92 TREATISE ON ALTERNATING CURRENTS. 



Then 



Since the circuit is wound on an iron core, Si will be large, and t'i 

 correspondingly small. 



If the power factor of the circuit is now determined, it will be 

 found to be comparatively small, showing that a considerable 

 portion of the current is at right angles to the applied P.D., and is 

 idle, or wattless. There will thus be an energy component of 

 the current in phase with the P.D., and a wattless component at 

 right angles to the P.D. 



We have to indicate the functions of these two components of 

 the primary current when the secondary circuit is open. 



Hysteresis LOSS. It is known that when iron is sub- 

 jected to a complete cycle of magnetic changes a certain amount 

 of energy is wasted due to hysteresis. The exact amount of 

 energy thus lost per cycle depends upon the quality of the iron 

 and the maximum induction in it (see Chap. X., Table II.). 



If, further, the cycle is such that the magnetizing force varies 

 continuously from zero to a positive maximum, back again through 

 zero to an equal negative maximum, and finally to zero again, the 

 energy lost per cycle due to hysteresis may be represented by the 

 formula 



H = kB 1 '* to rc (Steinmetz's law) 



where If is the energy lost, and k is a constant depending upon the 

 quality of the iron, and B is the maximum value of the induction. 



It should here be mentioned that Steinmetz's formula holds 

 good only for somewhat low induction densities, such as are prac- 

 tically met with in transformers. As the induction density in- 

 creases, the exponent of B diminishes. 



Eddy-euppent Loss. Another source of waste energy is 

 eddy euppents. 



The iron core being itself a conductor of electricity, secondary 

 currents are induced in it. These currents flow in the mass of the 

 iron in closed circuits, approximately in planes at right angles to 

 the magnetic flux. The result is that the core becomes heated, 

 and energy is dissipated. 



Lamination of Cope. To reduce these eddy-current 

 losses as much as possible the core is built up of thin sheets of 



