Effect of rotor resistance on T-S characteristics

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 $T_{max} = \frac{3E_2^2}{2\omega_s X_2}$.

 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.