237] INDUCTION OF CURRENTS. 475 



constants by means of the initial values of the currents J x and 

 7 2 . These being 1^ and / 2 (0) we have for the induced currents 

 when t = 0, 



! 1 <>=I 1 -I 1 v=A 1 + A. i , 



//o )= / 2 (o)_/ 2 (i) = J5 i+j g 2 . 



These equations with (9) and (10) determine the four constants, 

 so that the solution is complete. The most important case is that 

 in which there is no electromotive force in one circuit, while the 

 other circuit originally open, and containing an electromotive force 

 E, is suddenly closed. The latter circuit is called the primary, and 

 will be taken as that denoted by the suffix 1, the former the 

 secondary, with the suffix 2. We accordingly have 



/, = J 2 (o) = / 2 d) = 0, /! w = E/R, 

 and 



E \ If RA-&L, \ 



R! ( 2 W( J? 2 A - R.L.Y + 4RAM* 



If _ R&-RA _ \ 



2W( 2 A-^i4) 2 + WUf 2 / 

 7" /M ^ f _ . ^ 



Since \ and X 2 are negative, the induced currents die away as the 

 time goes on. The function 



vanishes when 



has a maximum or minimum when 

 t = loer 



and the curve representing it has a point of inflexion for 



These three points are equidistant, and, since Xj and X 2 have 

 the same sign, are real if Ci and (7 2 have opposite signs. This is 

 the case for the secondary current J 2 , but the primary current has 

 both coefficients negative, and consequently has no maximum nor 



