--- title: "Effect of rotor resistance on T-S characteristics" subject: "Electrical Machines" chapter: 5 key: "semester_4/electrical_machines:rotor-resistance-effect-ts" source: https://www.bctengineer.com/q/semester_4/electrical_machines/rotor-resistance-effect-ts site: BCT Engineering --- # Effect of rotor resistance on T-S characteristics Electrical Machines · Chapter 5: Three Phase Induction Machines - Asked in: 2065 Chaitra (old course), 4 marks - Video: [#Electrical Machines-II | L23 | Effect of Slip on Rotor Parameters,Induction Motor as a Transformer](https://www.youtube.com/watch?v=cb_EstG7t2g) — Shivanand Shakya - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_4/electrical_machines/rotor-resistance-effect-ts - Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machines/chapter-5 ## Question Explain the effect of rotor resistance on the torque slip characteristics of induction motor. ## Short answer Increasing rotor resistance leaves maximum torque unchanged, but moves the peak to higher slip (sm=R2/X2) and boosts starting torque, peaking when R2=X2. Speed regulation worsens because slip increases for a given load, and rotor copper loss rises, lowering efficiency. ## Answer The torque developed is $T = \frac{3}{\omega_s}\cdot\frac{sE_2^2R_2}{R_2^2+(sX_2)^2}$. The slip at which the torque is maximum is $s_m = R_2/X_2$, and the maximum torque is $T_{max} = \frac{3E_2^2}{2\omega_s X_2}$. ```text T | R2 = X2 (peak at start) | _.-*-._ R2 higher | / _-*-. . | / /' `-. R2 low |*/ / `. +--+--+--+-------> s 1 .6 .3 0 ``` Effects of increasing rotor resistance: 1. **$T_{max}$ is unchanged**, since it is independent of $R_2$. 2. **$s_m$ increases** in proportion to $R_2$: the peak moves toward lower speed (higher slip). 3. **Starting torque increases** (as $R_2$ rises toward $X_2$); when $R_2 = X_2$, $s_m = 1$ and $T_{st} = T_{max}$. Beyond that it decreases again. 4. **Speed at a given load falls**, because slip $\propto R_2$ in the linear part, so speed regulation gets worse. 5. **Rotor copper loss increases** and efficiency decreases. 6. Starting current falls and the starting power factor improves. This is why a slip-ring motor uses external resistance at starting (high torque, low current) and cuts it out when running. A cage rotor with permanently high resistance gives high starting torque at the cost of higher running slip and lower efficiency; double-cage and deep-bar rotors avoid this, because their effective resistance is high only at starting (high rotor frequency) and low at running speed. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Increasing rotor resistance makes T_max: A. Increase B. Decrease C. Remain unchanged D. Become zero Answer: C. T_max is independent of R_2. (Key point: Tmax with R2) 2. Starting torque rises with R_2 until: A. R_2 = X_2 B. R_2 = 0 C. R_2 = 2X_2 D. It never changes Answer: A. At R_2 = X_2, T_st = T_max. (Key point: Starting torque) 3. A drawback of high rotor resistance in running is: A. Higher starting current B. Greater speed with load C. More rotor copper loss and lower efficiency D. Higher T_max Answer: C. Slip and rotor copper loss increase, so efficiency falls. 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