Study of Transformers. 175 



It is to be observed that in the tables, 1000, A, A', and a' 

 divided by \^2 give the readings on dynamometers of the 

 primary voltage and primary current and secondary current 

 and secondary voltage respectively, or their effective values. 



Note that the lag e varies considerably from no load to small 

 ordinary loads, but the lag e / is always nearly 180°. And 

 hence the secondary voltage and currents are almost identi- 

 cally the same kind of function of time (only of opposite 

 sign) as the primary voltage. To make this certain : — the 

 general term in Y, whatever V may be, may be written 



a. sin ikt + b i cos i k t, 

 and the general term in v l is 



J sin (ikt — tt) + J cos (ikt— it), 

 s s 



where 5 is the same for all terms, 

 only the ith. term. 

 Evidently this is 



We are here considering 



— -1 sin ikt — J cos i k t, 

 s s 



and it is to be noted also that the lag is more nearly 180° as 

 i is greater. I have here used k to represent — , the reci- 

 procal of t being the frequency. This is true also of the 

 primary current when B/ is not great. 



With these tables before us, certain generalizations may be 

 made in the formulae given above. I assume, as in the tables, 

 no magnetic leakage, so that M 2 = LL'. 



27T 



1st. When R/ is very great. Let — be written as k. 



I' = R', 

 Z=L, 



M 2 



//^ £ 2 M 2 \ 2 79TC 



A= 



A . . MA Ma 



TF = R/L n y ' 



tan e = k 



LB! 



K'ExW y. (4) 



tane'=— k . 



RR' 



-pivprr? or e ' nearl y 180 °- 



/R+R'L + kJ ^, 



