Electrical Science and Principles
This domain tests the physics and circuit mathematics you use to size, diagnose and explain installations: Ohm's law and power, series and parallel networks, AC quantities, reactance and impedance, three-phase relationships, transformers and power factor.
Core relationships
- V = IR; P = VI = I²R = V²/R; energy in kWh = kW × hours.
- Series: resistances add, current is common. Parallel: 1/R total is the sum of the reciprocals, voltage is common.
- AC: Vrms = Vpeak/√2; XL = 2πfL; XC = 1/(2πfC); Z = √(R² + (XL − XC)²); cos φ = R/Z.
- Star: IL = Iph and VL = √3 Vph. Delta: VL = Vph and IL = √3 Iph. Three-phase power P = √3 VL IL cos φ.
Worked example
A 400 V three-phase motor draws 28 A at 0.78 power factor lagging. P = 1.732 × 400 × 28 × 0.78 = 15.1 kW. To correct the factor to 0.95: tan φ1 = tan(cos⁻¹ 0.78) = 0.802 and tan φ2 = tan(cos⁻¹ 0.95) = 0.329. Required capacitor rating Qc = P(tan φ1 − tan φ2) = 15.1 × 0.473 ≈ 7.1 kvar. Note the active power is unchanged - correction reduces the line current and therefore the losses in the supply cables, and frees capacity in the supply.
Traps
Mixing rms and peak values inside power formulae; omitting √3 in three-phase current calculations; treating kVA as kW when finding current; forgetting that copper resistance rises with temperature, R2 = R1[1 + 0.00393(T2 − T1)], which shifts both fault current and loop impedance; and assuming capacitors reduce the kW billed rather than the kvar.