Alternate Current Transformer. 63 



put of a transformer is proportional to 'V ^^—r- 



This is not proportional to the square root of w or of the 

 frequency as, when w increases, fx for the same flux density will 

 diminish and SinS will increase. 



Most Efficient Shapes of Transformers. 

 56. It has been shown (§ 21) that when consideration of leak- 

 age is neglected, the measure of excellence of a transformer is 



T 



ShTS' 

 hence the most efficient transformer of a given type and capacity 

 and made of similar iron will be that one for which t is a maximum. 



If a, a be the total cross sections (insulation, etc., included) of 

 the copper and iron circuits respectively, and /, A. their mean 

 lengths, then 



must both be minima, and as the output 



where h is a constant, as the flux and current densities will be 

 fixed, the problem resolves itself into finding values for the 

 dimensions of the carcass that will make 



^ , ^ , , • - 



— and - botli minima when aa is constant. 



a a 



Specifying the dimensions of a shell transformer in the usual 

 way (window = 26, 26', tongue = 2y8, 2;S'), 



a = Ub', /=4(^ + ^' + 2^), 



a=4/5^', X=i{b+b'+(i). 

 and proceeding by the method of indeterminate multipliers 

 (A, B, C), 



