io8 ALTERNATING CURRENTS 



in a direction parallel to 00', and 1 cm. wide in a direction normal 

 to the plane of the paper, of thickness dx, and at a distance x from 

 00'. The e.m.f. maintaining the current in this strip is that induced 

 around the rectangle CDEF. Assuming, for the sake of simplicity, 

 that the induction follows the simple sine law, we have for the value 

 of the e.m.f. around CDEF, by (2) of 52 



4-44rc.2zB.10- 8 



2 

 The resistance of the double strip is p-j-, p being the resistivity 



of the material. Hence the watts lost in the double strip amount to 



(8-88?tzB.10- 8 ) 2 39-5, 



- -dx = -- (nxR x W~ 8 fdx 

 Zp p 



In order to find the watts lost in a strip of the entire thickness 

 of the sheet, we have to integrate the above expression between the 

 limits and ty, t being the thickness of the sheet, in cms. Now 



f* * f*' 



] '^(nx% x 10- 8 )%e = - ^(nB . 10~ 8 ) 2 x*dx 



1-65 x 10- 1C 



But since the volume of iron in such a strip is t, the loss per c.c. 

 of the sheet is 



1-65 x 10- 16 



- . 



p 



The resistivity of iron at C. may be taken to be 10~ 5 , and 

 the temperature coefficient 0'0045. If, then, the core be at a 

 temperature C., we have 



eddy-current loss per c.c. = /i i o-nfU'ifll ' n ^^ 



The eddy-current loss is generally from J to ^ of the hysteresis 

 loss. The following table contains the core losses, at a frequency 

 of 60, of four modern transformers : 



Output ...... 0-6 k.w. 2-5 k.w. 7'5 k.w. 30 k.w. 



Core loss, in watts ... 23 45 96 230 



Core loss as percentage 3-85 1/8 1*3 077 



