104 



TREATISE ON ALTERNATING CURRENTS. 



The values of the hysteresis losses in good soft iron, in micro- 

 watts per cubic centimetre for a frequency of 50 alternations per 

 second, for various values of the maximum induction, are given in 

 the following table : 



TABLE IV. 



63. Effect of Shape of P.D. Curve on Iron 

 Losses in Transformer Cores. We have seen that, as 

 a rule, we cannot in general expect the wave-form of the P.D. 

 applied between the primary terminals of a transformer to be a 

 true sine curve. It may, in fact, have almost any shape of a 

 periodic nature. It becomes a matter of interest, therefore, to 

 inquire how the iron losses in transformer cores are affected by the 

 shape of the P.D. curve. We proceed to attack the problem from 

 a theoretical point of view. 



Assuming that the iron losses are independent of the load on 

 the transformer, we may proceed on the supposition that the 

 secondary circuit is open. Let v be the instantaneous counter 

 E.M.F. in the primary circuit, A the cross-sectional area of the 

 core, N the number of primary turns, b the instantaneous value of 

 the induction, and S the area of the v curve taken over half a 

 period. 



We then have, neglecting leakage 



(31) 



Integrating this over half a period, we get 



