Electrical engineering
Three-phase power
Line versus phase, Y and Δ, √3 power, and a motor sketch.
Basics
Line and phase
Three-phase means three sinusoids 120° apart. Phase voltage sits across one winding (or one load leg); line voltage is between two lines. In a balanced wye, V_L = √3 V_Ph and I_L = I_Ph. In delta, V_L = V_Ph and I_L = √3 I_Ph. A neutral gives unbalanced current a return path. Distribution often uses four wires (three phases plus neutral).
Wye and delta
Wye (Y) shares a neutral node with three legs outward. Delta closes a triangle and needs only three line wires. Y–Δ motor starting can cut inrush. The same line voltage presents a different winding voltage after a reconnect. Write V_L and V_Ph before sketching the diagram.
Three-phase power
Balanced three-phase real power is P = √3 V_L I_L cos φ, with φ between phase voltage and phase current. Reactive and apparent power use the same √3 form. Three single-phase sets 120° apart smooth instantaneous power — kinder to rotating machines. Power-factor correction shrinks φ with capacitors. Meters often use two-wattmeter or three-element schemes.
Motor sketch
An induction motor’s stator rotating field induces rotor current and torque. Synchronous speed is n_s = 120 f / p (r/min, p poles). Slip is required for induction torque. Inrush is large, so soft starters and inverters are common. Brushless builds dominate plant drives. Swap two phases and the shaft reverses.
Formulas
Wye line and phase
Balanced assumption.
Symbols
-
V_Lline voltage -
V_Phphase voltage
Delta line and phase
Balanced assumption.
Symbols
-
I_Lline current
Three-phase real power
Balanced. φ is the power-factor angle.
Symbols
-
φvoltage–current phase angle
Synchronous speed
Revolutions per minute. f frequency, p pole count.
Symbols
-
ffrequency -
pnumber of poles
Key table
| 120° | electrical spacing of the three phases; vector sum near zero when balanced |
|---|---|
| Power factor | cos φ; lagging usually means inductive loads |
| Wire colours | varies by country; check local code before work |
In this field
DC circuits
Ohm, Kirchhoff, series/parallel, power.
Capacitors, inductors, AC
Charge/discharge, reactance, impedance, resonance.
Power, semiconductors, digital
Transformers, three-phase, diodes, gates.
Magnetism, motors, control
Faraday, motors, filters, feedback.
Signals and logic
Fourier sketch, sampling, Boolean algebra.
Semiconductors
Carriers, diodes, a MOSFET sketch.
Measurements and electrical safety
Multimeters, RMS versus peak, transformer ratio, and electrical safety.
Op-amps and filters
The ideal op-amp, inverting and non-inverting gain, RC low- and high-pass, cutoff frequency.
Digital logic
Boolean algebra, gates, flip-flops, and timing.
Batteries and photovoltaics
Capacity and C-rate, series/parallel packs, PV I–V curves, and the maximum-power point.