jK1996: In the big scheme of things developed torque (at any speed point) is dependent on the applied voltage, the current flowing in the winding, the power factor at that particular speed point, the resistance of the winding(s) involved, and how far away from synchronism the specific speed point is (i.e, the slip).
If the contacts close simultaneously
(Torque) = (Tlockrotor) + (lock rotor current)*(rotor leakage reactance/(stator leakage reactance + rotor leakage reactance)) * (factor) + sin(2*pi*line hz*time)
where
(factor) = e^((-1)*(2*pi*line hz)*(Stator cct resistance)*(rotor cct resistance) / (magnetizing reactance * (stator cct resistance + rotor cct resistance)))*time
Note: calculated torque, lock rotor torque, lock rotor current, leakage and magnetizing reactance, and all resistances are in PER UNIT.
As any added resistance (e.g. a liquid rheostat or a switched resistor bank) in the rotor circuit becomes part of the rotor circuit during the start, it can be seen that the addition of resistance will have an effect on both the starting torque and the lock rotor current. More resistance in the circuit reduces inrush current (because there's only so much voltage to go around) and consequently the torque developed will also be less than a full-voltage condition.
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