Electrical Machines and Transformers: EMF, Losses, Efficiency and Slip
Machines and transformers questions reward formula recall plus quick loss accounting: EMF equations, equivalent circuits, efficiency conditions, slip and torque relations.
Transformers
- EMF equation: E = 4.44 f N Φ_m, using flux per pole (per core limb) and turns per phase.
- The open-circuit test (usually on the LV side) gives core loss and magnetizing branch parameters; the short-circuit test gives copper loss and leakage impedance.
- Efficiency peaks when copper loss equals core loss, at load fraction x = √(P_i/P_cu,FL).
- Parallel operation needs matching voltage ratio, polarity, percentage impedance and phase-sequence/vector group.
Machines
- DC machine: E = PΦNZ/60A; torque = PΦI_a Z/(2πA); separately excited speed N ∝ (V − I_aR_a)/Φ.
- Induction motor: slip s = (N_s − N)/N_s, rotor frequency = sf, torque ∝ V², so a 10% voltage dip cuts torque by about 19%.
- Synchronous machine: excitation controls reactive power; over-excitation exports Q (lagging current).
Worked example
A 100 kVA transformer has 1 kW iron loss and 2 kW full-load copper loss. Maximum efficiency occurs at x = √(1/2) = 0.707, i.e. 70.7 kVA. At full load, unity power factor: output = 100 kW, losses = 3 kW, so η = 100/103 = 97.09%.
Traps
Using line voltage where the EMF equation needs phase voltage, assuming maximum efficiency occurs at rated load, and reporting slip as a percentage when the formula needs a fraction.