*7 6 TRANSFORMERS. [Exp. 



n" 

 lower* voltage E" = , E', let the core loss be W". We may com- 



pute the watts eddy current loss at the higher frequency (n') and 

 normal voltage by the formula 



Watts eddy currents = 



n" 



Eddy current loss is substantially the same for all frequencies, but 

 varies as the square of the voltage and so can be computed for any 

 frequency and voltage. Hysteresis loss is found by subtracting eddy 

 loss from total loss. 



* ( 53a). If the wave form of electromotive force for the two frequen- 

 cies is different, E" = ("/" -r- n'f)E', where the form factor / is the 

 ratio of the effective to the average value. (For a sine wave, /=i.i.) 

 The eddy current loss in watts at the higher frequency n' and normal 

 voltage is then 



The above equations can be derived as follows : Eddy current loss, 

 irrespective of frequency and wave form (49), varies as E 2 and equals 

 aE z , where a is a constant. Similarly, for any wave form, hysteresis 

 loss equals bnB*, where b and x are constant; no assumption is made 

 that x= 1.6. At the two frequencies the total losses are 



(1) W = a(E') 2 +bn' (')*; 



(2) W" = a(E"Y-\-})n"(B"y. 



For B", write B' t this being the condition of the test ; for E", write 

 fi'(J5"-f*J5') Multiply (2) by n'-^-n", subtract from (i) and solve 

 for eddy current loss a(-E') 2 . When the wave form of electromotive 

 force is the same at the two frequencies, (E" -=- E') = (n" -r- n'). 



The separation of losses by measurements at two frequencies was first 

 made by Steinmetz ; the influence of form factor was introduced by 

 Roessler. There are various methods for making the calculations, differ- 

 ing somewhat in detail. The formulae here given are from a paper by the 

 author before the Cornell Electrical Society, May 4, 1898. Note 35, 

 Exp. 5-A, and Appendix I., Exp. 2-B ; also Bedell's Transformer, p. 312 

 et seq. (Some of these references, following Roessler, use form factor 

 as the reciprocal of /, as defined above.) M. G. Lloyd has recently pub- 

 lished a very complete investigation of the subject; see Bull. Bureau oj 

 Standards, February, 1909. 



