Electrical Machines and Transformers
Electrical Machines and Transformers
This section covers DC machine action, three-phase induction motor speed and slip, the transformer EMF equation and ratio, losses and efficiency, and starting methods.
Core rules
- Transformer EMF: E = 4.44 f N Φm. For an ideal transformer V1/V2 = N1/N2 = I2/I1.
- Transformer losses: iron loss (hysteresis and eddy current) is essentially constant; copper loss varies with I². Maximum efficiency occurs when copper loss equals iron loss.
- Induction motor synchronous speed Ns = 120f/P; slip s = (Ns − N)/Ns; rotor frequency = s × supply frequency.
- A star-delta starter reduces phase starting voltage by 1/√3 and starting current and torque to one-third of direct-on-line values.
- DC motor speed is approximately proportional to back EMF and inversely proportional to flux; a series motor must never be started unloaded.
- Efficiency = output/input × 100; for a three-phase motor, input = √3 V I cos φ.
Worked example
A 4-pole induction motor runs at 1440 rpm on a 50 Hz supply. Ns = 120 × 50 / 4 = 1500 rpm. s = (1500 − 1440)/1500 = 60/1500 = 0.04, i.e. 4%. Rotor frequency = 0.04 × 50 = 2 Hz. At standstill slip is 1 and rotor frequency equals supply frequency.
Traps that cost marks
- Quoting synchronous speed as the running speed; an induction motor always runs below Ns.
- Inverting the turns ratio or treating a step-up transformer as step-down.
- Adding iron and copper losses at all loads as if both were constant.
- Assuming a star-delta starter reduces torque by 1/√3 when the reduction is one-third.
- Omitting power factor when calculating motor input current.