Electrical Machines (Transformers, DC and AC Machines)
Electrical Machines covers transformers, DC machines, three-phase induction motors, and synchronous machines. The exam tests equivalent circuits, losses, efficiency, speed control, starting, and slip calculations.
Core rules
- Transformer emf: E=4.44 f N Φm; turns ratio a=N1/N2≈V1/V2; ideal transformer VA is constant.
- Transformer losses: core loss is constant at fixed voltage/frequency; copper loss varies as I² and is found by short-circuit test. Efficiency peaks when copper loss equals core loss.
- DC machine emf: E=PΦNZ/(60A); lap winding A=P, wave A=2. Torque T=PΦIaZ/(2πA).
- Shunt motor has nearly constant speed; series motor has high starting torque and must never run unloaded.
- Induction motor synchronous speed Ns=120f/P; slip s=(Ns−Nr)/Ns; rotor frequency sf.
- Synchronous machine runs at Ns and can supply lagging or leading reactive power by field excitation.
Worked example
A 4-pole, 50 Hz induction motor runs at 1440 r/min. Ns=120×50/4=1500 r/min. Slip=(1500−1440)/1500=0.04=4%. Rotor frequency=0.04×50=2 Hz.
Traps
Transformer rating is kVA because losses depend on voltage and current, not load power factor. Do not use output/input efficiency with input unknown; check whether efficiency is full-load or part-load. DC series motor at no load can overspeed.