70 PROBLEMS IN ALTERNATING CURRENT MACHINERY 



(c) Plot the distribution of the magnetomotive force in the 

 air-gap at one-quarter of a period later than 'in (a). 



6. A 3-phase induction motor has a stator with 4 slots per pole 

 per phase. There are 4 inductors per slot, two of which are in 

 one coil and two in another. The coil pitch is 10 slots. There are 

 two coil sides in each slot. The effective value of the current in 

 each phase of the stator winding is 7.07 amperes, and the current 

 in phase two lags behind the current in phase one by 120 electrical 

 degrees and leads the current in phase three by the same amount. 

 Place the first slot in phase one at the extreme left of the paper and 

 draw the zero lines to allow for a maximum ordinate of 4 in 

 Use the following scales in these plots: 



Abscissae Pole pitch = 3 in. 



Ordinates 40 ampere turns = 1 in. 



(a) Plot the distribution of the magnetomotive force in the air- 

 gap due to the stator currents at the time that the current in phase 

 one is a maximum. 



(b) Plot the distribution of the magnetomotive force in the 

 air-gap at one-eighth of a period later than in (a). 



(c) Plot the distribution of the magnetomotive force in the 

 air-gap at one-quarter of a period later than in (a). 



6. Assume that the stator winding of a 3-phase induction motor 

 is uniformly distributed. The coil pitch is unity and the phase 

 spread is one-third the polar pitch. The current in phase two 

 lags behind the current in phase one by 120 degrees and leads 

 the current in phase three by the same amount. Place the be- 

 ginning of phase one at the extreme left of the paper and draw 

 the zero lines to allow for a maximum ordinate of 3 in. As 

 ordinates let 1 in. equal the maximum ampere turns per pole 

 per phase, and as abscissae let 3 in. equal the pole pitch. 



(a) Plot the distribution of the magnetomotive force in the 

 air-gap at the time that the current in phase one is a maximum. 



(b) Plot the distribution of the magnetomotive force in the 

 air-gap at one-eight of a period later than in (a). 



(c) Plot the distribution of the magnetomotive force in the 

 air-gap at a time one-quarter of a period later than in (a). 



7. Assume that the stator winding of a 3-phase induction 

 motor is uniformly distributed. The coil pitch is unity and 

 the phase spread is two-thirds the polar pitch. The current in 

 phase two lags behind the current in phase one by 120 degrees 



