306 



THE POLYPHASE CIRCUIT. 



of one phase, and consequently C and c are in phase. The 

 line voltage E is the resultant of the voltages e and e in 

 two phases which differ from one another by 120, 

 and is 30 out of phase with either of them, as 

 will be seen from the diagram Fig. 150. Consequently, in 

 a non-inductive circuit, where c and e are in phase, E and 

 C will differ in phase by 30. Hence the reading of the 

 wattmeter connected as shown in Fig. 155 will read the 



/q 



product C E cos 30 = -<r @ E when there is no lag or 



lead in the circuit, i.e., when the power-factor is unity. 



Thus for a non-inductive circuit a single reading of the 

 wattmeter will give the power of the circuit when 

 multiplied by two since, as will be remembered, the total 

 power is */3 C E. Similar reasoning will lead to the same 

 result with a mesh-connected generator, as the current 

 and voltage are in this case also 30 out of phase. 



If the load is inductive, so that the branch current c is 

 not in phase with the voltage e, as assumed above, but has an 

 angle of phase difference <f>, then the phase difference 



Load non-inductive. Load inductive. 



FIG. 163. PHASE RELATIONS IN THREE-PHASE LINE (STAR CONNECTED GENERATOR.) 



between the current and voltage in the line will not be 

 30 but 30 <f> according as </> is an angle of lag or of lead, 

 in the case of a mesh-connected generator, or 30 + < under 

 like conditions for a star-connected generator. This case 

 is illustrated by Fig. 153. 



Here the vectors E ly E 2 , E 3 , represent the phase 

 of the three voltages measured from line to line as 

 derived from a star-conn 3cted generator, and the lines 

 C,, C 2 , C 3 , show the phase of the currents flowing in 



