Alternate Current Transformer. 25 



''"2 Ta . .> /j\ 



-=^(see^6) 



or f/ie secondary numerics are proportional to the permeances of the 

 ttvo magnetic circuits. 



If tlie closed-circuit transformer be of the core type, so that 

 its windings are similarly arranged to those of the other, then 

 approximately, 



-i^'io and hence TSinS=T"SinS''. 

 cr a- 



If the method of treating leakage was equally legitimate for 



the two types, we have also, approximately, 



^=-^ = — (see § 34), provided the windings are similar. 



1 2 ^ 



For a non-inductive load, 



^_P,_ P,Sin8 



Pq Iron loss 



to the first order for both, hence if 6 and 6° refer to the same 



output, that is to the same fraction of full load in each 



SinS a- 

 ^u = gj^o = ^ approximately 



that is, the values of the co-ordinate 6 ]or the same output are 

 proportional to the permeances of the magnetic circuits. 



26. In order to compare the rates of approach to opposition of 

 Oj and C2 in transformers of the two types, let us consider the 

 equation 



Cot^ = tan(8,*).g-^ (see §19) 



which is correct to the first order for both, where tt - ^8 is the 

 angle C2 is behind C^ in phase. 

 For a non-inductive load 



P,^ P,Sin8 ^Pjg-^^g 



Pq Iron loss H3 

 so that 



Cot/3 = tanS(l +jj') 



for both types when <^ = 0. 



But 8 for the closed circuit type will be 50° or over, and for 

 the open circuit (hedgehog) type will be about 4° ; and if we 

 assume (which will be sufficiently accurate for our present 

 purpose) that in transformers of equal capacity of the two types 



