Module 3: Electrical Fundamentals

1. Module Overview

Module 3 of the EASA Part-66 syllabus (Appendix I) establishes the fundamental principles of electricity and electronics that are essential for all aircraft maintenance certifying staff. This module is the bedrock upon which all other electrical and avionic system knowledge is built. It covers the behaviour of DC and AC circuits, the characteristics of essential passive components (resistors, capacitors, inductors), the principles of magnetism and transformers, the basics of semiconductor devices, and the use of electrical measuring instruments.

The knowledge levels for this module range from a general overview (Level 1) to a detailed theoretical understanding (Level 3), requiring candidates to not only recall facts but also to apply fundamental laws (e.g., Ohm's Law, Kirchhoff's Laws) to solve practical problems encountered in maintenance. The content is directly applicable to tasks such as troubleshooting wiring faults, verifying component performance, and understanding the operation of aircraft electrical power generation and distribution systems.

2. Key Concepts Explained in Detail

_S = 12 V R1 4 Ω R2 6 Ω R3 2 Ω I = 1 A Key properties: • Same current flows through all components: I = I₁ = I₂ = I₃ • Supply voltage is divided: V = V₁ + V₂ + V₃ Formulas: R_total = R₁ + R₂ + R₃ R_total = 4 + 6 + 2 = 12 Ω Ohm's Law: I = V / R I = 12 V / 12 Ω = 1 A Voltage drop across R1: V₁ = I × R₁ = 1 × 4 = 4 V PARALLEL CIRCUIT V_S = 12 V R1 4 Ω I₁=3A R2 6 Ω I₂=2A R3 12 Ω I₃=1A I_total = 6 A Key properties: • Same voltage across all branches: V = V₁ = V₂ = V₃ • Total current is the sum of branch currents: I = I₁ + I₂ + I₃ Formulas: 1/R_total = 1/R₁ + 1/R₂ + 1/R₃ 1/R_total = 1/4 + 1/6 + 1/12 = 6/12 → R_total = 2 Ω Ohm's Law: I = V / R I₁ = 12/4 = 3 A, I₂ = 12/6 = 2 A, I₃ = 12/12 = 1 A Total: I = 3 + 2 + 1 = 6 A

2.1 DC Circuits (Syllabus Ref: 3.2, 3.3, 3.4)

This section covers the fundamental laws governing Direct Current (DC) circuits.

Ohm's Law: This is the most fundamental relationship in electrical engineering. It states that the current (I) flowing through a conductor between two points is directly proportional to the voltage (V) across the two points and inversely proportional to the resistance (R) of the conductor.
Formula: I = V / R
SI Units: Current (I) in amperes (A), Voltage (V) in volts (V), Resistance (R) in ohms (Ω).
Application: If voltage is doubled and resistance remains constant, the current will also double. This law is used to calculate any one of the three parameters if the other two are known.
Electrical Power: Power (P) is the rate at which electrical energy is converted into another form of energy (e.g., heat, light, mechanical work).
Formula: P = V × I
Derived Formulas (using Ohm's Law): P = I² × R and P = V² / R
SI Unit: The watt (W).
Application: To calculate the power dissipated by a coil, use P = V² / R. For example, a 28 V solenoid coil with a resistance of 80 Ω dissipates P = 28² / 80 = 9.8 W. If voltage is doubled and resistance is halved, the power increases by a factor of eight: P_new = (2V)² / (R/2) = 8 × (V²/R) = 8P.
Resistance in Circuits:
Series Circuits: The total resistance is the sum of individual resistances. R_total = R1 + R2 + R3 + ... The same current flows through all components, and the supply voltage is divided across them. For example, two identical 24 V, 5 W lamps in series across a 24 V supply will each receive 12 V, operating below their rated voltage and producing less light.
Parallel Circuits: The reciprocal of the total resistance is the sum of the reciprocals of the individual resistances. 1/R_total = 1/R1 + 1/R2 + 1/R3 + ... The same voltage appears across all branches, and the total current is the sum of the branch currents. For example, for resistors of 4 Ω, 6 Ω, and 12 Ω in parallel: 1/R_total = 1/4 + 1/6 + 1/12 = 6/12, therefore R_total = 2 Ω.
Temperature Coefficient of Resistance: The resistance of a material changes with temperature.
Positive Temperature Coefficient (PTC): Resistance increases with temperature. This is a characteristic of most metals, including copper and aluminium. The change is calculated using the formula: R_T = R_0 [1 + α(T - T_0)], where R_T is the resistance at temperature T, R_0 is the resistance at reference temperature T_0 (usually 20°C), and α (alpha) is the temperature coefficient of resistance (for copper, α ≈ 0.00393 per °C).
Application: A copper wire measuring 0.5 Ω at 20°C will measure approximately 0.54 Ω at 40°C (a 20°C rise, with an 8% increase). This is critical when comparing resistance measurements to specifications that are defined at a standard reference temperature (e.g., 20°C). A measurement taken in a warm hangar must be corrected to the reference temperature before comparison.

