482 'THE ELECTROMAGNETIC FIELD. [PT. III. CH. XII. 



As we increase the ratio L 2 co/R 2 the values of the apparent resist- 

 ance and self-induction approach the limiting values 



' M 2 



These values are nearly approached in actual transformers, par- 

 ticularly when fully loaded with a number of lamps in parallel in 

 the secondary. Now although we have in general 



L^ 2 > M*, 



still when the primary and secondary are toroidal coils wound on 

 the same core ( 231), so that very nearly the whole induction-flux 

 due to either is linked with the other, we have very nearly 



The transformer is then said to have no magnetic leakage. In this 

 case the apparent inductance L n ' is reduced to zero, the current 

 does not lag, and takes on the largest value that it can have, 

 namely 



The expression (12) for the power becomes, if we neglect the 

 square of R 2 /L 2 <o in comparison with unity, 



2 {(R, + RiM'/Lfy + o> 2 (A - M*/ltf\ ' 



as we see on dividing numerator and denominator by Z 2 2 a> 2 and 

 then adding and subtracting the term R/M^/L^ in the deno- 

 minator. If there is no magnetic leakage, this increases as R 2 

 decreases, until it reaches the limiting value 



\EI 



2 JV 



while if there is magnetic leakage, the power absorbed is a 

 maximum when 



_ M 2 



*+& z? 



becoming equal to 



and thence decreasing as R 2 decreases. 



