

[ 195 ] 



XII. A Theory of the Synchronous Motor. 

 By W. G. Rhodes, M.Sc* 



[Continued from p. 63.] 



Armature Reaction in a Single Phase Alternate Current 



Machine. 



12. IN the foregoing analytical treatment the magnitudes 

 A only of 0, <£, and ty are considered. We proceed to 

 investigate the signs of these angles in order to determine the 

 lags or leads of the E.M.F.'s over the current and to apply 

 the results to find out whether the field excitation of gene- 

 rator and motor is strengthened or weakened by the reaction 

 of the armature currents. 



13. It will now be convenient to slightly alter the meanings 

 of the symbols. 



Let E = virtual value of generator E.M.F. 



e = ,, „ counter E.M.F. of motor (as be- 



fore) ; 



R = total resistance in circuit consisting of generator, 

 motor, and line : 



L = sum of coefficients of self-induction of generator 

 and motor armatures; or, if the line possesses self- 

 induction, the coefficient of self-induction of the 

 whole circuit ; 



I = impedance of the complete circuit ; 



S = reactance of the complete circuit. 



14. The E.M.F. Re which drives the current is the re- 

 sultant of E, e, and Sc ; so that E, e, Sc, and Re reversed 

 form a system of E.M.F/s in equilibrium. 



In fig. 3 let the positive direction of rotation be counter- 

 clockwise, and let Oc be the direction of the current. The 

 instantaneous value of the current does not concern us at 

 present. Take OR x equal to Re reversed, and consequently 

 opposing the current; let OS'= Sc, lagging behind the current 

 by a quarter of a period. The resultant, OT', of OR' and OS' 

 will then be equal and opposite to the resultant of E and e. If, 

 therefore, we produce T v 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 parallelogram law. Now two 

 parallelograms can be constructed having OT as diagonal 



* Communicated by the Physical Society: read June 28, 1895. 



