58 



Mr. W. Gr. Rhodes on a Theory 



To find the corresponding value of e we notice that E, e, and 

 lc (the resultant of Sc and Re reversed) are in equilibrium 



Fiff. 1. 



He (reversed) 



amongst themselves ; so that taking components of these along 

 and at right angles to the direction of E, we have 



and 



therefore 



and 



— e cos <f> = E — Re ~) 

 e sin <\> = Sc J 



e cos <f> = 2Rc — Re = Re 



e sin = Se 



} 



from (3). 



Squaring and adding, we get 



therefore 



Also, by division, 



e 2 =(R2 + S 2 )c 2 =I 2 e 2 , 



= Ic = 



B 



IE 

 2R 



(4) 



— tan ^> = tt =tan (see fig. 1). 



4. We thus find that when working at maximum output : — 



(1) The impressed E.M.F. is in phase with the current in 

 the armature. 



E 2 



(2) The maximum output is p= jp • 



(3) The corresponding current in armature is c= ^r. 



TF 



(4) The corresponding counter E.M.F. is e= ^ . 



(5) The angle of phase between the armature-current and 

 the E.M.F. necessary to overcome the resistance and 

 self-induction of the armature is equal and opposite to 

 the angle between the current and the counter E.M.F. 



