iclien the Frequency is below a certain Critical Value. 403 



~ ?2jE ?2 X E 



LjTl = -nr = 7 --- 



J-i nvi + a 



oJ 



Then we know the critical value of oc= \/ - 



- t-Vn^ • ■ <"> 



Evidently, then, the magnetizing effect is always diminished 

 on closing the secondary. 



The curve GGG (Plate X.) is plotted from equation (21). 



It will be seen, on inspecting Plate X., that in the cases of 

 the impedance-curve and the current-curve the critical value 

 for ol = ^2 = 1*414, while the value of a that makes them a 



maximum and a minimum respectively is a = — ^ ='707. 



This latter value of a is the critical value for the curve PPP, 

 while, as may be seen by differentiating equation (20) and 

 equating to zero, the value of a that makes this curve a 



minimum is = : , or *4278. 



Jj 



Consider, now, the case of primary and secondary having 

 the same time-constants but with magnetic le akage. 



2_ 



The value of a to make-r a maximum from (156)= , 



Ii V J >/3-/3 2 



Let 7 represent the ratio of the former value of a to the 

 latter, then 



A /Hf . 



I 2 



also the maximum value of t = , . 



From equation (11), 



fcmtf=-% = ^ 



/?N ex.' 



and 6 is the angle by which the secondary current is in 

 advance of the primary, and it lies between ir and r— ; it 

 therefore follows that the angle by which the secondary cur- 

 rent lags behind the primary lies between - and ir, and is 

 2 + tan -1 a. The following Table gives values of the above 

 quantities for values of (3 from 1 to *1. 



