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Delta IM slip, rotor frequency, turns ratio

Short answer

Slip = (1500−1440)/1500 = 0.04. Rotor frequency = 0.04×50 = 2 Hz. Rotor induced emf per phase = 0.04×130 = 5.2 V. Stator to rotor turns ratio = 440/130 = 3.38.

A 3-phase delta connected 440 volts, 50 Hz, 4-pole induction motor has a rotor stand-still emf per phase of 130 volts. If the motor is running at 1,440 RPM, calculate for this speed: (i) the slip, (ii) the frequency of rotor induced emf, (iii) the value of rotor induced emf per phase, and (iv) stator to rotor turn ratio.

Given: 3-phase delta stator, 440 V, 50 Hz, 4-pole; standstill rotor emf per phase E₂ = 130 V; speed N = 1440 rpm.

N_s = 120 × 50 / 4 = 1500 rpm.

(i) Slip

s = (N_s − N)/N_s = (1500 − 1440)/1500 = 0.04 (4 %)

(ii) Frequency of rotor induced emf

f₂ = s f = 0.04 × 50 = 2 Hz

(iii) Rotor induced emf per phase at 1440 rpm

E₂ᵣ = s E₂ = 0.04 × 130 = 5.2 V

(iv) Stator to rotor turn ratio

In a delta stator the phase voltage equals the line voltage, E₁ = 440 V. At standstill the induced emf ratio equals the turns ratio:

K = E₁/E₂ = 440/130 = 3.38 : 1 (about 3.4)

ItemResult
Slip0.04
Rotor frequency2 Hz
Rotor emf per phase5.2 V
Turns ratio (stator : rotor)3.38

✓ Answer checked by Claude Opus 5.5 (high effort)

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