Alternate Current Transformer. 61 



The Transformer Numerics. 



55. The numeric t { = Tj, = t., (q.p.) ) for transformers of any 

 given type can be expressed in terms of the full-load output, 

 periodicity, and tli.e magnetic and electric qualities of the iron 

 and coppei-. 



Let us consider the case of transformers of the shell type 

 similar to the one designed in Section II., with square windows 

 (2/>,2i>), and iron tongue of square cross section (2^,2/3). 



From ;^ 33 



r=A'^ ^^ (I.) 



where A is a constant depending on the iron and copper space 

 factors. 



From the solution, as in § 32 of the equation 



which expresses the relation between the iron and copper losses 

 at full load, we get 



/3-B^ (II.) 



in which B will be a constant, if, for all ti-ansformers of the 

 series 



QK 



be constant. 



We may consider /> the iron space factor as fixed, and, 

 provided the primary and secondary pressures remain the same, 

 Q, the harmonic mean of the copper space factors, also as fixed ; 

 and the above expression will be constant if z, the ratio of the 

 copper to the iron losses at full load, be the same for all trans- 

 formers of the series as well as the ratio K/I of copper to iron 

 loss per cm^ at full load, both however, diminishing slightly in 

 the same proportion as the capacity increases ; or 



s=Const. K = Ko(l -wP,) I=Io(l -;«P,). (HI.) 

 where //i is a small fraction. 



Another way in which Is/K would be constant, and one more 

 in accordance with the practice of some manufacturers, would 

 be for K and Is each to be constant, I diminishing as the capacity 

 increased, and z increasing in the same ratio ; or 



