How it works
Torque T = (3V1²R2/s) / [ωs × ((R1 + R2/s)² + (X1+X2)²)]. For the simplified case neglecting stator impedance, T ∝ sR2/(R2² + s²X2²). Maximum torque Tmax = 3V1²/[2ωs(X1+X2)] — independent of rotor resistance R2. The slip at maximum torque sm = R2/X2, so increasing R2 (possible in slip-ring motors by adding external resistance in steps of, say, 0.5 Ω per phase) shifts the peak torque to higher slip without reducing its magnitude. Starting torque Tst = T|s=1 = 3V1²R2/[ωs(R2²+X2²)]; maximum starting torque occurs when R2 = X2.
Key points to remember
The ratio Tst/Tmax = 2sm/(1 + sm²) — at sm = 0.1 this ratio is only about 0.198, meaning starting torque is much less than maximum torque for typical squirrel-cage motors. The curve has two regions: stable (s < sm) where motor self-corrects load changes, and unstable (s > sm) where a load increase causes further speed drop and eventual stall. Voltage affects torque as T ∝ V1²; a 10% voltage dip reduces torque by 19%, which is why motors struggle during grid sags. This curve must be drawn accurately with both Tst and Tmax labelled.
Exam tip
Every Anna University model paper asks you to derive the condition for maximum torque (dT/ds = 0 leading to sm = R2/X2) — work through the differentiation at least once so you can reproduce it in the exam.