i2 TRANSFORMERS. [Exp. 



9. With Core Loss. A transformer with an iron core differs 

 from the ideal transformer just discussed because there is a loss 

 in the iron due to hysteresis and eddy currents. The open- 

 circuit diagram now becomes as shown in Fig. 2. The flux 

 $ is still in quadrature with EP and Es, in accordance with 

 Faraday's fundamental law of induced electromotive force, 

 e S(d<f>--dt). The exciting current / , however, can no 

 longer be a wattless quadrature current, for it must have an 

 in-phase power component to supply the core losses due to 

 hysteresis and eddy currents. This core loss component is 



IH = watts core loss-f-Ep. 



The exciting current 7 is, accordingly, advanced in phase by 

 an angle a, called the hysteretic* angle of advance. 



It is seen, therefore, that 7 consists of two components 

 the core loss component /H and the true magnetizing component 

 /M which is wattless and in phase with the flux. The total ex- 

 citing currentf is the vector sum of these two components : 



/ = V/H 2 + /M 2 . 



10. A constant potential transformer (one in which Ep is 

 constant) is a constant flux transformer. It therefore follows 



* (Qa). As here defined, this angle includes the effect of eddy currents. 



t(9b). The exciting current of a transformer is distorted, i. e., has 

 a wave form different from that of the electromotive force, on account of 

 harmonics introduced by hysteresis. (See Appendix II. , Exp. 6-A.) 

 These harmonics currents of 3, 5, 7, etc., times the fundamental fre- 

 quency are necessarily wattless. They do not appear, therefore, in the 

 power component /H, but are included in the wattless component /M. 

 Strictly speaking, alternating currents in which harmonics are present can 

 not be represented by vectors in one plane ; for practical purposes, how- 

 ever, the plane vector diagram, as here given, is sufficiently accurate. 

 (See 47, Exp. 6-A; also "The Effect of Iron in Distorting Alternating 

 Current Wave Form," by Bedell and Tuttle, A. I. E. E., Sept., 1906; and 

 " Vector Representation of Non-Harmonic Alternating Currents," by B. 

 Arakawa, Physical Review, 1909.) These harmonics have the same value 

 at all loads; at full load they form such a small part of the total current 

 that the distortion which they produce is very small. 



