402 Mr. E. C. Rimington on an Air- Core Transformer 



E 2 f — 

 P 1= : /-.-;- p sinpt. sin {pt + 6)dt 



Hence, from (16) and (19), 



P (l+2« 2 )(l + « 2 ) l + 3a 2 + 2« 4 . m 



I\~ l + 4a 2 " l + 4a 2 ' • * ' ^ } 



and from this equation (20) the curve marked PPP (Plate X.) 

 is plotted. 



The curves for P, H, P 2 , and T*i are plotted in Plate XI. 

 for values of a up to 2. 



Magnetizing Effect of the Coils. 



Let g be the number of effective current-turns at any 

 instant when the secondary is closed, and G its maximum 

 value. 



Then g = n x c x + n 2 c 2 , 



where n x and n 2 are the number of turns in the primary and 

 secondary respectively, and 



G = v/^ 2 (V + n 2 2 C 2 2 + 2/1,7*2 OA cos 0, 



where is the phase-angle between the two currents. 



If we assume the primary and secondary to occupy equal 

 volumes, and we can neglect the relative difference in thickness 



n-t / r-i 



of the insulation of the two coils, — = \ / — , 



n% V r 2 



... G=n 1 \/c l 2 + C 2 2 ^ + 2C 1 C 2 \/-- C0S ^ 

 v r± v rj_ 



or (since M 2 is assumed =LN) 

 G= 



?2 1 E> , 2 Tl^Et 



s/d l + b' 1 n\/l+ 4a 2 ' 



Call Gi the maximum value of # when the secondary is 

 open ; then 



