Part-66 Module 3 formulas: Ohm's law to three-phase AC

The formulas Module 3 Electrical Fundamentals expects you to use: Ohm's law, series and parallel circuits, power, RC and L/R time constants, reactance and transformers.

Checked against the rules in force on 2026-10-26

Module 3 is 52 multiple-choice questions in 65 minutes for category B1, with three choices per question and a 75% pass mark. Many questions are short calculations. These are the relationships you need to know without looking them up.

DC circuits

Ohm's law: V = I × R. If you know two values you can find the third.
Series: resistances add. The same current flows everywhere and the voltage divides in proportion to resistance.
Parallel: 1/R = 1/R1 + 1/R2 + … For two resistors use product over sum. The voltage is the same across every branch and the total is always less than the smallest branch.
Kirchhoff: currents into a junction equal currents out; voltage drops around a loop add up to the supply.
Power: P = V × I = I²R = V²/R. In series the largest resistor dissipates most; in parallel the smallest does.
Resistance of a wire: R = ρL/A. Double the length, double the resistance; double the diameter, a quarter of the resistance.

Cells and batteries

A lead-acid cell gives about 2 V, a nickel-cadmium cell about 1.2 V. In series voltages add; in parallel capacity adds. Terminal voltage = EMF − I × internal resistance.

Capacitors and inductors

C = Q/V. Capacitors in parallel add; in series they combine like parallel resistors.
Time constant τ = RC (or L/R for an inductor). One time constant gives about 63%; five give practically full charge.
Stored energy: ½CV² and ½LI².
Inductance rises with the square of the number of turns. Lenz's law: an induced EMF opposes the change that caused it.

AC

RMS = 0.707 × peak, average = 0.637 × peak, peak = 1.414 × RMS. Period T = 1/f, so 400 Hz has a period of 2.5 ms.
XL = 2πfL rises with frequency; XC = 1/(2πfC) falls with frequency.
Impedance Z = √(R² + (XL − XC)²). At series resonance XL = XC and Z = R.
Resonant frequency f = 1/(2π√LC).
Power factor = true power / apparent power = cos φ. Units: W, VA and VAR.
In an inductor voltage leads current; in a capacitor current leads voltage (ELI the ICE man).

Three-phase, transformers and machines

Phases are 120° apart. In star, line voltage = √3 × phase voltage, so 115 V phase gives about 200 V line.
Transformer: Vs/Vp = Ns/Np, and current changes the opposite way.
Generator frequency f = P × N / 120. An 8-pole alternator at 6,000 rpm gives 400 Hz.
Induction motor synchronous speed Ns = 120f/P; the rotor runs slightly slower (slip).

Practise each formula until you can do it in under a minute: the exam allows about 75 seconds per question.

Sources: Part-66 Appendix I, Module 3 · FAA-H-8083-30A, Fundamentals of Electricity and Electronics