω connected to a 5.5 Ω load:

• Total resistance = 0.5 + 5.5 = 6.0 Ω
• Current = 24 / 6.0 = 4 A
• Terminal voltage = 24 - (4 × 0.5) = 22 V

Higher internal resistance causes a greater voltage drop under load, reducing terminal voltage.

Ideal Voltage Source: An ideal voltage source maintains constant terminal voltage regardless of load current, which requires zero internal resistance.

2.3 Capacitance and Capacitors

Basic Principles

A capacitor stores electrical energy in an electrostatic field. Capacitance (C) is measured in farads (F), where 1 F = 1 coulomb per volt. Aircraft applications typically use microfarads (µF = 10⁻⁶ F) and picofarads (pF = 10⁻¹² F).

Charge Storage: Q = C × V (charge in coulombs)

Series and Parallel Capacitors

• Series: 1/C_total = 1/C₁ + 1/C₂ + ... (total is always less than the smallest individual capacitor)
• Parallel: C_total = C₁ + C₂ + ... (total is the sum of individual capacitances)

Charge Sharing (Conservation of Charge)

When a charged capacitor is connected to an uncharged capacitor, charge is conserved:

Q_initial = Q_final

Example: A 10 µF capacitor charged to 200 V is connected in parallel with an uncharged 30 µF capacitor:

• Initial charge: Q = 10 µF × 200 V = 2000 µC
• Total capacitance: C_total = 10 + 30 = 40 µF
• Final voltage: V = Q / C_total = 2000 / 40 = 50 V

Capacitive Reactance

In AC circuits, a capacitor offers opposition to current flow called capacitive reactance:

X_C = 1 / (2πfC)

Where:

• X_C is in ohms (Ω)
• f is frequency in hertz (Hz)
• C is capacitance in farads (F)

Example: 20 µF capacitor on 100 V, 50 Hz supply:

X_C = 1 / (2π × 50 × 20 × 10⁻⁶) = 159.15 Ω

Phase Relationship: In a purely capacitive circuit, current leads voltage by 90°. This occurs because the capacitor charges and discharges, allowing current to flow before voltage builds up across the plates.

2.4 Inductance and Inductors

Basic Principles

An inductor stores energy in a magnetic field. Inductance (L) is measured in henries (H). When current through an inductor changes, a back EMF is induced opposing the change (Lenz's law).

Inductive Reactance

X_L = 2πfL

Inductive reactance is directly proportional to frequency. As frequency increases, inductive reactance increases.

Example: 50 mH inductor on 200 V, 400 Hz supply:

X_L = 2π × 400 × 0.05 = 125.66 Ω

Phase Relationship: In a purely inductive circuit, current lags voltage by 90°.

Time Constant (RL Circuit)

The time constant (τ) represents the time for current to reach approximately 63.2% of its final value:

τ = L / R

Where:

• τ is in seconds (s)
• L is in henries (H)
• R is in ohms (Ω)

Example: R = 50 Ω, L = 0.5 H:

τ = 0.5 / 50 = 0.01 s (10 ms)

Power in Purely Inductive Circuits: The phase angle is 90°, so the power factor (cos φ) is zero. True power P = V × I × cos φ = 0. All energy is alternately stored in the magnetic field and returned to the source—no real power is dissipated.

2.5 AC Theory

Sinusoidal Waveforms

AC voltage and current vary sinusoidally with time. Key parameters:

• Peak value (V_peak): Maximum instantaneous value
• RMS value (V_RMS): The equivalent DC value that produces the same heating effect
• Average value: Mean of instantaneous values over a specified interval

RMS-Peak Relationships (for sinusoidal waveforms):

• V_peak = V_RMS × √2 ≈ V_RMS × 1.414
• V_RMS = V_peak / √2 ≈ V_peak × 0.707

Example: RMS value of 115 V:

V_peak = 115 × 1.414 = 162.6 V

Average Value: The average of a symmetrical sine wave over one complete cycle is zero because the positive and negative half-cycles cancel. Over a half-cycle, the average is 0.637 × peak value.

