Electrical Machines
Electrical Machines
This domain tests transformers, DC machines and induction motors: their equations, losses, starting methods and the numerical relations the exam expects.
Core rules
- Transformer EMF: E = 4.44 f N Φm. Turns ratio a = N1/N2 = V1/V2 = I2/I1.
- Transformer losses: iron (hysteresis + eddy, nearly constant) and copper (I²R, load-dependent). Maximum efficiency occurs when copper loss equals iron loss.
- DC machine EMF: E = (PΦNZ)/(60A); in a motor the back EMF opposes the supply, so Ia = (V − Eb)/Ra.
- Synchronous speed Ns = 120f/P; slip s = (Ns − Nr)/Ns; rotor frequency fr = s × f.
- Three-phase star: VL = √3 Vph, IL = Iph. Delta: VL = Vph, IL = √3 Iph.
- Starting: DOL for small motors, star-delta or autotransformer for larger ones; star-delta cuts starting current and starting torque to one third.
- Single-phase motors - capacitor-start, split-phase, shaded-pole - need an auxiliary phase to produce starting torque.
Worked example
A 4-pole, 50 Hz three-phase induction motor runs at 1440 rpm. Ns = 120 × 50 / 4 = 1500 rpm. Slip = (1500 − 1440)/1500 = 0.04, i.e. 4 %. Rotor frequency = 0.04 × 50 = 2 Hz. Because the rotor runs at 96 % of synchronous speed, the motor's efficiency cannot be inferred from slip alone - slip describes speed, not losses.
Mark-losing traps
- Quoting three-phase line values where a phase value is required, or vice versa.
- Confusing slip with efficiency or with percentage regulation.
- Dropping the 4.44 factor in the transformer EMF equation.
- Forgetting that star-delta starting also cuts starting torque to one third.