Electrical Machines and Transformers
Electrical Machines and Transformers tests transformer ratios, losses and efficiency, induction-motor speed and slip, DC-machine EMF, and the purpose of starters.
Core rules
- Transformer: V1/V2 = N1/N2 = I2/I1 for a single phase. For three-phase, use line quantities with √3 and keep kVA consistent.
- Transformers work on alternating flux; a DC supply gives no induced secondary EMF and can overheat the primary.
- Losses: copper loss I²R varies with load; iron loss is approximately constant. Efficiency = output/(output + losses), with maximum efficiency near full load at unity power factor.
- Induction motor synchronous speed Ns = 120f/P; slip s = (Ns − N)/Ns; rotor frequency = sf.
- DC motor back EMF Eb = V − IaRa; it limits armature current, so a starter is needed to avoid a large starting current.
Worked example
A 25 kVA, 11 kV/415 V three-phase transformer has a turns ratio per phase of about 11000/415 = 26.5. Full-load secondary line current = 25000/(√3 × 415) = 34.8 A. Full-load primary line current = 25000/(√3 × 11000) = 1.31 A. If the transformer delivers 18 kW at 0.9 pf, output kVA = 18/0.9 = 20 kVA, so loading is 80% of rating. Copper loss at 80% load is 0.8² = 0.64 of full-load copper loss.
Traps
Do not use kW and kVA interchangeably; do not treat a transformer as a rotating machine or connect it to DC; do not use Ns = 120f/P for a DC motor; and remember slip is a fraction, often asked as a percentage.