---
title: "Max-torque speed and value of 8-pole motor"
subject: "Electrical Machines I"
chapter: 5
key: "semester_4/electrical_machines_i:im-8pole-50kgm-max-torque"
source: https://www.bctengineer.com/q/semester_4/electrical_machines_i/im-8pole-50kgm-max-torque
site: BCT Engineering
---

# Max-torque speed and value of 8-pole motor

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

- Asked in: 2075 Baisakh, 8 marks
- Video: [Numerical problems on 3-phase induction motors: Maximum Torque & Corresponding slip](https://www.youtube.com/watch?v=14-83DFgA4Q) — Gargi Basu
- 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-8pole-50kgm-max-torque
- Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machines_i/chapter-5

## Question

An 8 pole, 50 Hz, three phase induction motor develops a starting torque of 50 Kg-m. The rotor has an impedance of (0.8+j4) ohm per phase. At what speed the motor will develop maximum torque and calculate the magnitude of maximum torque.

## Short answer

Maximum torque occurs at slip 0.2, corresponding to 600 rpm. The maximum torque is 130 kg-m, approximately 1275.3 N·m.

## Answer

**Given:** 8 poles, 50 Hz, $T_{st} = 50$ kg-m, rotor impedance at standstill $= 0.8 + j4\ \Omega$/phase. Stator impedance neglected.

#### Speed at maximum torque

$$
\begin{aligned}
N_s &= \frac{120 \times 50}{8} = 750\ \text{rpm} \\
s_m &= \frac{R_2}{X_2} = \frac{0.8}{4} = 0.2 \\
N_m &= (1 - 0.2) \times 750 = 600\ \text{rpm}
\end{aligned}
$$

#### Maximum torque

$$
\begin{aligned}
\frac{T_{max}}{T_{st}} &= \frac{R_2^2 + X_2^2}{2R_2X_2} = \frac{0.8^2 + 4^2}{2 \times 0.8 \times 4} = \frac{16.64}{6.4} = 2.6 \\
T_{max} &= 2.6 \times 50 = 130\ \text{kg-m}
\end{aligned}
$$

In SI units ($g = 9.81$ m/s²): $T_{max} = 130 \times 9.81 = 1275.3$ N·m.

**Answer: Maximum torque occurs at 600 rpm (slip 0.2); $T_{max} = 130$ kg-m $\approx 1275.3$ N·m.**

## Check yourself

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

1. For 8 poles at 50 Hz, what is Ns?
   A. 1500 rpm
   B. 375 rpm
   C. 3000 rpm
   D. 750 rpm
   Answer: D. Ns = 120 x 50/8 = 750 rpm. (Key point: Synchronous speed)

2. With R2 = 0.8 Ω and X2 = 4 Ω, what is the speed at maximum torque?
   A. 600 rpm
   B. 150 rpm
   C. 750 rpm
   D. 700 rpm
   Answer: A. sm = 0.8/4 = 0.2, N = 0.8 x 750 = 600 rpm. (Key point: Speed at max torque)

3. What is Tmax/Tst and Tmax?
   A. 2.6 and 130 kg-m
   B. 0.385 and 19.2 kg-m
   C. 5 and 250 kg-m
   D. 1.3 and 65 kg-m
   Answer: A. Tmax/Tst = (0.64 + 16)/(2 x 0.8 x 4) = 2.6, so Tmax = 130 kg-m. (Key point: Tmax from Tst)

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## Related in other subjects

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