Electrical Machines (Transformers, DC, Induction and Synchronous Machines)
Electrical Machines
This domain covers transformer operation and testing, DC machine EMF and torque, induction motor slip, and synchronous machine speed and excitation. Expect formula-based numericals and conceptual comparisons.
Core rules
- Transformer induced EMF: E = 4.44 f N Φm. Turns ratio a = N1/N2 = V1/V2; for an ideal transformer I1/I2 = 1/a.
- The open-circuit test gives iron loss and the shunt branch; the short-circuit test gives copper loss and series impedance. Efficiency is maximum when copper loss equals iron loss.
- DC generator EMF: Eg = PΦNZ/(60A), where A is the number of parallel paths. For a lap winding A = P; for a wave winding A = 2. Torque T = PΦIZ/(2πA).
- Induction motor synchronous speed Ns = 120f/P; slip s = (Ns − Nr)/Ns; rotor frequency fr = sf; rotor copper loss = s × air-gap power.
- Synchronous machine speed is Ns = 120f/P. The prime mover controls active power; field excitation controls reactive power.
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%. Rotor frequency = 0.04 × 50 = 2 Hz. If air-gap power is 20 kW, rotor copper loss = 0.04 × 20 = 0.8 kW.
Traps
Transformer rating is in kVA because losses depend on voltage and current, not on load power factor. Use the correct parallel path A in DC EMF formulas. Slip is per unit in formulas but often asked as a percentage. A synchronous motor is not self-starting.