---
title: "Rotor emf and frequency at 1460 rpm"
subject: "Electrical Machines"
chapter: 5
key: "semester_4/electrical_machines:im-rotor-emf-500v-1460rpm"
source: https://www.bctengineer.com/q/semester_4/electrical_machines/im-rotor-emf-500v-1460rpm
site: BCT Engineering
---

# Rotor emf and frequency at 1460 rpm

Electrical Machines · Chapter 5: Three Phase Induction Machines

- Asked in: 2071 Magh (old course), 8 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/electrical_machines/im-rotor-emf-500v-1460rpm
- Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machines/chapter-5

## Question

A 4-pole, 50 Hz, 3 phase induction motor with star connected rotor gives 500 V between the slip rings at standstill. Calculate the magnitude and frequency of emf induced per phase in rotor circuit at a speed of 1460 RPM.

## Short answer

Synchronous speed 1500 rpm, slip = 0.02667. Rotor phase emf = 288.68 V × slip = 7.70 V (line 13.33 V). Rotor frequency = 1.33 Hz.

## Answer

**Given:** 4-pole, 50 Hz, star rotor, 500 V between slip rings at standstill, speed 1460 rpm.

$$
N_s = \frac{120\times 50}{4} = 1500\ \text{rpm}, \qquad s = \frac{1500 - 1460}{1500} = 0.02667
$$
Standstill emf per phase (star):
$$
E_2 = \frac{500}{\sqrt3} = 288.68\ \text{V}
$$
Rotor emf per phase at slip $s$:
$$
E_{2s} = sE_2 = 0.02667\times 288.68 = 7.70\ \text{V}
$$
Rotor frequency:
$$
f_r = sf = 0.02667\times 50 = 1.33\ \text{Hz}
$$

**Answer:** emf per phase $= 7.70$ V (line value between slip rings $= 13.33$ V) and frequency $= 1.33$ Hz.

## Check yourself

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

1. What is the synchronous speed of a 4-pole, 50 Hz motor?
   A. 1000 rpm
   B. 1500 rpm
   C. 3000 rpm
   D. 1460 rpm
   Answer: B. Ns = 120f/P = 120 x 50/4 = 1500 rpm. (Key point: Synchronous speed)

2. What is the slip at 1460 rpm?
   A. 0.0267
   B. 0.0274
   C. 0.0400
   D. 0.9733
   Answer: A. s = (1500-1460)/1500 = 0.02667. (Key point: Slip calculation)

3. How is the running rotor emf per phase found?
   A. Multiply the standstill phase emf (500/sqrt3) by the slip
   B. Multiply the 500 V line value by the slip only
   C. Divide the standstill emf by the slip
   D. Use 500/sqrt3 unchanged
   Answer: A. E2s = s x E2 = 0.02667 x 288.68 = 7.70 V. (Key point: Rotor emf per phase)

4. What is the rotor emf frequency at this speed?
   A. 50 Hz
   B. 48.67 Hz
   C. 1.33 Hz
   D. 2.67 Hz
   Answer: C. f_r = s x f = 0.02667 x 50 = 1.33 Hz. (Key point: Rotor frequency)

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