Electrical Machines
Electrical Machines tests DC machines, transformers, induction machines and synchronous machines. Expect EMF equations, speed and slip calculations, losses, efficiency and starting methods.
DC machines and transformers
- DC generator EMF: E = PφNZ/(60A), where P is poles, φ is flux per pole, N is speed in rpm, Z is conductors and A is parallel paths.
- DC motor: back EMF Eb = V − IaRa; torque T ∝ φIa.
- Transformer EMF: E = 4.44 fNφm; ideal transformer has V1/V2 = N1/N2 and I1/I2 = N2/N1.
- Transformer losses are core loss (roughly constant) and copper loss (load-dependent); maximum efficiency occurs when copper loss equals core loss.
Induction and synchronous machines
- Synchronous speed Ns = 120f/P; slip s = (Ns − Nr)/Ns.
- Induction motor rotor frequency = sf; torque is proportional to slip near normal operation.
- Synchronous machine speed is locked to Ns; field excitation controls reactive power and power factor.
Worked example
A 4-pole, 50 Hz induction motor runs at 1440 rpm. Ns = 120 × 50/4 = 1500 rpm. Slip s = (1500 − 1440)/1500 = 60/1500 = 0.04, i.e. 4%. Rotor frequency = sf = 0.04 × 50 = 2 Hz.
Traps that cost marks
Using line voltage where phase voltage is required, confusing generator and motor EMF equations, treating slip as a percentage in formulas, and assuming transformer flux falls with load are frequent mistakes. In DC machines, check whether the machine is lap or wave wound before choosing A = P or A = 2.