82 



Referring to the figure, the new positions assumed by the variable vectors, owing 

 to the introduction of Li, are designated by the subscript letter (1). The cur- 

 rent will decrease and its vector head move along the circle OBcBoBjO until a 

 state of equilibrium exists between the forces involved. The E. M. F. that over- 

 comes the resistance and inductance of the armature will decrease also and move 

 to the position OAi, its vector head following the circle OAc AqAjO, and the E. 

 M. F. at the collector rings will first decrease and then increase to a final value 

 AjA. The introduction of inductance into the external circuit brings the E. M. 

 F. at the collector rings and the total internal E. M. F. (OA) more nearly into 

 phase; it, however, causes a lag angle FjOBi to be introduced between the col- 

 lector E. M. F. and the current. The inductance E. M. F. of the armature de- 

 creases along the circle ODoDqDiO to a value ODi and the inductance E. M. F. 

 of the external circuit increases from zero along the circle YQcOQi Y to a value 

 OQi. The resultant M. M. F. will be ONi, and it is seen that while the arma- 

 ture reaction has remained very nearly constant the cross-magnetizing eflect has 

 been reduced about 50 per cent. 



From our initial conditions as indicated by the subscript letter (o) we can 

 also study the effects produced by the introduction of capacity into the external 

 circuit. If the value of L\ is reduced from infinity to some value C'c, the vir- 

 tual value of the current will change to 



1= (10) 



^;(R + Ri)^ + (-^-Lit')' 

 and the angle between OA and the current will have a value 



= tan- [(i^^^^)Ce.. - (R + Rj] ^^^^ 



In consequence of this change the current vector will assume the position OBc and 

 the other variable vectors will move to their corresponding positions shown by 

 the subscript letter (c). The current in its new position is not only in/advance of 

 the E. M. F. (AcO) at the brushes, but is also in advance of the E. M. F. OA, 

 since it has moved from Bq to a maximum value when passing OA, and then de- 

 creased in value. ^ 



1. See Bedell and Crehore's Alternating Currents, p. 297. 



