18i>2.] 



Transformers. 



461 



Such experiments as have hitherto been made do not enable ns to 

 say to what extent the eddy current loss is increased by this cause. 

 In the above-mentioned 1500- watt transformer there is 10 per cent, 

 less eddy current waste at full load than at no load, because of the 

 change in q 2 and also because of magnetic leakage, and there may be 

 50 per cent, less eddy current waste due to the higher temperature of 

 the iron. 



VII. Unloaded Transformer. — When there is a fair load on the 

 transformer, the primary current may be calculated on the assump- 

 tion that the permeability is constant, without much error. But when 

 there is no load, or small load, on the transformer it is necessary to 

 know the law connecting A and I. Everybody who has studied this 

 subject takes A in an unloaded transformer as being Nid. Now, in 

 reality, this is an assumption that there are absolutely no eddy currents ; 

 but as there are always eddy currents, however finely the iron may be 

 divided, and even small eddy currents produce great effects upon Ci, 

 the magnetic law which has been deduced from experiments on this 

 assumption must be quite untrue. Taking eddy currents effect as 

 represented by a circuit (w, r) with no magnetic leakage ; taking as 

 our magnetic law that, when I = ga sin x, 



A = g(sinx— b sin 3 # + m sin 5 a*), 



if V is a simple sine function of the time, I is so also with very great 

 accuracy, but not perfect accuracy. Assuming that I is a simple sine 

 function, the neglected terms in V may be calculated ; this serves no 

 useful purpose, so far as I can see at present, as they are so insignifi- 

 cant. The only problem of importance is really the calculation of Ci, 

 assuming that with great, but not perfect, accuracy V has the value 

 V sinAtf. Our equations are V = Bud + Nifll and = rc + w0l, and 

 hence NjVi/Ri = A + g0l, where A = NA + w and q — N^/^ + ji 2 /?-. 

 Now n 2 jr is negligible in comparison with N^/Bi in transformers, and 

 we may take q = Ni 8 /Ri. Hence — I = (Y /NJc) cos kt very nearly, 

 and if e = n 2 akjr, being called the eddy current effect, / being the 

 hysteresis term, 



d =(V /N 1 2 ^){ v/(l+2 e sin/+e 2 ) sin [ta-90 + tan" 1 



(tanfH — -— „)1 — & cos Skt — m cos 5 Jet] (4). 



cos/ 



We see that the effect of eddy currents without hysteresis is to 

 increase the amplitude of the fundamental term in 0], and to produce 

 a lead of 90°— cot _1 e, whereas the effect of hysteresis without eddy 

 currents is to keep the amplitude unaltered, and to produce a lead /. 

 If / is put equal to 0, that is if we assume no hysteresis, we obtain 



2 i 2 



