Altei'iiate Current Trans former. 65 



from which /», and hence the transformer, is determined. 

 The equation for t can be put in the form 

 _ TT/i-Pa 1 



orr=''^ 1^ (V.) 



by means of which it can be quickly calculated, and it will be 

 found that the result is a true maximum. 



For example, assuming the same data for design as are adopted 

 in §§41 and 52, 



.|-^= 1.029, 



and equation III. gives 



u=l.l, 

 hence by means of II. we find that ^' = 2.35^, (3' = 2A8/3, which 

 with /3=l.lb, give the most etficient shape for a shell transformer 

 in which z/I/QK= 1.029. 



If P.2 = 12.5 K. W., the same capacity as that of the transformers 

 in § 41, equation IV gives 



6=4.55, 

 and equation V., 



T=7300. 



The losses being a/ QK and aA/I, we find that each is equal to 

 181 watts, so that the efficiency at full load is 97.2 per cent. 



This maximum efficiency transformer will not have such good 

 regulation on inductive loads as others less efficient, but with 

 relatively wider windows. A compromise between efficiency and 

 regulation can always be made suitable to the nature of the work 

 the transformer is intended for. 



For the above transformer, if wound in five sections, Xi + X2:= 

 .00075; and the regulation would be, for a non-inductive load, 1.55 

 per cent., and for an inductive load of .8 power factor, 3.7 per 

 cent. These figures can be compared with those in § 52. 



57. A core transformer of the H type, in which the magnetic 

 circuit is rectangular (2(3, 2/?') in section and the coils rect- 

 angular in plan, is exactly the same in geometrical shape as a 

 shell transformer, but the copper and iron circuits of the former 

 occupy the places of the iron and copper circuits of the latter. 