2.2 Capacitance and Capacitors (Syllabus Ref: 3.6, 3.13)

Capacitance is the ability of a component (a capacitor) to store an electrical charge.

Basic Principle: A capacitor consists of two conductive plates separated by an insulating material (dielectric). When a voltage is applied, an electric field is established, and charge is stored.
Key Behaviour in DC Circuits: A capacitor blocks direct current (DC) in a steady state. When a DC voltage is applied, it charges up to the supply voltage. Once fully charged, no further current flows in the circuit. A fully discharged capacitor has zero volts across its plates.
Capacitance (C): The amount of charge (Q) stored per unit voltage (V).
Formula: C = Q / V
SI Unit: The farad (F). In aircraft systems, capacitors are typically in microfarads (µF = 10⁻⁶ F), nanofarads (nF = 10⁻⁹ F), or picofarads (pF = 10⁻¹² F).
Energy Storage: A capacitor stores energy in its electric field.
Formula: E = ½ × C × V²
SI Unit: The joule (J).
Application: A 100 µF capacitor charged to 50 V stores E = 0.5 × 100×10⁻⁶ × 50² = 0.125 J.
RC Time Constant (τ): The time it takes for a capacitor to charge to approximately 63.2% of the supply voltage or discharge to approximately 36.8% of its initial voltage.
Formula: τ = R × C
SI Units: Resistance (R) in ohms (Ω), Capacitance (C) in farads (F), Time constant (τ) in seconds (s).
Application: A 10 µF capacitor discharging through a 5 kΩ resistor has a time constant of τ = 5000 Ω × 10×10⁻⁶ F = 0.05 s = 50 ms.
Capacitor Markings: Capacitors are often marked with a code. For example, a ceramic disc capacitor marked '104' has a value of 10 × 10⁴ pF = 100,000 pF = 100 nF. It is crucial to consider the capacitor's tolerance (often ±20% for this type), meaning a measured value of 95 nF is within acceptable limits.
Safety: Large capacitors can store a dangerous charge. Before maintenance, they must be discharged safely using a suitable resistor to limit the discharge current and prevent arcing or damage. Direct shorting is unsafe and can damage the component.

2.3 Inductance and Inductors (Syllabus Ref: 3.7, 3.13)

Inductance is the property of a circuit that opposes a change in current.

Basic Principle: An inductor is typically a coil of wire. When current flows through it, a magnetic field is created. A change in current causes a change in the magnetic field, which induces a voltage (Electro-Motive Force, EMF) in the coil that opposes the change in current (Lenz's Law). This self-induced EMF is the basis of inductance.
Self-Induced EMF:
Formula: E = L × (di/dt)
SI Units: Inductance (L) in henries (H), Rate of change of current (di/dt) in amperes per second (A/s), EMF (E) in volts (V).
Application: If the current through a 5 H inductor is increasing at a rate of 2 A/s, the self-induced EMF is E = 5 H × 2 A/s = 10 V.
Behaviour in DC Circuits: An inductor opposes the initial flow of current when a DC supply is connected. Once the current reaches a steady state, the inductor acts like a short circuit (a piece of wire with negligible resistance).

