54 ALTERNATING CURRENTS 



vi is opposed to the positive direction of v 3 , the wattmeter reading 

 will represent the mean value of Vi'i 3 , and hence will, in Fig. 38, 

 correspond to Vi'I 3 cos < 3 = Vi'I 3 ' cos < 3 ' = Vi' x CE. 



Now, it is evident that under certain conditions of load CE may 

 be of opposite sign to CB or "VY, i.e. the reading of W 2 may become 



FIG. 38. Vector Diagram of Three-phase Circuit. 



negative. If the wattmeter is only capable of reading to one side of 

 zero, this will necessitate a reversal of its shunt-coil connections, and 

 the total power will then be given by the arithmetical difference of the 

 readings of the two wattmeters. This case, although possible,, is not 

 of frequent occurrence, and, as may be seen by an examination of the 

 vector diagrams, requires a very large angle of lag of I 3 behind V 3 . 



We have already ( 7) defined the power factor of a single-phase 

 circuit as the ratio of the true power to the volt-amperes, and the 

 question now arises as to what meaning is to be attached to this term 

 in the case of an unbalanced inductive three-phase load. When, as 

 in Fig. 37, the currents all lag by different amounts behind their 

 respective p.d.'s, it is clear that the term " power factor " can have 

 no definite physical meaning. 



Having considered the most general case of power measurement 

 in three-phase circuits, we may next examine certain special cases. 

 The most interesting of these, from a practical point of view, are (1) 

 that of a balanced circuit, and (2) that of an unbalanced non-induc- 

 tive load. The first may be closely approached by either a sym- 

 metrical lamp load or a load of induction motors, and the second 

 frequently arises in connection with a lamp load. 



