Electrical Theory, Load Calculations, and Conduit/Box Fill
Theory and formula work
Ohm's law (E = IR) and power relationships (P = EI, P = I²R) underpin everything else. Series circuits share current and add resistance; parallel circuits share voltage and add by reciprocals. Three-phase power uses the 1.732 factor, and power factor converts apparent power to real power. Conductor resistance rises with length and temperature, while ampacity falls as ambient temperature climbs above 30°C or when more than three current-carrying conductors share a raceway (310.15).
Voltage drop for single phase is VD = 2KIL/CM; for three phase it is VD = 1.732KIL/CM, where K is about 12.9 for copper and 21.2 for aluminum, I is amperes, L is one-way length in feet, and CM is circular mils from Chapter 9 Table 8. The factor of 2 accounts for the return path. Divide the result by source voltage for percent drop.
Fill calculations
Conduit fill uses Chapter 9 Table 1 percentages (53/31/40) with Table 4 raceway areas and Table 5 conductor areas; a nipple 24 in or less may use 60%. Box fill uses 314.16(B) volumes: 2.0 in³ per 14 AWG, 2.25 per 12 AWG, 2.50 per 10 AWG, with one allowance for all EGCs, one for clamps, and two per yoke or device. Pull boxes follow 314.28 - 8 times the largest raceway for straight pulls, 6 times plus the sum of the other raceways in the same row for angle pulls.
Trap: using the total circuit length instead of the one-way length, or forgetting the 1.732 factor on three-phase voltage drop.
Worked example: 20 A at 120 V, 150 ft one way, 12 AWG copper (6530 cm): VD = 2 × 12.9 × 20 × 150 ÷ 6530 = 11.9 V, about 9.9% - too high, so a larger conductor is needed.