Electrical Theory and Fundamentals
Electrical Theory and Fundamentals underpins every calculation you will make on site and in the exam: Ohm's law, series and parallel networks, AC quantities, and the power relationships used on 230/400 V, 50 Hz systems.
Core relationships
- Ohm's law V = I·R; power P = V·I = I²R = V²/R.
- Series: resistances add and the current is common. Parallel: 1/R = Σ1/Ri and the voltage is common.
- AC: Vrms = Vpeak/√2. Reactances XL = 2πfL and XC = 1/(2πfC); impedance Z = √(R² + (XL − XC)²).
- Single-phase: P = U·I·cosφ, S = U·I, Q = U·I·sinφ.
- Three-phase balanced: P = √3·UL·IL·cosφ, where UL is the line-to-line voltage (400 V), not 230 V.
- Power-factor correction: Qc = P(tanφ1 − tanφ2).
Worked example
A three-phase 400 V motor draws 18 A at cosφ = 0.82. Apparent power S = √3 × 400 × 18 = 12.47 kVA. Real power P = 12.47 × 0.82 = 10.2 kW. Reactive power Q = √(12.47² − 10.2²) ≈ 7.1 kvar. To correct to cosφ = 0.95: tanφ1 = 0.70, tanφ2 = 0.33, so Qc = 10.2 × (0.70 − 0.33) ≈ 3.8 kvar. Every √3 formula used the 400 V line voltage.
Traps
- Substituting 230 V into a three-phase formula, or omitting √3 altogether.
- Adding kW and kVA together when totalling loads.
- Using peak voltage when the instrument reads rms.
- Forgetting that a capacitor bank carries current of its own, so the cable and protection must be sized for the corrected current plus harmonics.