TRANSFORMERS 307 



current density. The iron loss consists of the hysteresis and eddy 

 current losses and does not vary with load. It can be measured 

 by applying full voltage to the primary with the secondary open 

 and reading the watts input, 



W o = #1/0 cos 0o = EJ C = Ei*g . . . . (294) 



Wo includes a small copper loss 7 Vi which may be neglected. 



187. Hysteresis Loss. The hysteresis loss is the energy con- 

 sumed in magnetizing and demagnetizing the iron. It is directly 

 proportional to the frequency /, varies as the 1.6th power of the 

 maximum induction density Bo, and also depends on the quality 

 of the iron. 



The hysteresis loss per cycle per cubic centimeter of iron is 



CO A = if)) 1 - 6 ergs, ...... . (295) 



where YJ is the hysteresis constant for the iron and has a value of 

 about 0.003 for good transformer punchings. 



The hysteresis loss per second in a volume of V cu. cm. at a 

 frequency / is 



W h = Yj/FSBo 1 - 6 ergs per second . . . (296) 

 10- 7 watts. 



188. Eddy Current Loss in Transformer Iron. The eddy 

 current loss is the energy consumed by the currents induced in the 

 iron of the transformer by the alternating flux cutting it. 

 In Fig. 281 



t = thickness of sheets in centimeters, 

 B = maximum induction density, 

 / = frequency, 

 7 = electric conductivity of iron. 



AB is a section of length 1 cm., depth 1 cm. and width dx cm., 

 parallel to the edge of the plate and distant x cm. from the centre. 

 DC is a similar section on the other side. 



The maximum flux inclosed by A BCD is 2 9$ Q x lines. Of this 

 9$ox lines cut across the section A B and generate in it an e.m.f. of 

 effective value, 



dE = V2 7r/BoZ c.g.s. units. 



The conductance of the section A B is 7 dx, and thus the current 

 induced in it is 



dl = dEydx = V'Zirffio'YX dx c.g.s. units. 



