Electrical Theory
Electrical theory questions test whether you can move fluently between Ohm’s law, power, and AC impedance without mixing units or phase relationships. For DC and resistive AC, V = I × R, P = V × I = I²R = V²/R. For AC, replace resistance with impedance Z, and remember that current and voltage may be out of phase. Real power is P = V × I × cos θ (watts), reactive power is Q = V × I × sin θ (VAR), and apparent power is S = V × I (VA). Power factor is the ratio P/S, not an efficiency percentage.
Three-phase relationships
In a balanced three-phase system, total real power is P = √3 × V_L × I_L × cos θ, where V_L and I_L are line values. In a wye connection, phase voltage is line voltage divided by √3 and phase current equals line current. In a delta connection, phase voltage equals line voltage and phase current is line current divided by √3. The common trap is applying single-phase formulas to three-phase loads or using phase voltage where line voltage is required.
AC behavior
Inductive reactance X_L = 2πfL increases with frequency; capacitive reactance X_C = 1/(2πfC) decreases with frequency. Impedance combines resistance and reactance vectorially: Z = √(R² + X²). RMS values are the effective values used by meters and nameplates; peak value is √2 times RMS for a sine wave. Transformers trade voltage and current by turns ratio while conserving power (ignoring losses).
Worked example
A balanced 480 V three-phase load draws 50 A at 0.85 power factor. P = √3 × 480 × 50 × 0.85 ≈ 35.3 kW. If someone uses 480 × 50 × 0.85, they get about 20.4 kW - a classic missing-√3 error.