348 ALTERNATING CURRENTS 



Below are tabulated these results : 



EMFS. 



D. C. 



SINGLE- THREE- FOUR- SIX- 



PHASE PHASE PHASE PHASE 



141.4 100 86.6 70.7 50 



RATIO OP A. C. EMFS. TO D. C. EMF. 

 0.707 0.612 0.50 0.354 



142. Current Ratios in a Synchronous Converter. The rela- 

 tions between the direct and alternating currents in a synchronous 

 converter may be determined as follows: 



Single-phase: 



If the efficiency is assumed to be 100 per cent, and the power- 

 factor unity 



VI = V l Ii 



7l V U1A T 1 414 T (7fi\ 



i = v 1 = ~m Ii = 



where V and I are the direct-current voltage and current respec- 



tively and Vi and /i are the single-phase voltage and current 



respectively. 



If the efficiency be rj and the power-factor P.P., 



VI = VJ l X P.F. X r, 

 The single-phase current 



7 1 ' 414/ (77) 



/[ ~ q X P.F. 



In practice, the efficiency is from 92 to 96 per cent, and the 

 power-factor is rarely allowed to drop below 0.9. 

 Three-phase: 

 At 100 per cent, efficiency and unity power-factor 



vi = 



where Y 3 is the three-phase line voltage and 7 3 the three-phase 

 line current. 



but 



V 141 4 



v, = m = i (par - 141) 



7 3 = 0.943 / (78) 



