---
title: "Delta IM slip, rotor frequency, turns ratio"
subject: "Electrical Machine"
chapter: 5
key: "semester_4/electrical_machine:im-delta-440v-4pole-1440rpm"
source: https://www.bctengineer.com/q/semester_4/electrical_machine/im-delta-440v-4pole-1440rpm
site: BCT Engineering
---

# Delta IM slip, rotor frequency, turns ratio

Electrical Machine · Chapter 5: Three Phase Induction Machines

- Asked in: 2071 Magh, 4 marks
- Video: [Simple problems on 3-phase induction motors: Slip, Rotor Frequency(Part-I)](https://www.youtube.com/watch?v=H0SaAq7sMN0) — Gargi Basu
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/electrical_machine/im-delta-440v-4pole-1440rpm
- Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machine/chapter-5

## Question

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.

## 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.

## Answer

**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)

| Item | Result |
|---|---|
| Slip | 0.04 |
| Rotor frequency | 2 Hz |
| Rotor emf per phase | 5.2 V |
| Turns ratio (stator : rotor) | 3.38 |

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What is the slip at 1440 rpm for a 4-pole 50 Hz motor?
   A. 0.96
   B. 0.04
   C. 0.4
   D. 0.0267
   Answer: B. Ns = 1500, s = 60/1500 = 0.04. (Key point: Slip)

2. What is the rotor emf frequency?
   A. 50 Hz
   B. 1440 Hz
   C. 2 Hz
   D. 25 Hz
   Answer: C. f2 = s f = 0.04 x 50 = 2 Hz. (Key point: Rotor frequency)

3. What is the rotor induced emf per phase at 1440 rpm?
   A. 130 V
   B. 3.25 V
   C. 5.2 V
   D. 13 V
   Answer: C. E2r = sE2 = 0.04 x 130 = 5.2 V. (Key point: Rotor emf per phase)

4. Why is E1 taken as 440 V in finding the turns ratio?
   A. Phase voltage equals line voltage in a delta stator
   B. Phase voltage is 440/sqrt(3)
   C. The rotor is delta
   D. It is the rotor emf
   Answer: A. K = E1/E2 = 440/130 = 3.38 because delta phase voltage equals line voltage. (Key point: Turns ratio for delta stator)

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