Electrical Theory and Circuits
The four relationships you must own
Ohm's law (V = I x R), the power equations (P = V x I = I squared x R = V squared / R), Kirchhoff's voltage law (sum of drops around a loop equals the source) and Kirchhoff's current law (current into a node equals current out). Series circuits share one current and divide voltage; parallel circuits share one voltage and divide current. Series resistances add; parallel resistances use reciprocals, and two in parallel give the product over the sum.
AC, impedance, and three phase
In AC, resistance becomes impedance built from resistance plus inductive and capacitive reactance. Real power (watts) equals apparent power (volt-amperes) times power factor. Inductive loads such as motors have lagging power factor. Stated AC voltages are RMS values; peak is 1.414 times RMS. Three-phase power is 1.732 x V x I x PF for a balanced load.
Traps
Mixing peak and RMS values; ignoring power factor when converting kVA to kW; applying a single-phase voltage-drop formula to a three-phase circuit (the three-phase form uses 1.732 rather than 2); treating an open neutral as harmless when it can put line voltage across a 120 V load.
Worked example
A balanced 480 V three-phase motor draws 25 A at 0.80 power factor. P = 1.732 x 480 x 25 x 0.80 = 16,627 W, about 16.6 kW, and the apparent power is 1.732 x 480 x 25 = 20,784 VA.
Rule of thumb
Single-phase VA is V x I; three-phase VA is 1.732 x V x I; kW is kVA times power factor. One horsepower is about 746 W.