Electrical Theory and Fundamentals
This domain tests the circuit laws, AC phasor methods, and power relationships that every later calculation depends on. Expect questions that combine Ohm's and Kirchhoff's laws with impedance, power factor, and balanced three-phase quantities.
Core rules
- Ohm's law and Kirchhoff's voltage and current laws apply in both DC and instantaneous AC form; for AC, use complex impedance Z = R + jX.
- Single-phase power: P = VI cos φ, Q = VI sin φ, S = VI. Balanced three-phase: S = √3 V_L I_L, with V_L the line-to-line voltage.
- Power factor is cos φ where φ is the angle by which current lags or leads voltage; lagging means inductive.
- In series, impedances add; in parallel, admittances add. Add phasors in rectangular form and convert to polar only at the end.
- RMS values are used for power; a pure sinusoid averages to zero, so never substitute peak values into power formulas without the √2 conversion.
Worked example
A balanced 400 V three-phase load draws 50 A at 0.85 power factor lagging. Apparent power S = √3 × 400 × 50 = 34.6 kVA. Real power P = 34.6 × 0.85 = 29.4 kW. Reactive power Q = √3 × 400 × 50 × sin(31.8°) = 34.6 × 0.527 = 18.2 kvar. Check: √(29.4² + 18.2²) = 34.6 kVA, confirming the triangle closes.
Traps
Using phase voltage in place of line voltage in the √3 formula, or applying √3 inside a per-phase calculation, is the most common error. Watch for power factor given as a percentage, and for loads stated in kVA where kW must be derived. A leading power factor gives negative Q, which changes later power-factor-correction answers.