Il8 ELEMENTS OF ELECTRICAL ENGINEERING. 



induced in every armature conductor at any given instant ; there- 

 fore the electromotive force between the collector rings at the 

 given instant is equal to Ze, Z being the number of armature 

 conductors in series between the collector rings ; the average 

 electromotive force between the collector rings is equal to Z 

 times the average electromotive force, pQn, in a single conduc- 

 tor ; and the effective electromotive force between the collector 

 rings is equal to Z times the effective electromotive force in a 

 single conductor. 



In a distributed winding, on the other hand, the same electro- 

 motive force is not induced in all of the armature conductors at 

 any given instant, because the conductors cannot be all similarly 

 situated under the respective field magnet poles. Or, in other 

 words, there is a phase difference between the electromotive forces 

 induced in the different conductors. On account of this phase 

 difference the average electromotive force between the collector 

 rings is not equal to Z times the average electromotive force in 

 a single conductor, and the effective electromotive force between 

 the collector rings is not equal to Z times the effective electro- 

 motive force in a single conductor. 



In the case of a concentrated armature winding the average 

 electromotive force between the collector rings is equal to p<&Zn, 

 but the effective value of the electromotive force cannot be com- 

 pletely expressed in terms of /, <l>, Z and n, because it depends 

 upon the size and shape of the pole pieces, as well as upon /, 

 <, Z and n. 



In the case of a distributed armature winding neither the aver- 

 age value nor the effective value of the electromotive force be- 

 tween the collector rings can be completely expressed in terms 

 of /, 4>, Z and n, because they both depend upon the size and 

 shape of the pole pieces and upon the exact mode of distribution 

 of the windings. 



A complete discussion of the dependence of average values and 

 effective values of electromotive force upon the size and shape of 

 pole pieces and upon the manner of distribution of the armature 



