Electrical Machines
Electrical Machines is a large, high-weight domain covering transformers, DC machines, induction machines, and synchronous machines. Questions usually combine one governing equation with one equivalent-circuit or performance idea.
Transformers
- E = 4.44 f N Φ_m for sinusoidal flux; the voltage per turn is identical on both windings.
- Open-circuit test gives core loss; short-circuit test gives copper loss and leakage reactance.
- Maximum efficiency occurs when copper loss equals core loss.
DC machines
- E = PΦNZ/60A and T = PΦIZ/2πA; back EMF sets the armature current.
Induction machines
- N_s = 120f/P, s = (N_s − N_r)/N_s, rotor frequency = sf.
Synchronous machines
- E = 4.44 f N Φ k_w and P = EV sin δ/X_s.
Worked example: a 4-pole, 50 Hz induction motor runs at 1440 rpm. N_s = 120 × 50/4 = 1500 rpm, so s = (1500 − 1440)/1500 = 0.04, i.e. 4%. Rotor frequency is sf = 0.04 × 50 = 2 Hz. Rotor copper loss equals s times the air-gap power: with 20 kW crossing the gap, rotor loss is 800 W and mechanical power is 19.2 kW.
Traps that cost marks
- Using 2.22 instead of 4.44 for a sinusoidal flux waveform.
- Signs of slip: negative in generating mode, greater than 1 in plugging.
- Neglecting the magnetizing branch when computing voltage regulation.
- Connecting a three-phase transformer in delta and forgetting that line current is √3 times phase current.