346 ALTERNATING CURRENTS 



conductors, cutting the same field. Therefore, there must be a 

 fixed ratio between the direct-current and the alternating- 

 current induced electromotive forces. 



In a single-phase converter, there are the same number of 

 active conductors between the direct-current brushes as between 

 the alternating-current slip-rings, as will be seen in Fig. 314. 

 The same number of conductors, cutting the same field, gives 

 both the direct-current emf. and the single-phase emf. 



It will be remembered that the electromotive force between 

 the brushes of a direct-current generator is the sum of the emf. 

 waves generated in each of the individual conductors connected 

 in series between the brushes. The resulting electromotive 

 force is the peak value of the resulting wave, as is shown in Fig. 



Resultant d.c. emf 



Resultant u.c. emf.- 



(a) (fc) 



FIG. 317. Relation between direct and alternating induced emfs. in a syn- 

 chronous-converter armature. 



317(a). (Also see Vol. I, page 219, Pars. 164 and 165). For 

 simplicity, Fig. 317(a) shows only the wave resulting from two 

 coils between slip-rings spaced 90 apart. 



In a single-phase machine, there are just as many conductors 

 between the slip-ring taps as between the brushes. Therefore, 

 the resultant alternating emf. wave between slip-ring taps is 

 found by adding together the alternating waves, 90 apart, point 

 by point, as shown in Fig. 317(6). Comparing Figs. 3 17 (a) 

 and 317(6), it will be noted that the direct-current emf. is equal 

 to the peak value of the alternating emf. 



Therefore, in a single-phase converter, the direct-current induced 

 electromotive force is equal to the \/2 limes the effective value of 

 the single-phase alternating-current induced electromotive force. 

 This ratio may be modified by wave form as in the split-pole 

 converter (page 361). 



141. Polyphase Voltage Ratios in a Synchronous Converter. 

 It will be remembered that the total single-phase electromotive 

 force generated in an alternator armature is the vector sum of 



