Electrical Machines and Transformers
Electrical Machines and Transformers tests the construction, operating principle, starting and protection of transformers, DC machines and AC motors. Questions cover turns ratio, losses and efficiency, synchronous speed and slip, starting methods, motor protection and nameplate data.
Core rules
- Ideal transformer: Vp/Vs = Np/Ns = Is/Ip. A step-down transformer raises secondary current in proportion to the voltage reduction.
- Losses: copper loss from winding resistance (I squared R) and iron loss from hysteresis and eddy currents. Efficiency = output power / input power, always below 100 percent.
- DC machines use a commutator and brushes; types include shunt, series and compound, distinguished by field connection.
- AC induction motor: a rotating field gives synchronous speed Ns = 120f/p, where f is frequency in Hz and p is the number of poles. Slip s = (Ns - Nr)/Ns. Squirrel-cage motors are the common industrial workhorse.
- Starting: direct-on-line for small motors, star-delta reduces starting current and torque to one third, soft starters and variable-frequency drives control acceleration.
- Protection: overload relay, short-circuit protection, phase-failure relay, embedded thermal protection. Select against nameplate current, duty and insulation class.
Worked example: transformer
A single-phase transformer has 480 primary turns and 60 secondary turns, with 240 V applied to the primary. Turns ratio = 480/60 = 8:1, so Vs = 240/8 = 30 V. If the secondary supplies 8 A, ideal primary current = 8/8 = 1 A, and input power 240 W equals output 240 W. At 90 percent efficiency, input power = 240/0.9 = 266.7 W and primary current = 266.7/240 = 1.11 A.
Worked example: motor slip
A 4-pole motor on 50 Hz: Ns = 120 x 50/4 = 1500 rpm. At a measured 1440 rpm, slip = (1500 - 1440)/1500 = 0.04, or 4 percent.
Traps
- Inverting the turns ratio and producing a secondary voltage larger than the supply.
- Assuming input power equals output power when efficiency is given.
- Confusing synchronous speed with rotor speed.
- Sizing a motor circuit without the nameplate power factor.