---
title: "Torque of 4-pole induction motor at 1400 rpm"
subject: "Electrical Machines I"
chapter: 5
key: "semester_4/electrical_machines_i:im-4pole-2ohm-8ohm-5nm-1400rpm"
source: https://www.bctengineer.com/q/semester_4/electrical_machines_i/im-4pole-2ohm-8ohm-5nm-1400rpm
site: BCT Engineering
---

# Torque of 4-pole induction motor at 1400 rpm

Electrical Machines I · Chapter 5: Three-Phase Induction Machines

- Asked in: 2075 Bhadra, 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_i/im-4pole-2ohm-8ohm-5nm-1400rpm
- Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machines_i/chapter-5

## Question

A 3 phase, 400 V, 50 Hz, 4 pole induction motor has rotor circuit resistance 2 Ω and rotor circuit reactance of 8 Ω at stand still. It develops a starting torque of 5 N-m. The stator to rotor turn ratio is unity. Calculate the torque developed by the motor when it runs at 1400 rpm.

## Short answer

Slip at 1400 rpm is 0.0667. Using the torque ratio with starting torque, the developed torque is 5.29 N·m.

## Answer

**Given:** 4 poles, 50 Hz, $R_2 = 2\ \Omega$, $X_2 = 8\ \Omega$ at standstill, $T_{st} = 5$ N·m, turns ratio 1, $N = 1400$ rpm. Stator impedance neglected.

#### Slip

$$
\begin{aligned}
N_s &= \frac{120 \times 50}{4} = 1500\ \text{rpm} \\
s &= \frac{1500 - 1400}{1500} = 0.0667
\end{aligned}
$$

#### Torque ratio

$$
T = \frac{K s E_2^2 R_2}{R_2^2 + (sX_2)^2}, \qquad T_{st} = \frac{K E_2^2 R_2}{R_2^2 + X_2^2}
$$

$$
\begin{aligned}
\frac{T}{T_{st}} &= \frac{s(R_2^2 + X_2^2)}{R_2^2 + (sX_2)^2} \\
&= \frac{0.0667 \times (4 + 64)}{4 + (0.0667 \times 8)^2} \\
&= \frac{4.5333}{4 + 0.2844} = \frac{4.5333}{4.2844} = 1.0581
\end{aligned}
$$

$$
T = 1.0581 \times 5 = 5.29\ \text{N·m}
$$

(The 400 V supply and unity ratio are not needed when the ratio method is used.)

**Answer: Torque at 1400 rpm $\approx 5.29$ N·m.**

## Check yourself

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

1. For a 4-pole 50 Hz motor at 1400 rpm, what is the slip?
   A. 0.0667
   B. 0.0714
   C. 0.933
   D. 0.25
   Answer: A. Ns = 1500 rpm so s = (1500 - 1400)/1500 = 0.0667. (Key point: Slip calculation)

2. Which expression gives T/Tst?
   A. s(R2^2 + (sX2)^2)/(R2^2 + X2^2)
   B. (R2^2 + X2^2)/(s R2^2)
   C. s(R2^2 + X2^2)/(R2^2 + (sX2)^2)
   D. s R2/(R2^2 + X2^2)
   Answer: C. Dividing the running torque by the starting torque cancels K and E2^2, leaving s(R2^2+X2^2)/(R2^2+(sX2)^2). (Key point: Torque ratio method)

3. The ratio T/Tst is about 1.058. What is the torque at 1400 rpm?
   A. 4.72 N-m
   B. 5 N-m
   C. 10.6 N-m
   D. 5.29 N-m
   Answer: D. T = 1.0581 x 5 = 5.29 N-m. (Key point: Result)

## Related in Electrical Machines I

- [Torque at 1450 rpm from starting torque](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Aim-4pole-150nm-1450rpm-0p5-2ohm) — Electrical Machines I, chapter 5
- [Speed and value of maximum torque of 2-pole motor](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Aim-2pole-2ohm-8ohm-max-torque) — Electrical Machines I, chapter 5
- [Max-torque speed and efficiency of 400 V slip ring motor](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Aslip-ring-400v-190v-600w-1380rpm) — Electrical Machines I, chapter 5, asked 2×
- [Starting current and rotor resistance for 150 kW slip ring motor](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Aim-150kw-3000v-starting-current-30a) — Electrical Machines I, chapter 5
- [Maximum torque and torque at 1430 rpm of slip ring motor](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Aslip-ring-400v-200v-10nm-1430rpm) — Electrical Machines I, chapter 5, asked 3×
- [Max-torque speed and efficiency at 1350 rpm](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Aslip-ring-380v-180v-500w-1350rpm) — Electrical Machines I, chapter 5, asked 2×

## Related in other subjects

- [4-pole motor: speed at max torque (50 N-m, j2)](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Aim-4pole-50nm-starting-torque-j2) — Electrical Machines, chapter 5, asked 4×
- [Delta induction motor: slip, rotor emf, turns ratio](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Aim-delta-440v-1440rpm-rotor-emf) — Electrical Machines, chapter 5, asked 2×
- [Induction motor plugging: braking current and torque](https://www.bctengineer.com/question.md?key=semester_7%2Futilization_of_electrical_energy%3Ainduction-motor-plugging-braking-current) — Utilization of Electrical Energy, chapter 3
- [Slip ring motor: speed at max torque, resistance](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Aim-slipring-max-torque-ratio) — Electrical Machines, chapter 5