1 82 ELEMENTS OF ELECTRICAL ENGINEERING. 



fore the effective electromotive force between the collector rings 

 of a two-ring converter is represented by the diameter, E v Fig. 

 151, of the polygon whose sides are equal and parallel to the 

 vectors a which represent the effective values of the electromo- 

 tive forces in the individual armature conductors. 



The electromotive force (effective) between two collector rings 

 which are connected to the armature winding at points 1 20 elec- 

 trical degrees apart, that is between any two rings of a three-ring 

 converter, is represented by that chord of the polygon, Fig. 151, 

 which subtends an angle of 120 ; the effective electromotive force 

 between two rings which are connected to the armature winding 

 at points 90 electrical degrees apart, that is between any two ad- 

 jacent rings of a four-ring converter, is represented by that chord 

 of the polygon, Fig. 151, which subtends an angle of 90 ; and, 

 in general, the effective electromotive force between adjacent 

 rings of an n-r'mg converter is represented by that chord of the 

 polygon, Fig. 151, which subtends an angle of 360 jn. There- 

 fore, treating the polygon of Fig. 151 as a circle, we have 



, TT 

 E = E 9 sm - 



n 2 n 



or, using the value of 2 from equation (i) we have 



which gives the following expressions for the effective values of 

 the alternating electromotive forces between adjacent rings of a 

 two-ring, a three-ring, a four- ring, and a six-ring converter in 

 terms of the electromotive force between the direct-current 

 brushes 



2 = 



0.707^ (17) 



