74 PROBLEMS IN ALTERNATING CURRENT MACHINERY 



rated frequency the leakage reactances of the windings are 3.2 

 times their effective resistances. What line voltage should be 

 impressed on this motor when starting to give a line current of 200 

 amperes? 



19. The ohmic resistances of the stator and rotor windings of 

 an indication motor are respectively 0.04 ohm and 0.01 ohm. 

 At normal freqency the ratios of effective resistance to ohmic 

 resistance are respectively 1.5 and 1.8 for the stator and rotor 

 windings and the leakage reactances are 3.1 times their effective 

 resistances. The stator winding has 108 inductors per phase and 

 the rotor winding has 54 inductors per phase. Assume that the 

 core loss due to leakage flux and the increase in the resistance 

 due to a non-uniform distribution of current over the cross- 

 section of the inductors both vary directly as the frequency. 



(a) If the voltage impressed on an induction motor when 

 starting is increased 30 per cent., how much is the starting current 

 increased? How much is the starting torque increased? 



(b) If the frequency of the voltage impressed on an induction 

 motor when starting is increased 10 per cent., how much is the 

 starting current decreased? How much is the starting torque 

 decreased. 



20. A 570-h.p. induction motor is designed to receive power 

 from a 3-phase, 1900-volt, 22.5-cycle circuit. The ohmic re- 

 sistances of the stator and rotor windings are 0.488 ohm and 

 0.0138 ohm per phase, and at the rated frequency the effective 

 resistances are 1.3 and 1.5 times as great. The leakage reactances 

 at the rated frequency are three times the effective resistances. 

 The stator has 864 inductors per phase and the rotor 144 in- 

 ductors per phase. The motor is wound for 36 poles, and both of 

 the windings are connected in delta. The friction and windage 

 loss is 12 kw. 



What is the slip at full load if the generated voltage in the stator 

 winding due to the air-gap flux is 93 per cent, of the impressed 

 voltage? What is the starting torque with full voltage impressed 

 on the stator windings? 



21. The effective resistances of the stator and rotor windings of 

 a 3-phase inducton motor are 0.071 ohm and 0.0218 ohm per 

 phase, and the leakage reactances at normal frequency are 0.22 

 ohm and 0.066 ohm per phase. The stator has 108 slots with 5 

 inductors per slot, and the rotor has 126 slots with 2 inductors 

 per slot. Both of the windings are connected in Y. At starting, 



