Alternating current (AC) is the backbone of power distribution worldwide. Generated by rotating machinery called alternators, AC voltage changes direction many times per second — 60 times per second in the United States. This fundamental property allows efficient voltage transformation using transformers, making AC the clear winner for long-distance power transmission.
The historic "War of Currents" in the late 1880s pitted Nikola Tesla and George Westinghouse (AC) against Thomas Edison (DC). Tesla's AC system prevailed because transformers can step voltage up for efficient long-distance transmission and back down for safe local use. DC at the time had no practical equivalent for this function.
Understanding AC principles is foundational to working safely and effectively on industrial electrical systems.
Upon completing this lesson, you will be able to:
Before starting this lesson, you should have completed:
Ohm's Law (V=IR) from Lesson 5.2 is extended in this lesson to AC circuits using impedance (V=IZ).
AC voltage follows a sinusoidal waveform — a smooth, repeating curve generated by the rotation of a coil in a magnetic field. Each complete rotation produces one complete cycle of the waveform.
A rotating coil in a uniform magnetic field produces a voltage proportional to the sine of the rotation angle. As the coil spins at constant speed, the voltage traces out the familiar sine wave. The phasor (rotating arrow on the left) represents the rotating coil — its vertical projection at each instant is the instantaneous voltage shown on the right.
Root Mean Square (RMS) is the DC-equivalent value of an AC waveform — the AC voltage that produces the same heating effect in a resistor as an equal DC voltage. This is what multimeters read.
| Nominal RMS | Peak Voltage (Vpk) | Peak-to-Peak (Vpp) | Application |
|---|---|---|---|
| 120V | 169.7V | 339.4V | Single-phase outlets, lighting, small tools |
| 208V | 294.2V | 588.4V | Single-phase from 3-phase 208Y/120 system |
| 240V | 339.4V | 678.8V | Single-phase 240V — dryers, HVAC, welders |
| 277V | 391.7V | 783.4V | Commercial fluorescent/LED lighting |
| 480V | 678.8V | 1,357.6V | 3-phase motor power, large drives |
A VFD rectifies AC to DC. The DC bus charges to approximately 1.35 x Vrms (line-to-line):
This is why VFDs require full lockout/tagout AND capacitor discharge verification before internal work. The DC bus remains energized for minutes after AC power is removed.
Inductance (L) is measured in Henries (H). An inductor resists changes in current. When current increases through a coil, the building magnetic field induces a back-EMF opposing the change. When current decreases, the collapsing field tries to sustain current flow.
Inductance you will encounter in the field:
XL increases proportionally with frequency. Inductors pass DC freely but increasingly oppose higher-frequency AC.
In a purely inductive circuit, current lags voltage by 90 degrees. In practical motor or transformer loads, winding resistance reduces the lag to typically 15°-45°. This phase lag is the primary cause of poor power factor in industrial facilities.
Capacitance (C) is measured in Farads (F) — in practice, microfarads (uF) or nanofarads (nF). A capacitor resists changes in voltage by storing energy in an electric field between two conductive plates. When voltage rises, the capacitor charges (absorbs current); when voltage falls, it discharges (releases current).
Capacitors you will encounter:
XC decreases as frequency increases — exactly opposite of XL. This complementary behavior is the basis for LC filters and resonant circuits.
Capacitors store charge and can release it long after AC power has been disconnected. A VFD with 1,000 uF bus capacitor charged to 800V contains:
320 joules is sufficient to cause severe arc flash injury or death. Always verify DC bus voltage is below 50V DC using a calibrated meter before touching internal VFD components. Never assume the capacitors have discharged — measure first.
Impedance is the total opposition to current flow in an AC circuit, combining resistance (R) and net reactance (XL - XC). Measured in Ohms. The AC equivalent of DC resistance.
