Electrical Theory, Ohm's Law, and Circuit Calculations
Core concepts
Nearly every calculation question reduces to Ohm's law (E = I × R) and the power wheel (P = E × I, P = I²R, P = E²/R), combined with the rules for series and parallel circuits. In series, current is identical everywhere and voltages add; in parallel, voltage is identical and branch currents add. Series resistances add directly; for two parallel resistors use R1R2/(R1+R2).
AC adds impedance. Inductive reactance X_L = 2πfL, capacitive reactance X_C = 1/(2πfC), and Z = √(R² + (X_L − X_C)²). Power factor is the cosine of the angle between voltage and current; watts are true power, volt-amperes are apparent power. For a balanced three-phase load, P = √3 × E_line × I_line × PF.
Traps
- Mixing line-to-line and line-to-neutral voltages (480/277, 208/120, 240/120).
- Substituting peak voltage where RMS is required - 120 V RMS has a peak of about 170 V.
- Assuming the neutral carries current in a balanced three-phase, four-wire wye system; it does not.
- Omitting power factor when converting kVA to kW.
- Forgetting that a purely resistive load has unity power factor while a motor does not.
Worked example
A balanced 480 V, three-phase motor draws 25 A at 0.85 power factor. Apparent power = √3 × 480 × 25 ≈ 20,785 VA (20.8 kVA). True power = 20,785 × 0.85 ≈ 17,667 W (17.7 kW). Using 480 × 25 = 12 kW is single-phase math and is the classic wrong answer offered on these questions.