Electrical Machines: Transformers, Induction and DC Motors
What this domain tests
Electrical Machines covers transformer EMF equation and turns ratio, three-phase induction motor synchronous speed and slip, and DC motor back emf and torque. Numerical questions often combine nameplate data with one formula.
Core rules
- Transformer: E = 4.44 f N Φm. Turns ratio a = N1/N2 = V1/V2; current ratio I1/I2 = N2/N1 ideally.
- A transformer does not change frequency. It changes voltage and current; losses are core and copper.
- Induction motor synchronous speed Ns = 120f/P. Slip s = (Ns − Nr)/Ns; rotor speed Nr = Ns(1 − s).
- DC motor back emf Eb = V − IaRa. Starting current is high because Eb is zero at standstill, so a starter is needed.
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, or 4%. If the load increases, slip rises slightly while synchronous speed stays fixed by supply frequency and poles.
Traps that cost marks
Using rotor speed instead of synchronous speed in the slip formula, thinking a transformer changes frequency, ignoring efficiency and power factor when calculating motor current, and forgetting that a DC motor has no back emf at start. Also check whether voltage is line or phase in three-phase calculations.