Unlike DC circuits, AC circuits have three contributors to opposition:
Since XL and XC are 180 degrees out of phase, they partially cancel. Net reactance is their difference:
| Load Type | Impedance Formula | Current vs. Voltage | Field Examples |
|---|---|---|---|
| Pure Resistive | Z = R | In phase (0 deg lag) | Heaters, incandescent lamps, resistive ovens |
| Inductive | Z = sqrt(R^2 + XL^2) | Current lags voltage | Motors, transformers, relay/contactor coils |
| Capacitive | Z = sqrt(R^2 + XC^2) | Current leads voltage | Power factor correction capacitor banks |
| RLC Mixed | Z = sqrt(R^2 + Xnet^2) | Depends on net reactance | VFD input circuits, motor + PFC combination |
In a purely resistive AC circuit, voltage and current peak simultaneously. All power does useful work. In circuits with L or C, current and voltage are out of phase — some power oscillates back and forth without doing useful work. Power Factor (PF) quantifies this efficiency:
| Power Factor | Condition | Industrial Impact |
|---|---|---|
| 0.95 – 1.00 | Excellent | Optimal efficiency, no utility penalty, minimal cable heating |
| 0.90 – 0.94 | Good | Acceptable; utility penalties unlikely at most tariffs |
| 0.85 – 0.89 | Marginal | At or near penalty threshold; PF correction warranted |
| 0.70 – 0.84 | Poor | Utility penalties, cables carry excess current, elevated heat |
| < 0.70 | Very Poor | Significant penalties, equipment de-rating required, fire risk |
Large industrial customers with PF below 0.85 typically face demand penalties. A facility consuming 100 kW true power at PF = 0.70 must supply 143 kVA apparent power. All cables, transformers, breakers, and switchgear must be sized for the higher 143 kVA level even though only 100 kW does useful work.
Power factor correction capacitor banks (switched automatically by a PF controller) counteract inductive motor loads and reduce both utility penalties and cable losses.
Enter circuit parameters to calculate impedance, current, power, and power factor for a series RLC circuit.
The United States uses 60 Hz nationwide. Voltage standards are defined by ANSI C84.1. Understanding the distribution hierarchy helps you anticipate what voltages you will encounter at each point in a facility.
| System | Voltage | Phase Configuration | Frequency | Typical Use |
|---|---|---|---|---|
| Residential | 120 / 240V | 1-phase split (2-wire + N) | 60 Hz | Lighting, appliances, small tools |
| Light Commercial | 120 / 208V | 3-phase, 4-wire Y | 60 Hz | Office buildings, retail, small HVAC |
| Industrial (standard) | 277 / 480V | 3-phase, 4-wire Y | 60 Hz | Motors, drives, large mechanical loads |
| Industrial (legacy) | 120 / 208V | 3-phase, 4-wire Y | 60 Hz | Older industrial and commercial facilities |
| Primary Distribution | 4.16 kV | 3-phase | 60 Hz | Large motor feeders, plant substations |
| Primary Distribution | 12.47 kV / 13.8 kV | 3-phase | 60 Hz | Utility primary feeders, campus distribution |
| European Standard | 230V | 1-phase | 50 Hz | All European single-phase equipment (IEC) |
| European Industrial | 400V | 3-phase, 4-wire Y | 50 Hz | European motors, drives, imported machinery |
European equipment rated for 50 Hz may run hotter and faster on a 60 Hz system (motors run ~20% faster; transformers may saturate and overheat). Always check equipment nameplates for rated voltage AND frequency before energizing.
VFDs can output any frequency between 0 Hz and 400+ Hz regardless of input frequency — but the input supply must still match the drive's rated input voltage and frequency.
Early US power systems used a range of frequencies (25 Hz, 50 Hz, 60 Hz, 133 Hz). The 60 Hz standard emerged from practical compromises:
Select the best answer for each question, then click Check Answer. A score of 4/5 or higher is required to proceed.
| Lesson | Connection to These AC Principles |
|---|---|
| 5.4 — Voltage, Current, Resistance & Power | Extends Ohm's Law and power calculations to practical field scenarios |
| 5.7 — Three-Phase Power Systems | Applies AC phase relationships to three-phase wye and delta configurations |
| 5.11 — Transformers | Transformer operation is entirely dependent on AC inductance and mutual magnetic coupling |
| 5.12 — AC Induction Motors | Motor theory builds on inductive reactance, rotating magnetic fields, and power factor |