2.4 Magnetism and Transformers (Syllabus Ref: 3.8, 3.14)

Magnetic Flux Density (B): A measure of the concentration of magnetic field lines.
SI Unit: The tesla (T). 1 T = 1 weber per square metre (Wb/m²).
Transformer Principle: A transformer is a static device that transfers electrical energy between two or more circuits through electromagnetic induction. It operates on AC only and can step voltage up or down while maintaining the frequency. Its primary purpose in an aircraft is to change voltage levels for different system requirements.
Transformer Equation: The ratio of voltages is equal to the ratio of turns.
Formula: Vp / Vs = Np / Ns
Application: A transformer stepping down 240 V to 24 V with 1000 primary turns has Ns = (Vs/Vp) × Np = (24/240) × 1000 = 100 turns.
Current and Power Relationship (Ideal Transformer): An ideal transformer is 100% efficient, meaning input power equals output power (Vp × Ip = Vs × Is). Therefore, the current ratio is the inverse of the voltage ratio.
Formula: Ip / Is = Ns / Np
Application: For a 1:10 step-up transformer (primary:secondary) with 115 V on the primary and a 2 A load on the secondary, the primary current is Ip = Is × (Ns/Np) = 2 A × 10 = 20 A.

2.5 AC Theory (Syllabus Ref: 3.13)

Alternating Current (AC) is a current that periodically reverses direction.

Frequency and Period:
Frequency (f): The number of complete cycles per second.
SI Unit: Hertz (Hz). Aircraft systems commonly use 400 Hz to reduce the size and weight of transformers and motors.
Period (T): The time taken for one complete cycle.
Formula: T = 1 / f
Application: For a 400 Hz supply, T = 1 / 400 = 0.0025 s = 2.5 ms.
Peak, Peak-to-Peak, and RMS Values: For a sinusoidal waveform:
Peak Voltage (V_peak): The maximum value of the voltage waveform.
Peak-to-Peak Voltage (V_pp): The voltage from the positive peak to the negative peak. V_pp = 2 × V_peak.
RMS Voltage (V_rms): The equivalent DC voltage that would produce the same heating effect in a resistor. For a sine wave: V_rms = V_peak / √2 ≈ 0.707 × V_peak.
Application: An oscilloscope trace showing 2.5 divisions peak-to-peak at 50 V/div gives V_pp = 125 V. The peak voltage is 125 / 2 = 62.5 V. The RMS voltage is 62.5 / √2 ≈ 44.2 V.
Phase Relationship in AC Circuits:
Purely Resistive Circuit: Voltage and current are in phase (phase angle, φ = 0°). They reach their maximum and zero values simultaneously.
Purely Capacitive Circuit: Current leads voltage by 90°.
Purely Inductive Circuit: Current lags voltage by 90°.
RC Series Circuit: The phase angle (φ) between the total voltage and current is between 0° and 90°. It is calculated using tan φ = Xc / R, where Xc is capacitive reactance and R is resistance.
RL Series Circuit: The total opposition to current flow is called impedance (Z). It is the vector sum of resistance (R) and inductive reactance (XL).
Power Factor (PF): In an AC circuit, the power factor is the cosine of the phase angle between voltage and current.
Formula: PF = cos φ
A purely resistive circuit has a PF of 1. A purely reactive circuit has a PF of 0.

2.6 Three-Phase AC Systems (Syllabus Ref: 3.13)

Three-phase systems are used in aircraft for their efficiency and constant power delivery.

