Electrical Theory, Principles, and General Knowledge
Ohm's law and power
Every calculation on the exam traces back to E = I × R and P = I × E. In series circuits current is common and voltage divides; in parallel circuits voltage is common and current divides. Resistance in series adds directly; in parallel the reciprocal sum (or product over sum for two resistors) gives the equivalent. Alternating current adds impedance, which includes reactance, so current and voltage can peak at different times. Power factor (PF) is the cosine of that angle: real power is watts, apparent power is volt-amperes, and reactive power is VARs.
Single-phase versus three-phase
Single-phase: P = V × I × PF. Balanced three-phase: P = √3 × V(line-to-line) × I × PF. A quick sanity check: √3 ≈ 1.732, so a 208 V three-phase circuit carries about 1.732 times the power of a 208 V single-phase circuit at the same current.
Traps
Watch for peak versus RMS (120 V RMS has a peak near 170 V); confusing line-to-line and line-to-neutral voltage; calling 240 V “two-phase”; ignoring PF when the load is inductive; and assuming a 120/240 V service is three-phase.
Worked example
A 208 V, three-phase, 40 A load at 0.85 PF: P = 1.732 × 208 × 40 × 0.85 ≈ 12,250 W, about 12.25 kW. Apparent power is 1.732 × 208 × 40 ≈ 14,410 VA. If the same load were single-phase at 208 V, it would draw 208 × 40 × 0.85 ≈ 7,072 W.