174 TRANSFORMERS. [Exp. 



If c and r represent the electromotive force and resistance of one of 

 these circuits, the watts loss is e*-s-r. But e<xE. It accordingly 

 follows that eddy current loss* varies as the square of the voltage 

 and is independent of frequency and wave form. As the tempera- 

 ture of a transformer increases the eddy current loss decreases.! 



Referring to Fig. 5, if all the core loss were due to eddy currents, 

 we would have b = o and a = 2. The curve for losses at different 

 frequencies and constant voltage would be a horizontal line; the 

 curves for losses at different voltages and constant frequency would 

 slope at an angle with a tangent 2. 



50. Hysteresis loss in watts per cu. cm. is practically equal to 

 rjnB^io- 1 . Here 77 is a coefficient of hysteresis, equals to about .002 

 for what was formerly good iron, but is now little more than half that 

 value for the best alloy steel. The hysteretic exponent 1.6, first 

 determined by Steinmetz, is only approximate, being less than this 

 for low magnetic densities and considerably more than this for high 

 densities. 



Referring to Fig. 5, if all the core loss were due to hysteresis, we 

 would have (taking 1.6 as the hysteretic exponent) = 1.6 and 

 bi a = 0.6. 



51. In an actual transformer both hysteresis and eddy current 

 loss are present, so that a has a value between 1.6 (hysteresis) and 2 

 (eddy currents), and b has a value between 0.6 (hysteresis) and o 



*(49a). In terms of B, eddy current loss in watts per en. cm. is 

 V(dnB) 2 lo" 21 , where d is the thickness of lamination expressed in mils 

 and 7 is the conductance (the reciprocal of resistance in ohms per cu. 

 cm.) of the material; for iron, 7 is about io 5 . There is a very slight 

 change of eddy currents with frequency and wave form due to local 

 inductance and " skin effect " in the local eddy current circuit. 



By decreasing the thickness of transformer plate, eddy current loss is 

 diminished; but hysteresis loss is increased, since some iron is wasted and 

 B is greater in the remainder. A thickness between io and 15 mils gives 

 the least total loss, according to particular conditions; see Elec. World, 

 Dec. 31, 1898. 



t (4Qb). Hysteresis loss, also, decreases with increase in temperature. 

 The total core loss of a transformer when hot may be 6 or 8 per cent, 

 less than when cold. 



$ (5<>a). By so called "aging " due to heat, this coefficient increases in 

 the course of time. Although not entirely eliminated, this effect has been 

 reduced in the best steel now used. 