Advantages: Three-phase generators deliver power continuously without the pulsations of single-phase systems, making them ideal for heavy loads like electric motors and large pumps.
Phase Difference: The three phases are separated by 120 electrical degrees.
Phase Sequence: The standard phase sequence is Red, Yellow, Blue (RYB). This sequence is critical for the correct rotation of AC motors (e.g., fuel pumps) and for the parallel operation of generators. Swapping any two phases reverses the sequence and the direction of motor rotation.
Voltage Relationships (Star/Wye Connection):
Phase Voltage (V_ph): The voltage measured between a phase and the neutral point (e.g., 115 V RMS).
Line Voltage (V_L): The voltage measured between any two phases.
Formula: V_L = √3 × V_ph
Application: For a 115 V phase voltage, the line voltage is √3 × 115 V ≈ 199.2 V, typically rounded to 200 V. This is the standard 115/200 V aircraft AC system.
Earth Faults: In a star-connected system with an earthed neutral, a solid earth fault on one phase effectively displaces the neutral point to the faulted phase's potential. This causes the healthy phase-to-neutral voltages to rise to the line-to-line voltage, which is a critical consideration for insulation coordination.

2.7 Semiconductors (Syllabus Ref: 3.9, 3.16)

Semiconductors are materials with conductivity between that of conductors and insulators.

Materials: Silicon is the most commonly used semiconductor material due to its stability, temperature characteristics, and low cost.
Doping and Carrier Types:
P-type: Doped to have an abundance of "holes" (positive charge carriers). The majority carriers are holes.
N-type: Doped to have an abundance of free electrons (negative charge carriers).
Temperature Effects: Increasing temperature generates additional electron-hole pairs in a semiconductor. In a P-type material, the number of majority carriers (holes) increases with temperature, which affects device performance.
PN Junction Diode:
Depletion Region: A region at the junction of P-type and N-type material where no free carriers exist.
Forward Bias: Applying a positive voltage to the P-type (anode) relative to the N-type (cathode). This reduces the potential barrier, narrows the depletion region, and allows current to flow.
Reverse Bias: Applying a negative voltage to the anode relative to the cathode. This widens the depletion region and blocks current flow.
Zener Diode: A special type of diode designed to operate in reverse breakdown. It maintains a nearly constant voltage across its terminals over a range of currents, making it ideal for use as a voltage reference in regulators. For example, a 5.6 V Zener diode will maintain 5.6 V across it as the input voltage varies from 8 V to 12 V.
Rectification: The process of converting AC to DC.
Half-Wave Rectifier: Uses a single diode to allow only one half of the AC cycle to pass. The peak voltage across the load is the peak of the AC supply. For a 115 V RMS supply, the peak is 115 × √2 ≈ 162.6 V.
Digital Logic (NAND Gate): A NAND gate outputs a LOW signal only when all its inputs are HIGH. If both inputs are tied together, it acts as an inverter (NOT gate). If the input is HIGH, the output is LOW.

2.8 Electrical Measuring Instruments (Syllabus Ref: 3.17)

Ammeter: Measures current. It must be connected in series with the circuit to ensure the full current flows through it.
Voltmeter: Measures voltage. It is connected in parallel across the component or supply.
Ohmmeter: Measures resistance. It is used to check continuity and winding integrity. It is essential to ensure the component is isolated from the aircraft's electrical system before measuring resistance. If the component is still connected, other components in parallel will provide alternative current paths, reducing the measured resistance and giving a false reading.
Megger (Insulation Resistance Tester): Measures very high resistances (in megohms) to test insulation integrity. It is critical to use a megger with an appropriate test voltage for the component being tested. Using a 500 V megger on a 28 V component can stress the insulation and produce misleading results. Low-voltage aircraft components typically require a 50 V or 100 V megger.
Oscilloscope: Displays voltage waveforms. It is used to measure voltage, frequency, and phase relationships. The vertical scale (V/div) and horizontal scale (time/div) must be set correctly to interpret the trace.

