DETAILED STUDY OF OPERATION WITH NORMAL LOAD 33 



current can be represented in magnitude and in phase by the same 

 vector as the resultant E.M.F. of the circuit. 

 As regards the magnitude, since we have 



it suffices to take, for the current 7, a scale of amperes Z times greater 

 than the scale of volts 'used for the E.M.F. values. 



As to the axis of reference, its choice depends on the axis selected 

 for the E.M.F. values. 



The bipolar diagram may therefore be established in two distinctly 

 different manners, according to whether it be the vector of the 

 generator E.M.F., E] or that of the motor, E 2 , which is taken as 

 the fixed line. 



We will indicate, successively, these two types of diagrams which, 

 in many cases, do not serve exactly the same purpose, as will be seen 

 later. 



Bipolar Diagram of the First Kind. Motor- Vector E^ taken as 

 Fixed Axis. Let us suppose the effective values EI and E 2 of the 

 E.M.F's. taken with the signs which they have when one follows the 

 circuit formed by the motor, the line, and the generator. It is known, 

 by experience, that the E.M.F's. are very nearly in opposition. The 

 two corresponding vectors can, therefore, be represented by two right 

 lines OA<2 and OA\, drawn in different directions (as indicated by 

 the arrow-heads) and making, a very small angle, 0, with each other 

 (Fig. 22). (This angle indicates the phase-difference between the two 

 E.M.F's., as* measured at the terminals of the two machines when 

 coupled in parallel.) 



When under load, the generator tends to lead with respect to the 

 motor. The vector EI will, therefore, turn in the positive direction 

 which is conventional in mechanics, i.e., in the direction contrary to 

 the hands of a watch. 



The resultant E.M.F. e, acting in the circuit, is represented by the 

 "vector A\A 2 , which is the resultant of EI and E 2 . By projecting 

 AiA 2 on a right line, A 2 F, which makes the angle f backward from 

 AiA 2 , we obtain the vector A 2 F=RI, representing the component that 

 is in phase with the E.M.F. EI. The angle DA 2 A^, therefore measures 

 the phase-difference of the current with respect to the E.M.F. E 2 with. 

 reversed sign, i.e., measured at the terminals, the same as the E.M.F. 

 of the generator. In order to be able to take A\A^ as equal in 



