Electrical Machines
Electrical Machines tests transformers, DC machines, three-phase induction motors and synchronous machines. ESE numericals focus on equivalent circuits, losses and efficiency, torque-speed behaviour, starting, and voltage regulation.
Core rules
- Transformer EMF: E=4.44 f N Phi_m; induced EMF per turn is the same in both windings. Referred impedance scales by (N1/N2)^2.
- OC test gives core loss and magnetizing branch; SC test gives copper loss and series branch. Core loss depends on voltage and frequency, copper loss on current squared.
- DC machine: E=Phi Z N P/(60A); torque T=Phi Ia Z P/(2pi A). Shunt and separately excited motors have nearly constant flux; series motors must not start unloaded.
- Induction motor: Ns=120f/P; slip s=(Ns-Nr)/Ns; rotor frequency sf; torque is proportional to slip at small slip and falls beyond breakdown torque.
- Synchronous machine: excited rotor locks to Ns; regulation is found by EMF, MMF or Potier methods; an infinite bus fixes voltage and frequency.
Worked example
A 4-pole, 50 Hz induction motor runs at 1440 r/min. Ns=120x50/4=1500 r/min. Slip s=(1500-1440)/1500=0.04. Rotor frequency=sf=2 Hz. The reasoning is direct use of synchronous speed and slip; no load torque data is needed.
Traps
A transformer is rated in kVA because copper loss depends on current and core loss on voltage, not on load power factor. An induction motor cannot reach synchronous speed because then there is no rotor EMF and no torque. In DC machines, check whether the field is series or shunt before using constant-flux formulas.