THEORY OF SYNCHRONOUS MOTOR. 



131 



]ine of a plant consisting of a simple alternating-current generator 

 and a synchronous motor, S now representing the total reactance 

 of the system. 



Let L be the sum of the self-inductions of the two armatures 

 and line, so that S = 2irnL. 



The E.M.F., ri, which drives the current is the resultant of 

 E, e, and Si, so that E, e, Si, with ri reversed, form a system of 

 E.M.F.s in equilibrium. 



In Fig. 43 let the positive direction of rotation be counter- 

 clockwise, and let Oi be 

 the direction of the cur- 

 rent. The instantaneous 

 value of the current 

 does not concern us at 

 present. 



Take OR' equal to 

 ri reversed, and, conse- 

 quently, opposing the 

 current ; let OS' = Si, 

 lagging behind the cur- 

 rent by a quarter of a 



period. The resultant, OT of OR' and OS', must then be equal, and 

 opposite to the resultant of E and e. If, therefore, we produce 

 TO to T, and make OT OT', OT will represent in magnitude 

 and direction the resultant of E and e. If, now, we are given the 

 magnitudes of E and e, we can find their directions by the paral- 

 lelogram law. Now, two parallelograms can be constructed, having 

 OT 7 as diagonal, and E, e as adjacent sides ; but, since E is the 

 E.M.F. of the generator, we take that which gives the component 

 of E along Oi in the same sense as the current. 



The other parallelogram would make e the E.M.F. of the 

 generator. We may notice that the possibility of constructing 

 these two parallelograms proves that, in general, either of two 

 alternating-current machines may be driven as a motor by the 

 other, irrespective of the magnitudes of their relative E.M.F.s. 



Let now 



angle iOE = \fr 



and 



angle iOT = 



angle iOe = 



