Electrical Theory and Fundamentals
Ohm's law and power
V = I x R, P = V x I = I^2 x R = V^2 / R. In series, resistances add and current is common; in parallel, voltage is common and 1/Rt = 1/R1 + 1/R2. AC circuits add impedance: Z = square root of (R^2 + (XL - XC)^2), where XL = 2 pi f L and XC = 1/(2 pi f C). Real power is P = V I x power factor for single phase and P = 1.732 x V I x power factor for three phase; kVA is the apparent power and kW is the real power. RMS values are 0.707 of peak. Transformers follow V1/V2 = N1/N2 with current in inverse ratio.
Voltage drop: single phase VD = 2 K I D / CM, three phase VD = 1.732 K I D / CM, where K is 12.9 for copper and 21.2 for aluminum, D is one-way distance in feet, and CM is circular mils.
Worked example: a 50 A, 240 V single-phase load 100 ft away on 8 AWG copper (16,510 circular mils): VD = 2 x 12.9 x 50 x 100 / 16,510 = 7.8 V, or 3.3% of 240 V - above the 3% branch-circuit recommendation. Upsizing to 6 AWG (26,240 circular mils) gives 4.9 V, or about 2.0%, which is acceptable.
Traps: using the factor 2 instead of 1.732 for three-phase voltage drop; using one-way distance twice; computing kW without power factor in inductive loads; mixing 120/240 V and 120/208 V systems when checking equipment ratings.