Learning objective: Calculate synchronous speed, slip, rotor current frequency and the air-gap power split for a three-phase induction motor.
Understand the idea
In an induction motor, the rotor normally turns below the speed of the stator rotating magnetic field. This speed difference is expressed by slip. Slip influences rotor current frequency and the fraction of air-gap power lost in the rotor resistance. Make sure the supplied speed is mechanical revolutions per minute, not electrical frequency.
Worked example: given data
- Three-phase, four-pole induction motor supplied at f = 50 Hz.
- Mechanical rotor speed N = 1440 rpm.
- Power transferred across the air gap Pag = 10 kW. Ignore extra rotor losses other than rotor copper loss for this exercise.
Detailed solution
Calculate synchronous speed
A P-pole induction motor has synchronous speed Ns = 120f/P rpm. For four poles and 50 Hz, Ns = (120 × 50)/4 = 1500 rpm.
Find slip
s = (Ns − N)/Ns = (1500 − 1440)/1500 = 0.04 = 4%. Slip is a ratio, not 60 rpm; 60 rpm is the slip speed.
Find rotor current frequency
The rotor electrical frequency is fr = sf = 0.04 × 50 = 2 Hz. At standstill, s = 1, so the rotor frequency is the full supply frequency.
Calculate rotor copper loss
Rotor copper loss is sPag = 0.04 × 10,000 = 400 W. This part of air-gap power is dissipated as heat in the rotor resistance.
Calculate converted mechanical power
Mechanical power developed before mechanical losses is (1 − s)Pag = 0.96 × 10 kW = 9.6 kW. Shaft output would be less if friction, windage and stray losses were included.
What the answer means
A common GATE distinction is between air-gap power, converted mechanical power, and output shaft power. Slip divides air-gap power into rotor copper loss and mechanical power developed; it does not account for all stator and mechanical losses of a real motor.
Three mistakes to avoid
- Using P = 2 instead of P = 4 when there are four poles.
- Using the slip speed in rpm directly as the decimal slip.
- Calling 9.6 kW the shaft output when mechanical losses are not supplied.
Try a related question
If the rotor runs at 1470 rpm with the same four-pole 50 Hz supply, find slip and rotor frequency.
Show the worked-answer check
The synchronous speed is still 1500 rpm. Slip = (1500 − 1470)/1500 = 0.02, or 2%. Rotor frequency = 0.02 × 50 = 1 Hz.
How to revise this concept
Practise torque–slip characteristics and distinguish starting torque from maximum torque. First attempt the example on paper without opening the answer, then compare the intermediate steps. Explain each assumption before memorising a formula.
Content note: This is a newly prepared practice example, not an official GATE previous-year question. It was drafted with AI assistance for this educational website. Students should verify calculations and exam requirements against standard textbooks and official sources; educator review is recommended before publication.