Alternate Current Transformer. 37 



When Si and x^ have been determined as before, /j and /« can be 

 expressed in terms of the two variables d and f3, and the ratio of 

 the losses 



I (volume of iron) 

 being equated to the selected value s gives us an equation, slightly 

 more complex than that for a shell transformer, for determining 

 (3/b and the rest follows as in the preceding cases. 



41. When we select for the section of the iron tongue and for 

 the windows or winding apertures different shapes from that 

 selected in ^ 28, the method of procedure is fairly obvious. In 

 general if 2^, 2/3', be the section of the tongue, 2y8' being measured 

 perpendicular to the planes of the laminae ; and if 2d, 2b' , be the 

 dimensions of the window 2b' being measured parallel to the 

 tongue; 



the volume of iron =16//3/3'(/^ + '^' + /3) 



and the volume of copper ^16Q/^^'(/3 + y8' + 2^) 

 [neglecting the small correcting terms in k depending on the dis- 

 tribution of current densities in the two coils], whei-e / and Q 

 have the same signification as before, and if the iron and copper 

 los.ses are to be equal at full load 



bb\^ + ^' + 2b )_ p\_ .9.10-' _i Q.,9 



pli'{b + b' + li) QK .583 . 15 . 10^ 

 if we adopt the same values for the data as before. 



The values of [ijb for a few special shapes are as follows : — 



[a) lib=b', 2/3'=3/3, 

 /3//^=.984. 



(/;) If b=b\ (S'=2f3, 

 f3/b=.886. 



(c) If 2^'=3/;, 2/3'=3/3, 

 /3lb=l.Ul. 



{d) If 2b'=?>b, /3'=2/3, 

 ^/^=1.025. 



{e) lib'=2b, 2/3'=5^, 

 /3/^=1.042. 



Let us determine approximate values of t for transformers of the 

 above shapes whose output on non-inductive load shall be 12.5 

 K.W. at 50 periods, the normal rating of the transformer already 

 designed. 



