162 



ELEMENTS OF ELECTRICAL ENGINEERING. 



to maximum value of cos (BI). But the maximum (negative) value of cos 

 is I, and the corresponding value of the angle (1) is 180. 



To calculate the value of A which will bring B and / opposite to each other 

 in phase, for the given values of B, X, .A* and P f/ , consider Fig. 135, in which / 



Fig. 135. 



represents the current, and E the resultant electromotive force of machines A and 

 B. From this figure we have 



from which A may be calculated when / is known. The value of / may be de- 

 termined from the equation P" = BI cos (BI). 



2. When the electromotive force B of the synchronous motor is adjustable, maxi- 

 mum efficiency is obtained when the current (and also JRI 2 } is a minimum ; values of 

 A, X t J? and P ff being given. This minimum current is obtained when B is ad- 

 justed until A and / are in phase with each other. The proof of this proposition 

 is given below. 



To calculate the value of B which will bring A and / into phase with each 

 other for the given values of A, X, fi and /*', consider Fig. 136, in which A rep- 



RI 



- -- - - - _._ 



resents the value of the electromotive force of machine A, and E represents the 

 resultant electromotive force of machines A and B. From this figure we have 



(A RI}*-\- X*P B* 



from which B may be calculated when / is known. The value of / m,, be cal- 

 culated from the relation 



,47 cos (AI) = P" + XI* 



Proof that I is a minimum when B is adjusted until A and I are in phase with 

 each other ; A, X, X and P" being given. Plot the curve of which the ordi- 

 nates represent values of (XI) and the abscissas represent values of [B cos (!)']. 



