)ETAILED STUDY OF OPERATION WITH NORMAL LOAD 37 



Limit -Circle of Current. Let I m be the maximum value of the cur- 

 rent which the armature can withstand. If, around A 2 as center, a 

 circle be drawn with a radius equal to I m according to the scale of 

 amperes (or equal to ZI. m according to the scale of volts), this circle 

 will constitute the boundary of a space having certain characteristics. 

 All load-points inside that space correspond to loads which can be 

 maintained indefinitely without the current, 7, exceeding that limit. 

 All load-points situated outside this space represent loads which can- 

 not be maintained indefinitely. This limit-circle of current is, therefore, 

 also a limit-circle of stability of operation, of the motor. 



Algebraical Relations Deduced from the Diagram. To facilitate 

 graphical calculation it is always useful to have the algebraical expres- 

 sions for the variables. What we are interested in knowing is the cur- 

 rent strength, its phase-angle, the power of the motor as a function of 

 the E.M.F.'s E 2 and EI, of the constants of the circuit, and of the 

 angle of lag 0, or conversely, any of these as a function of the power, etc. 



The solution of the triangles represented in Fig. 23 gives imme- 

 diately the relation sought. In the triangle A^DA 2 we have 



Id=I sin 0, ........ (i) 



I w =Icos<j) ......... (2) 



Again, the projection ZI is equal to the projection of the broken 

 line AiDA 2 : 



ZI cos (? (/>)=Z/(jcos f+Z/dsin f ....... (3) 



The triangle OA 2 Ai enables EI or / to be expressed in terms 

 of other quantities, thus: 



-^), . ... (4) 

 (5) 



Finally, if the triangle OA 2 Ai be projected on the line A 2 D and 

 on a line DA 1 perpendicular thereto, we will have I w and I d as a func- 

 tion of EI, E 2 and 0: 



ZI w =E lC os( r -0)-E 2 cos r , ...... (6) 



ZI d =E l sm( r -0)-E 2 sm r ....... (7) 



