Alternate Current Transformer. 27 



volume, and method of cooling to be adopted, decide on the per- 

 missible copper and iron losses per unit volume. 



If K be the copper loss decided on, per second, per unit volume, 

 at full load, then 



whence c, the amplitude of the full-load current density, is 

 known, p being the specific resistance of copper at the expected 

 working temperature. 



When the iron loss per second, per unit volume, (I. say) is 

 given, the corresponding retardation 8, permeability and flux 

 density can be got from curves similar to those in Fig. I., that have 

 been obtained from a sample of the iron to be used with (f.p.) 

 sine wave magnetising currents whose period was the given one. 



If y be the flux density ( = B the abscissae in Fig. I.), then we 

 should have between these quantities the relation, 



-^ = I. (see § 1). 



Once tlie form of the magnetic circuit has been selected, its 

 dimensions can be completely specified by two variables. The 

 output at full load, P.j say, can V)e expressed in terms of tliese two 

 variables, for P'^, the power passed down to the secondary and 

 developed in it, is given by the equation, 



and F = iron .section x permissible flux density (y), 



fi^C'z^ total copper section x permissible current density at 



full load (c). 



P'2 can be obtained from P^ the given output, and Cos<^' from 



Cos<^, the given power factor of the load, by the equations, 



p',={i + ,^}p> 



, , I tan<^i 

 and tan(^ =tan<5!)+ 1 x.^ V^, 



or Cos^'^Cos^- 1 - f a:.^— )Sin(/)Cos<^^j !- 



where 0^ is the full load value of 6, when approximate values of 

 the transformer numeric and of the secondary leakage coefficient 

 are known. 



[In future t will be used for either tj or t.j when approximate 

 values only are required]. 



