--- title: "Define RMF; torque-speed characteristics" subject: "Electrical Machines" chapter: 5 key: "semester_4/electrical_machines:rmf-definition-torque-speed" source: https://www.bctengineer.com/q/semester_4/electrical_machines/rmf-definition-torque-speed site: BCT Engineering --- # Define RMF; torque-speed characteristics Electrical Machines · Chapter 5: Three Phase Induction Machines - Asked in: 2078 Poush, 2+6 marks - Video: [Torque speed Characteristics of three phase induction Motor](https://www.youtube.com/watch?v=i-eagFqa5UQ) — SuccessMantra - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_4/electrical_machines/rmf-definition-torque-speed - Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machines/chapter-5 ## Question Define rotating magnetic field in three phase induction motor. Explain the Torque-Speed (T-N) characteristics of three phase induction motor. ## Short answer A rotating magnetic field has constant magnitude 1.5 phi_m and rotates at synchronous speed Ns = 120f/P. Torque-speed curve rises from starting torque at standstill to maximum at sm = R2/X2, then falls to zero at Ns; stable region is between maximum and Ns, with rated slip 2-5%. ## Answer #### Rotating magnetic field (RMF) A rotating magnetic field is a magnetic field of **constant magnitude** ($1.5\phi_m$ for a three-phase winding) whose axis rotates in space at synchronous speed $N_s = \frac{120f}{P}$ rpm. It is produced by feeding balanced three-phase currents to three windings displaced $120^\circ$ in space. #### Torque-speed (T-N) characteristics The torque developed is $$ T = \frac{3}{\omega_s}\cdot\frac{s E_2^2 R_2}{R_2^2 + (sX_2)^2} $$ ```text T | Tmax | _.-*-._ | Tst / \ | *--' \ | / \ | / \ +--+------+----------------+--> N N=0 N(Tmax) Ns ``` Main points of the curve: 1. **Starting (N = 0, s = 1):** the torque is the starting torque $T_{st}$. For a squirrel-cage motor it is about 1.5 to 2 times full-load torque. 2. **Between standstill and pull-out:** the torque rises with speed, because the rotor reactance $sX_2$ falls and the power factor improves, until it reaches the **maximum (breakdown) torque** at $s_m = \frac{R_2}{X_2}$, where $T_{max} = \frac{3E_2^2}{2\omega_s X_2}$. 3. **Stable region ($s < s_m$):** from $T_{max}$ down to $N_s$ the torque falls almost linearly with speed. The motor works here at rated load with slip of 2 to 5 %. 4. **At $N = N_s$ ($s=0$):** the torque is zero. 5. **Unstable region ($s > s_m$):** if the load torque exceeds $T_{max}$, the speed falls and the torque falls too, so the motor stalls. Increasing the rotor resistance moves $s_m$ toward standstill (the same $T_{max}$), and with $R_2 = X_2$ the maximum torque occurs at starting. A fall of supply voltage reduces torque in proportion to $V^2$. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. A rotating magnetic field in a three-phase motor is one that: A. Has constant magnitude and rotates at synchronous speed B. Alternates in magnitude along a fixed axis C. Rotates at rotor speed D. Has magnitude changing with slip Answer: A. It is constant (1.5 phi_m) and rotates at N_s. (Key point: Definition of RMF) 2. At what slip does maximum (breakdown) torque occur? A. s_m = X_2/R_2 B. s_m = R_2/X_2 C. s_m = 1 always D. s_m = 0 Answer: B. s_m = R_2/X_2. (Key point: Maximum torque slip) 3. Which part of the T-N curve is stable? A. From standstill to T_max B. Only the starting point C. From T_max to N_s D. Beyond N_s only Answer: C. Between T_max and N_s the torque rises with slip, so a load increase is met stably. (Key point: Stable region) 4. A fall of supply voltage changes torque as: A. Proportional to V B. Proportional to V^2 C. Unchanged D. Proportional to 1/V Answer: B. T is proportional to V^2. (Key point: Voltage effect) ## Related in Electrical Machines - [Rotating magnetic field, slip and standstill torque equation](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Armf-synchronous-speed-slip-standstill-torque) — Electrical Machines I, chapter 5 - [Production of rotating magnetic field](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Arotating-magnetic-field-production) — Electrical Machines, chapter 5 - [Synchronous speed; rotor follows rotating field](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Asynchronous-speed-rotor-direction) — Electrical Machines, chapter 5 - [Torque equation of 3-phase induction motor](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Atorque-equation-induction-max-condition) — Electrical Machines, chapter 5 - [Shunt motor speed with 50 Ω field resistance and lower torque](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Ashunt-motor-220v-25a-50ohm-torque) — Electrical Machines I, chapter 4, asked 4× - [Induction motor working and torque equation](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Aim-working-torque-equation) — Electrical Machines I, chapter 5 ## Related in other subjects - [Rotating field in 3-phase IM](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machine%3Arotating-field-3ph-im-vector) — Electrical Machine, chapter 5 - [Output equation of three phase induction motor](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machine_design%3Ainduction-motor-output-equation) — Electric Machine Design, chapter 4, asked 6× - [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 - [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×