Electrical Machines and Transformers
Machines covered
The syllabus covers DC machines, three-phase induction motors, single-phase induction motors and transformers. The three-phase squirrel-cage induction motor is the workhorse; the single-phase capacitor-start motor is common for pumps and compressors.
Key relationships
- Synchronous speed: Ns = 120f/P.
- Slip: s = (Ns − N)/Ns, often expressed as a percentage.
- Transformer EMF: E = 4.44 f N Φm; turns ratio a = N1/N2 = V1/V2; current ratio is inverse.
- Star connection: phase voltage = V_L/√3. Delta connection: phase current = I_L/√3.
- A transformer does not change frequency and has no moving parts; core loss is constant, copper loss varies with load squared.
Worked example
A 4-pole, 50 Hz induction motor runs at 1440 rpm. Ns = 120 × 50/4 = 1500 rpm. Slip = (1500 − 1440)/1500 = 0.04 = 4%. If the same motor were 6-pole, Ns = 1000 rpm and at the same 4% slip it would run at 960 rpm.
Traps
Using 1440 rpm as synchronous speed, forgetting that slip must use consistent units, and confusing transformer turns ratio with current ratio. A motor nameplate's kW is mechanical output, not input; input = output/efficiency.