Electrical Machines (Transformers, DC Machines, Induction and Synchronous Machines)
Electrical Machines covers transformer operation, DC machine equations, induction motor slip, and synchronous machine excitation. The exam favors equivalent circuits and speed-torque relationships over descriptive history.
Core rules
- Transformer induced emf: E = 4.44 f N Phi_m. Core loss is approximately constant with load; copper loss varies as I^2R.
- DC machine back emf: E_b = P Phi N Z/(60A); torque T = P Phi Z I_a/(2piA). A series motor must never be started unloaded.
- Induction motor synchronous speed N_s = 120f/P; slip s = (N_s - N)/N_s; rotor frequency f_r = s f.
- A synchronous machine is doubly excited, runs at N_s, and is not self-starting. Excitation controls reactive power.
- Maximum torque of an induction motor is independent of rotor resistance, while slip at maximum torque is proportional to rotor resistance.
Worked example
A 4-pole, 50 Hz induction motor runs at 1440 r/min. N_s = 120 × 50/4 = 1500 r/min. Slip s = (1500 - 1440)/1500 = 0.04 = 4%. Rotor frequency f_r = 0.04 × 50 = 2 Hz. The reasoning uses synchronous speed first, then slip, then rotor frequency; do not use supply frequency directly for rotor quantities.
Traps
Confusing mechanical speed with synchronous speed; treating transformer core loss as load-dependent; forgetting that a DC shunt motor field is connected across the armature; and ignoring that synchronous motors need a starting method.