Phase Relationships in AC Circuits

• Purely resistive: Voltage and current are in phase (0° phase difference)
• Purely inductive: Current lags voltage by 90°
• Purely capacitive: Current leads voltage by 90°

Impedance in Series RLC Circuits

Impedance (Z) is the total opposition to current in an AC circuit:

Z = √(R² + (X_L - X_C)²)

Example: R = 30 Ω, X_L = 50 Ω, X_C = 20 Ω:

Z = √(30² + (50 - 20)²) = √(900 + 900) = √1800 = 42.43 Ω

Resonance in RLC Circuits

Resonance occurs when X_L = X_C. The resonant frequency is:

f = 1 / (2π√(LC))

At resonance:

• Impedance is purely resistive and minimum (Z = R)
• Current is maximum
• Circuit is in phase (power factor = 1)

AC Power

• Apparent power (S): Measured in volt-amperes (VA), S = V × I
• True power (P): Measured in watts (W), P = V × I × cos φ
• Reactive power (Q): Measured in volt-amperes reactive (VAR), Q = V × I × sin φ
• Power factor (PF): PF = cos φ = True power / Apparent power

Example: Apparent power = 5 kVA, PF = 0.8 lagging:

True power = 5 kVA × 0.8 = 4 kW

2.6 Transformers

Operating Principle

A transformer transfers electrical energy between circuits through electromagnetic induction. It consists of a primary winding and a secondary winding on a common magnetic core. Transformers operate only on AC because they rely on a changing magnetic flux to induce voltage. With DC, a steady magnetic field is produced, and no voltage is induced in the secondary (after the initial transient).

Turns Ratio

V_s / V_p = N_s / N_p

Where:

• V_s = secondary voltage
• V_p = primary voltage
• N_s = secondary turns
• N_p = primary turns

Examples:

• Turns ratio 1:5 (primary:secondary), primary = 28 V AC: V_s = 28 × 5 = 140 V
• Turns ratio 5:1 (primary:secondary), primary = 115 V AC: V_s = 115 × (1/5) = 23 V

Functions in Aircraft: Transformers step up or step down AC voltages for various aircraft systems, provide isolation, and match impedances.

2.7 Three-Phase Systems

Basic Configuration

Three-phase systems consist of three AC voltages separated by 120° electrical. This configuration provides more efficient power transmission and smoother operation of motors.

Star (Wye) Connection

• Line voltage (V_L) = √3 × Phase voltage (V_ph)
• Line current (I_L) = Phase current (I_ph)

Example: Line voltage = 200 V:

V_ph = 200 / √3 = 200 / 1.732 = 115.47 V

Delta Connection

• Line voltage (V_L) = Phase voltage (V_ph)
• Line current (I_L) = √3 × Phase current (I_ph)

Power Measurement (Two-Wattmeter Method)

For a balanced three-phase load:

• Total power: P_total = P₁ + P₂
• Power factor: tan φ = √3 × (P₁ - P₂) / (P₁ + P₂)

Example: P₁ = 4000 W, P₂ = 1500 W:

P_total = 5500 W

tan φ = √3 × (4000 - 1500) / 5500 = 0.787

φ = 38.2°, cos φ = 0.786

AC Generator Frequency

The frequency of a generator output depends on the number of poles and rotational speed:

f = (P × N) / 120

Where:

• f = frequency in Hz
• P = number of poles
• N = rotational speed in RPM

Example: 4-pole generator, 400 Hz output:

N = (120 × 400) / 4 = 12,000 RPM

2.8 Semiconductor Devices

PN Junction Diode

A diode is a two-terminal device that conducts current in the forward bias direction and blocks it in the reverse bias direction. This unidirectional behaviour makes diodes essential for rectification.

Zener Diode

A Zener diode is specifically designed to operate in the reverse breakdown region. In this region, the voltage across the diode remains nearly constant over a range of currents. This property makes Zener diodes ideal for:

• Voltage regulation
• Reference voltage elements in power supplies
• Overvoltage protection

Bipolar Junction Transistor (BJT)

A BJT has three terminals: emitter, base, and collector. It comes in two types: NPN and PNP.

Operating Regions:

• Active (linear) region: Base-emitter junction forward biased, base-collector junction reverse biased. The transistor operates as an amplifier.
• Saturation region: Both junctions forward biased. The transistor acts as a closed switch.
• Cut-off region: Both junctions reverse biased. The transistor acts as an open switch.

Varistor (Voltage-Dependent Resistor)

A varistor has resistance that decreases significantly when the voltage across it exceeds a threshold. It is used to clamp transient overvoltages and protect sensitive electronic equipment from voltage spikes.

2.9 DC Motors

Operating Principle

A DC motor converts electrical energy into mechanical energy. The interaction between the magnetic field and the current-carrying armature conductors produces torque.

Back EMF

When the armature rotates, it generates a back EMF (E_b) opposing the applied voltage:

V = E_b + (I × R_a)

Where:

• V = applied voltage
• E_b = back EMF
• I = armature current
• R_a = armature resistance

Example: V = 28 V, I = 4 A, R_a = 2 Ω:

E_b = 28 - (4 × 2) = 20 V

Commutator Function

The commutator reverses the current direction in the armature windings as the rotor turns. This ensures that the torque remains in the same direction, allowing continuous rotation.

