126 



SINGLE-PHASE CURRENTS. 





and the locus of D (the current locus) will be a semicircle* with 

 diameter E-+-X, at right angles to E. The theoretical semi- 

 circles are shown by. dotted lines in Fig. 2. 



12. If, however, the power consumption in the reactance coil 

 is more than 7? 2 / 2 ,the locus of C will be flattened so as to lie inside 

 of a semicircle. This would be the case in a reactance with iron, 

 and is likely to be the case even in a coil without iron on account 

 .of eddy currents in the copper. Eddy currents have the effect of 

 increasing R 2 above the value determined by direct currents, so 



that RJ, in Fig. 2, should be 

 increased from BC to BF. 

 The locus of C is affected 

 by energy losses, but not by 

 wave form. 



13. The current locus 

 (the locus of D) will not 

 be affected by energy losses, 

 but will be flattened if the 

 current is not a sine wave 

 due to an impressed electro- 

 motive force which is not a 

 sine wave, or to distortion 

 caused by hysteresis. Wlren 

 the current is not a sine wave, the apparent value of X varies 

 somewhat with R ; since X is not constant, the locus of D is not 

 an exact semicircle. 



14. Constant Current Operation. It is seen that when 6 is 

 large, i. e., when X -f- R is large, the current remains nearly con- 

 stant, irrespective of any variation of R and 0; between 6 = 70 

 and = 90 the value of the current varies only 6 per cent. Thi* 

 is the condition for constant current operation and is obtained 



*(na). If this is a semi-circle, /=(-f-X) sin 6 and XI = E sin 0; 

 this accords with facts (see Fig. 2, Exp. 4-A) and the proposition is 

 accordingly proved. 



Resistance 



FIG. 3. Values of 7 and for different 

 values of R. 



