THE DYNAMO. 43 



brushes is one thirty-sixth of the resistance of the whole winding 

 considered as one long coil. 



Another type of multipolar armature winding, namely the wave 

 winding, is described in Appendix C. The wave winding has but 

 two paths between positive and negative brushes irrespective of 

 the number of poles and brushes. 



When an armature provides /' similar paths in parallel between 

 positive and negative brushes, then evidently I //'-th of the arma- 

 ture windings are in series in each path. 



30. The fundamental equation of the direct-current dynamo. 

 The equation which expresses the relation between the induced 

 electromotive force of a dynamo, the amount of magnetic flux 

 from each field pole, the number of field poles, the number of 

 conductors on the outside of the armature, the number of paths 

 in the armature winding between brushes, and the speed of the 

 armature, is called the fundamental equation of the dynamo on 

 account of its importance in the theory of the design and opera- 

 tion of generators and motors. 



Let < = magnetic flux which enters the armature from each 

 north pole of the field magnet and leaves the 

 armature at each south pole of the field magnet. 

 / = number of field poles. 



Z = number of conductors on the outside of the armature. 

 p' = number of electrical paths in parallel between the 



brushes. 



E a = total electromotive force induced in the armature. 

 This is the same as the electromotive force between 

 the brushes, as measured by a voltmeter, when the 

 current in the armature is negligibly small. 

 n = speed of armature in revolutions per second. 

 Then 



abvolts 

 or 



volts (2i&) 



x io 



