Electrical Machines (Transformers, DC Machines, Induction and Synchronous Machines)
What the exam tests
Electrical Machines tests transformer equivalent circuits and testing, DC machine EMF/torque, induction motor slip behaviour, and synchronous machine excitation. Expect numerical questions on losses, efficiency, regulation, and speed control rather than descriptive definitions alone.
Core rules
- Transformer induced EMF: E = 4.44 f N Φm; voltage per turn is fixed by flux and frequency. OC test gives core loss and magnetizing branch; SC test gives copper loss and leakage impedance.
- DC machine: Eb = PΦNZ/60A and T = PΦIaZ/(2πA); back EMF opposes armature current in motoring.
- Induction motor: slip s = (Ns − N)/Ns, rotor frequency = s f, and torque is proportional to slip at small slip.
- Synchronous machine: excitation controls reactive power; load angle controls real power. It is not self-starting.
Worked example
A 50 kVA, 2000/200 V transformer has core loss 200 W and full-load copper loss 800 W. Maximum efficiency occurs when load fraction x satisfies x²Pcu = Pi, so x = √(200/800) = 0.5. At unity power factor the output is 25 kW; input = 25,000 + 200 + 0.5²×800 = 25,400 W. Efficiency = 25,000/25,400 = 98.43%.
Traps
Transformer rating is in kVA because copper loss depends on current and core loss on voltage, not on load power factor. An induction motor cannot run at synchronous speed in motoring mode. A DC series motor must not be started unloaded. Synchronous motors need damper windings or a starting motor.