POLYPHASE SYSTEMS 85 



The coil currents of Fig. 82 are shown in Fig. 83 in phase 

 with their respective voltages, balanced conditions being assumed. 

 The line current 



I a a' = Jba + / ea 



This addition is made vectorially in Fig. 83 (a), giving l aa > 30 

 from E^ a . It will be observed that I aa ' is \/3 times the coil 

 current. Line currents Iw and l cc > may be found in a similar 

 manner, with the result shown in Fig. 83 (6). Therefore, in the 

 delta-system there is a phase difference of 30 between the line 

 currents and the line voltages at unity power-factor, just as in 

 the Y-system. 



It is obvious that the line voltage is equal to the coil voltage 

 in a delta-system. Moreover, the sum of the three voltages 

 net in^ around the delta must be zero by Kirchhoff's second law. 



Bab 



(a) 



*4. Showing that the sum of throe delta voltages is 



/// a balanced delta-system, the line voltage is equal to the coil 

 ;, but the line current is \/3 times the coil cum nt. 



36 shows three lamp loads, each requiring 10 amp. at 

 115 volts. They are first connected in Y and then in delta. In 

 order to supply the proper voltage in each case, there are 199 

 volts across lines in the Y-sy-tem and 115 volts in the delta- 

 i. Then- are M) amp. per line in the Y-system and 17. '.\ 

 amp. IMT line in the delta-system. The power -upplird i> the 

 same in cadi system. 



cr in Delta-system. The total power in a delta-system is 



P = 3 / ,/ cos 



