of the Synchronous Motor. 57 



chiefly claims originality is the method of attacking the 

 problem. 



2. We consider the case of an alternating-current machine 

 whose field is excited by a direct current, while a simple 

 alternating current passes round the armature. 



Let p = output of motor ; 



c — virtual value of armature current ; 



R = resistance of armature ; 



E = virtual value of impressed E.M.F. ; 



e = „ „ counter E.M.F. ; 



L = coefficient of self-induction of armature ; 



n = frequency of armature current ; 



I = impedance of armature == {R 2 + (27mL) 2 }a ; 



S = reactance = 2*7rnL ; 



yfr= phase-difference between c and E ; 



<£= ,, ,, c and e ; 



= ,, c and Ic. 



Then the input = p + c 2 R ; 



and also = cE cos i/r ; 

 therefore p + c 2 R = cE cos yfr. 



Solving for c we get 



c= 2R C0S ^- 2R ^i^ 0082 ^-" 4 ^}' 



Since c is always real, we must have 



E 2 cos 2 T|r>4jt?R; 



therefore the maximum value of p is 



E 2 

 ^=4R 



• (1) 



(2) 



This occurs when y]r = ; that is, when the current and the 

 impressed E.M.F. are in phase with each other. 



3. We notice that the maximum output is the same as the 

 maximum energy which can be given to an external circuit 

 by a generator of constant E.M.F., E. From (1) we get the 

 corresponding value of the current 



c= 



E_ 

 2R 



(3) 



