238] INDUCTION OF CURRENTS. 481 



or making use of complex variables as before, 



(g) Af + Jf' 



A particular solution is given as before by putting 



I 

 giving 



(Ljco + RJA 



' + (L& + ft) 5 = 0. 



Eliminating 5 from these equations we get 

 do) 



Comparing this with equation (3) above we find that the current 

 in the primary is the same as if the secondary were absent, and 

 the resistance and self- inductance of the primary were R f and L', 

 where 



(II) 



These results were first given by Maxwell in 1864 in his celebrated 

 paper "A Dynamical Theory of the Electromagnetic Field*." 

 They constitute the basis of the theory of the alternating current 

 transformer. 



We see from equations (n) that the effect of the presence of 

 the secondary circuit is to cause an apparent increase of resistance 

 and decrease of self-inductance in the primary. Both of these 

 effects cause a decrease in the angle of lag of the primary current 

 behind the electromotive-force, and accordingly, by (6), an increase of 

 power. Inserting the values ( 1 1 ) in (6) we obtain for the power 



* Phil Trans. Vol. CLV. 

 W. E. 31 



