76 THE MAGNETIC CIRCUIT [ART. 31 



The relation between the number of turns in series and the total 

 number of turns on the armature depends upon the kind of the 

 armature winding. 1 If the armature has a multiple winding N is 

 equal to the total number of turns on the armature divided by the 

 number of poles. For a two-circuit winding the number of turns 

 ies is equal to one-half of the total number of turns. The num- 

 ber of poles and the speed of the machine do not enter explicitly 

 into formula (37), but are contained in the value of /. 



Prob. 36. A 90-slot armature is to be used for a 6-pole, 580-r.p.m., 250- 

 v.. direct-current machine with a multiple winding. How many conduc- 

 tors per slot are necessary if the permissible flux per pole is about 3 mega- 

 lines? Ans. 10. 



Prob. 36. A 550-v., 4-pole railway motor has a two-circuit armature 

 winding which consists of 59 coils, 8 turns per coil. The total resistance 

 of the motor is 0.235 ohm. When the motor runs at 675 r.p.m. it takes in 

 SI amp. What is the flux per pole at this load? Ans. 2.5 ml. 



Prob. 37. Show that in a direct-current machine the use of a fraction Hi- 

 pitch winding has no effect whatever upon the value of the induced e.m.f ., 

 as long as the winding-pitch somewhat exceeds the width of the pole shoe. 



Prob. 38. Prove that formula (37) is identical with the expression 



#Hp/p')(r.p.m./60)C0XlO- 2 , (38) 



where C is the total number of armature conductors, p is the number of 

 poles, and p' is the number of circuits in parallel. 



Prob. 39. Show that the induced e.m.f. is the same when the armature 

 conductors are placed in open or in closed slots as when they are on the 

 surface of a smooth-body armature. See Prob. 18, Art. 26. 



Prob. 40. Considerable effort has been made to produce a direct-cur- 

 rent generator with alternate poles, and without any commutator. One of 

 the proposals which is sometimes urged by a beginner is to use an ordinary 

 alternator, and to supply the exciting winding with an alternating current 

 of the synchronous frequency. The apparent reasoning is that the field 

 being reversed at the completion of one alternation the next half wave of 

 the induced e.m.f. must be in the same direction as the preceding one, thus 

 giving a unidirectional voltage. Show that such a machine in reality 

 would give an ordinary alternating voltage of double the frequency. 

 Hint : Make use of the fact that an alternating field can be replaced by two 

 constant fields revolving in opposite directions. Or else give a rigid 

 mathematical proof by considering the actual rate at which the armature 

 conductors are cut by the field, which field is at the same time pulsating 

 and revolving. 



1 For details concerning the direct-current armature windings see the 

 author's Experimental Electrical Engineering, Vol. 2, Chapter 30. 



