80 



the results of which are exhibited in the figure opposite page 80, aad are dis- 

 cussed in the following paragraphs : 



Suppose a circuit in which the inductance is zero, the capacity infinite and 

 the resistance variable, to be subjected to the influence of a simple harmonic 

 E. M. F. that is generated by an alternator having a constant armature inductance 

 for all values of armature current, a constant field excitation and a constant 

 speed. Uuder these conditions the virtual value of the E. ^I. F. at the brushes 

 of the alternator just before the circuit is closed will be, — 



E = W X„,ax ^ ^/2■ (5) 



which is represented by the vector OA in the figure. The rector OX is laid off 

 at right angles to OA to represent the value of the M. M. F. producing Nmax. 

 It is drawn 90° in advance of the E. M. F. it induces in accordance with the 

 relation exhibited in equations (1) and (2). At the time of closing the circuit 

 suppose the external variable non-inductive resistance to have a value Rj, and 

 that the constant armature resistance has a value R and the constant armature 

 inductance a value L. Then the equation of the current will assume the form : 



E • r t * -1 ^^^ "i 



sin u»t — tan ,^v 



1 = "- R + R,J (6) 



V iR + Ri) -^ + L^ ir' 



and its virtual value — 



E" 



I = (7) 



V (R + RJ 2 + h^u- 



which we can represent l)y tlie vector OB^ lagging tan degrees behind 



R -j- Rj 



OA. This armature current will react upon the magnetizing forces due to the 

 constant field excitation, and by virtue of the inductance of the armature will 

 produce an M. M. F. in phase with itself whicli is represented b_v the vector NNq, 

 drawn parallel to the current vector from the positive extremity of OX. This 

 armature M. M. F. sets up a cyclic magnetization developing a counter E. ]\1. F. 

 ODq lagging 90° degrees behind the current, and there is a loss of effective 

 E. M. F. due to the armature resistance that is shown by the short E. M. F. vec- 

 tor in phase with OP>o, therefore the total loss of E. M. F. in tlte armature will 

 be the resultant of these two vectors or OA^. The efi'ective E. M. F. that over- 

 comes the resistance of the non-inductive external circuit will be the vector A^A, 

 since it completes the E. M. F. triangle on OA and is in phase with the current 



