

THE SYNCHRONOUS MOTOR. 143 



tantf = J (ii) 



R being the resistance and X(= a>L) the reactance of the circuit. 

 The power P' delivered to the circuit by machine A is 



F = AIcos(AI) (in) 



where (A I) is the angle between A and / in Fig. 124, and 

 the power P" delivered to the circuit by machine B is 



P" = BIcos(JBI) (iv) 



where (BI) is the angle between B and / in Fig. 124. 



For certain values of (f> the angle (AI) may be less than 

 90 and the angle (BI) greater than 90, and if this condition 

 occurs, then P' will be positive and P" will be negative. 

 That is, machine A will give out power and machine B will 

 take in power, or in other words, machine A will act as a gen- 

 erator and machine B will act as a motor. 



For certain values of <f> the angle (A I) may be greater than 

 and the angle (BI) less than 90, and if this condition 

 occurs, machine A will act as a motor and machine B will act 

 as a generator. 



69. Variation of P' and of P" with the phase angle <. 



Before the physical aspects of either of the above conditions can 

 be discussed, it is necessary to examine carefully into the geomet- 

 rical relations involved in Fig. 124 on the assumption that </> 

 may have any value whatever. It is sufficient for our purpose 

 however to consider the power output (or intake) of one machine, 

 say machine B. For this purpose it is convenient to take the 

 line B in Fig. 124 as a fixed reference axis. Then, as the 

 angle < changes, the point P will describe a circle about 

 the point C, for the line CP is of constant length, being equal 

 to A [the electromotive forces (effective) of machines A and B 

 are of course supposed to be constant and their phase difference 

 </>, only, is supposed to change]. The triangle OCP in Fig. 

 125 is the triangle OCP of Fig. 124, and the circle in Fig. 125 

 is the above mentioned locus of the point P. 