3. Important Formulas and Relationships

Concept	Formula	SI Units	Notes
Ohm's Law	`V = I × R`	V, A, Ω	Fundamental to all circuit analysis.
Electrical Power	`P = V × I`	W	Can be combined with Ohm's Law.
Power (Derived)	`P = I² × R` or `P = V² / R`	W	Useful for calculating coil dissipation.
Series Resistance	`R_total = R1 + R2 + ...`	Ω	Current is the same through all components.
Parallel Resistance	`1/R_total = 1/R1 + 1/R2 + ...`	Ω	Voltage is the same across all branches.
Temperature Coefficient	`R_T = R_0 [1 + α(T - T_0)]`	Ω	α for copper ≈ 0.00393 /°C.
Capacitance	`C = Q / V`	F	Charge stored per unit voltage.
Energy in a Capacitor	`E = ½ × C × V²`	J	Energy stored in the electric field.
RC Time Constant	`τ = R × C`	s	Time to charge to ~63.2% or discharge to ~36.8%.
Self-Induced EMF	`E = L × (di/dt)`	V	Opposes a change in current.
AC Period	`T = 1 / f`	s	Time for one complete cycle.
RMS Voltage (Sine)	`V_rms = V_peak / √2`	V	Equivalent DC value for heating effect.
Peak Voltage (Sine)	`V_peak = V_rms × √2`	V	Maximum value of the waveform.
Transformer Voltage Ratio	`Vp / Vs = Np / Ns`	V, turns	Voltage is proportional to turns.
Transformer Current Ratio	`Ip / Is = Ns / Np`	A	Current is inversely proportional to turns.
Three-Phase Line Voltage	`V_L = √3 × V_ph`	V	For a balanced star-connected system.
Power Factor	`PF = cos φ`	-	φ is the phase angle between V and I.
RC Phase Angle	`tan φ = Xc / R`	-	For a series RC circuit.

4. Common Relationships Between Concepts

Ohm's Law and Power: These are intrinsically linked. Knowing any two of the four variables (V, I, R, P) allows the calculation of the other two. This is essential for verifying component ratings.
Capacitance and AC/DC: A capacitor's behaviour is entirely different in DC (blocks current) versus AC (offers reactance). This dual nature is key to its use in filtering and power supply circuits.
Inductance and Transformers: A transformer relies on mutual inductance between its primary and secondary windings. The principles of self-inductance and Faraday's Law are the foundation of transformer operation.
AC Theory and Three-Phase Systems: Three-phase power is a specific application of AC theory. The RMS and peak values, frequency, and phase relationships all apply, with the added complexity of the 120° phase separation between the three phases.
Semiconductors and Rectification: The diode's ability to conduct in one direction (forward bias) and block in the other (reverse bias) is the fundamental principle behind rectifiers used in aircraft power supplies.
Measuring Instruments and Circuit Theory: The correct use of an ammeter (series) and voltmeter (parallel) is a direct application of Kirchhoff's laws. The need to isolate a component for resistance checks is based on understanding parallel circuit paths.

5. Typical Exam Focus Points

Calculations: Be prepared to perform calculations using Ohm's Law, the power formulas, series/parallel resistance, the RC time constant, transformer ratios, AC period/frequency, and RMS/peak voltage conversions.
Circuit Behaviour: Understand the qualitative behaviour of components in circuits. For example, what happens to current when voltage is doubled? What is the current through a fully charged capacitor in a DC circuit? What is the phase relationship in a purely resistive circuit?
Component Characteristics: Know the defining characteristics of resistors, capacitors, inductors, diodes (including Zener), and transformers. This includes their units, symbols, and key applications.
Three-Phase Systems: Understand the advantages, phase separation, phase sequence (RYB), and the relationship between phase and line voltages (√3 factor).
Measurement Techniques: Know how to connect ammeters (series) and voltmeters (parallel). Understand the critical safety and procedural steps for resistance and insulation resistance measurements, including circuit isolation and correct megger voltage.
Safety: Understand the safe discharge procedure for capacitors and the importance of using the correct test voltage for insulation testing.
Practical Application: Be able to apply theoretical knowledge to practical scenarios, such as troubleshooting an open winding (infinite resistance), a short circuit (near-zero resistance), or a normal coil (calculated current and power draw).
Temperature Effects: Understand how temperature affects resistance, especially for copper, and be able to correct measurements back to a reference temperature.