68 TREATISE ON ALTERNATING CURRENTS. 



TWO REACTIVE AND MUTUALLY INDUCTIVE CIRCUITS CONNECTED 



IN PARALLEL. 



48. In this case the vector equations to be solved are 



(7*1 -}- ksi)ii -f- JcpMi^iz = c' 

 2 t iii -f- (TZ + A'S 2 )^2 = e 



and 



^ -f ?' 2 = 



whence, on putting 



-3/i,2 = M*,\ = -3f 

 and solving as simultaneous equations for i\ and i%, we get 



\ 

 J ' 



Putting, for shortness 



- s lS , 

 these equations become 



which, by multiplying both sides of the equations by P &, and 

 simplifying, may be written 



-pM) + /^ 



These are the vector- current equations giving the components 

 of ii and ? 2 along and at right angles to e. By addition, we 

 have 



s 2 - 2pM) - Q(n + r 2 )}]e . (27) 



which gives the components of the main current along and at 

 right angles to e ; thus the component in phase with e is 





