54 THE MAGNETIC CIRCUIT [ART. 22 



(A) If two or more curves for the same material are available, 

 taken at different frequencies, the hysteresis is first separated from 

 the eddy -current loss as is explained before, for several flux densi- 



ithin the range of the curves. Then the exponent, according 

 to which the hysteresis loss varies with the flux density is found, 

 by plotting the hysteresis loss to a logarithmic scale (see problems 

 18 and 19 above). Finally the two losses are extrapolated. In 

 extrapolating, the hysteresis loss is assumed to vary according to 

 the same law, and the eddy current loss is assumed to vary as the 

 square of the flux density; see eq. (22). 



(B) Should only one curve of the total loss be available for 

 extrapolation, this curve may be assumed to be a parabola of the 

 form P=aB + bB 2 . Dividing the equation throughout by B we 

 get 



(24) 



This is the equation of a straight line between P/B and B. Plot- 

 ting P/B against the values of B as abscissae, a straight line is 

 obtained which can be easily extrapolated. In some cases the 

 values of P/B thus plotted give a line with a perceptible curva- 

 ture. Nevertheless, the curvature is much smaller than that of 

 the original P curve, so that the P/B curve can be extrapolated 

 with more certainty, especially if the lower points be disregarded. 1 



Prob. 23. From the curves in Fig. 10 calculate the core loss per cubic 

 decimeter of 29-gauge silicon-steel laminations, at a flux density of 10 

 kl/sq.cm. and at 40 cycles. Ans. About 10 watts. 



Prob. 24. Using the data obtained in the solution of the preceding 

 problem calculate the figure of loss of 26-gauge laminations at 60 cycles. 



Ans. 2.7 watt/kg. 



Prob. 26. Check the curve of total core loss for the ordinary carbon 

 steel at 40 cycles with the curves for 25 and 60 cycles. 



Prob. 26. Extrapolate the curve of core loss for the silicon steel at 25 

 cycles up to the density of 20 kl/sq.cm. Which method is the more 

 pivf< Table? Ans. 22 watts per cu.dm. at # = 20. 



Prob. 27. Show that the core loss curve for ordinary carbon steel, at 

 60 cycles, follows closely eq. (24). 



1 If the P/B curve should prove to be a straight line, then it is probable 

 that the hysteresis loss follows eq. 21a more nearly than eq. 20. In this case, 

 even if we had data for two frequencies, method (B) would be both more 

 accurate, and more simple than method (A). 