2.10 Electrical Protection and Safety

Circuit Breakers

A circuit breaker is a protective device designed to automatically interrupt the circuit when current exceeds a predetermined value. This prevents damage to wiring and components. Key principles:

• The breaker rating should be lower than the cable's safe current-carrying capacity
• This ensures the breaker trips before the cable reaches its maximum safe current

Example: A 5 A breaker protecting a 10 A cable—if a fault causes 15 A to flow, the breaker trips, protecting the cable.

Bonding Straps

Bonding straps ensure electrical continuity between metallic parts, providing:

• A low-impedance path for fault currents
• Prevention of dangerous voltage differences between components
• Lightning protection
• Reduction of electromagnetic interference (EMI)

Voltage Regulators

A voltage regulator ensures that the output voltage of a generator or alternator remains stable under varying load and speed conditions. This is critical for protecting sensitive avionics equipment.

Rectification

• Half-wave rectifier: Uses one half of the AC cycle. Output ripple frequency equals the input frequency.
• Full-wave rectifier: Uses both halves of the AC cycle. Output ripple frequency is twice the input frequency.

3. Important Formulas and Relationships

4. Common Relationships Between Concepts

Resistance vs. Reactance vs. Impedance

• Resistance (R) opposes current in both DC and AC circuits
• Reactance (X) opposes current only in AC circuits
• Impedance (Z) is the vector combination of resistance and reactance
• In purely resistive circuits, Z = R; in reactive circuits, Z > R

Frequency Effects

• Inductive reactance increases with frequency (X_L ∝ f)
• Capacitive reactance decreases with frequency (X_C ∝ 1/f)
• At resonance, X_L = X_C and the circuit behaves purely resistively

Phase Relationships

• Resistive circuits: voltage and current in phase (0°)
• Inductive circuits: current lags voltage (90°)
• Capacitive circuits: current leads voltage (90°)
• The power factor is the cosine of the phase angle between voltage and current

Charge Conservation

• In capacitor circuits, charge is always conserved
• When charged capacitors are connected together, the total charge redistributes according to the new total capacitance

Transformer Relationships

• Transformers work only with AC (changing magnetic flux)
• Voltage ratio equals turns ratio
• For an ideal transformer, power in = power out (V_p × I_p = V_s × I_s)

Three-Phase Relationships

• Star connection: V_L = √3 × V_ph, I_L = I_ph
• Delta connection: V_L = V_ph, I_L = √3 × I_ph
• Phase voltages are separated by 120°

5. Typical Exam Focus Points

Based on the EASA Part-66 Module 3 B2 syllabus and typical examination patterns, candidates should focus on:

Level 2 Topics (General Knowledge)

• SI units for all electrical quantities (ohm, volt, ampere, watt, henry, farad, tesla, weber)
• Resistor colour coding (four-band system)
• Conductor, insulator, and semiconductor materials and their applications
• Circuit breaker function and protection principles
• Bonding strap purpose and application
• Diode and Zener diode characteristics
• Phase relationships in AC circuits
• Three-phase system basics (120° phase separation, star/delta relationships)

Level 3 Topics (Detailed Theory)

• Ohm's law calculations and power calculations
• Series and parallel resistance/capacitance calculations
• Capacitor charge sharing problems (conservation of charge)
• RL time constant calculations
• RLC impedance calculations
• Resonant frequency calculations
• Transformer turns ratio calculations
• AC generator frequency/speed/pole calculations
• Motor back EMF calculations
• Battery internal resistance and terminal voltage calculations
• AC power calculations (true power, apparent power, power factor)
• RMS/peak value conversions
• Reactance calculations (X_L and X_C)
• Two-wattmeter method for three-phase power

Common Exam Pitfalls

• Confusing series and parallel formulas for resistors and capacitors (they are opposite)
• Forgetting that average value of a full sine wave cycle is zero
• Applying transformer principles to DC circuits (transformers do not work on DC)
• Mixing up line and phase quantities in three-phase systems
• Incorrectly applying the power factor formula
• Confusing the direction of current lead/lag in inductive vs. capacitive circuits
• Forgetting that holes move in the same direction as conventional current in P-type material

Practical Applications

• Understanding why circuit breakers are rated below cable capacity
• Recognising the importance of bonding for lightning protection
• Understanding Zener diode use in voltage regulation
• Knowing which insulating materials are suitable for high-temperature aircraft areas
• Understanding the function of the commutator in DC motors
• Recognising the relationship between generator poles, speed, and output frequency