Alternate Current Transformer. 29 



From these two relations the two variables, and hence the 

 dimensions of the transformer, are determined, and the formulae 

 in Section I. enable us to arrive at the different details such as 

 «i, //.J, rtj, a^, ^1, r.^, Ti, T,, etc., when the e.m.f.'s on the primary 

 and secondary sides are given. 



28. As an illustration of this method I will work out the 

 theoretical* design of transformer, to transform from 2200 to 220 

 virtual volts at 50 periods, and to carry an inductive load of 

 10 K.W. whose power factor is .8. 



Selecting the shell type of transformer, one of the laminae of 

 which is shaped as in Fig. 5, we will suppose the iron tongue 

 to be of square cross section (2^, 2^) and the windows or 

 winding apertures to be also square (2^, 2b).'\ 



Hence the mean length of the magnetic circuit is 4 {2l> + fi), 

 and the mean length of a turn of either primary or secondary 

 coil (so wound as to be the same for botli) is 8 (d + fS). 



If /J the space factor of the iron be taken =.9, then the cross 

 section of the iron circuit is =4/^'^ = 3. 6/3', and the volume of 

 the iron 



= 1 6//3-( 2(^ + ^) = 1 4. 4/3'^( 2^ + /?). 



The space factor / will not only enable us to allow for insula- 

 tion between the laminae, but also for ventilating or cooling 

 ducts, if such are deemed necessary. 



Let us decide that the iron loss shall be 10* ergs, per second, 

 per unit volume. 



With a sample of transformer iron .045 cm. thick I have 

 found with my wave tracer,|| when the iron loss per cm.^ per 

 second was 10'' ergs, at 50 periods, the magnetising current wave 

 form being slightly peaked, that 



y = 4800, 8 = 52° iJL = 2250 (q.p.) 

 so for the present design I will assume, for the iron to be used, 



* Called theoretical because the details are full)' worked out iti accordance with the 

 theory already given. A knowledge of the theory and experience will, however, enable one 

 to make sufficiently accurate allowance for most of the small correcting terms, instead of 

 having to calculate them in each particular case. 



f This is far from being the most efficient shape, as will be shown in Section III. 



t The different factors and constants assumed are not given with any authority. The 

 purpose of this part of the paper is merely illustrative. 



II Phil. Mag., Nov., 1903. 



