Admittance and Impedance Loci. 305 



The electromotive force has the position OJ on open circuit 

 and ON on short circuit. OH is the power electromotive 

 force on open circuit, and includes the effects of primary 

 resistance and the losses due to hysteresis and eddy currents ; 

 HJ is the electromotive force to overcome the primary self- 

 induction. These are in the direction of the primary current, 

 and at right angles to it, respectively. A line from J to K, 

 at right angles to the secondary current, would show the 

 reaction of the secondary upon the primary. It is to be 

 noted that the line NH represents the effects due to magnetic 

 leakage. It is desired to find the locus for the primary cur- 

 rent when the primary electromotive force has a constant 

 value, and is drawn in the direction OA. The angle of lag U 

 between the primary electromotive force and current on open 

 circuit, is JOH. Accordingly, with a constant electromotive 

 force in the direction OA, the open circuit current I is laid 

 off lagging behind the electromotive force at an angle of 

 AOj f = ± = JOH. The open circuit current I miy be laid 

 off to any convenient scale. To construct the locus for the 

 primary current proceed as follows : — Lay off the line OC 2 

 so that the angles AOOi and AOC 2 are equal. The point 2 

 is located so that OC 2 : OC 2 : : Of: Oj. The primary current 

 locus is then drawn as the arc of a circle with C 2 as a centre, 

 passing through/. 



The limits of the primary electromotive force locus are the 

 points J and N. The corresponding limits of the primary 

 current locus are the points f and n f . It will be noted that 

 these points correspond to the points j and n on the circle C 1? 

 which are reciprocal to the points J and N. 



In the absence of magnetic leakage the points N and H 

 coincide. The point n' would then lie in the line OA. The 

 deviation of the primary current locus from the line OA is 

 produced by magnetic leakage. 



An experimental curve showing the primary current locus 

 for a constant potential transformer, as affected by magnetic 

 leakage, is shown in fig. 5. 



The reciprocal relation between admittance and impedance 

 vectors gives a simple method for determining the conditions 

 for consonance and resonance in transformer circuits*. 



Figure 6 is given as a particular instance in illustration of 

 the statement given above that loci produced by the variation 

 of any one constant are usually arcs of circles. The primary 

 loci are always arcs of circles. The diagram shows the 

 changes due to a variation in the secondary self-induction. 



* " Resonance in Transformer Circuits," by Bedell and Crehore, ' The 

 Physical Review,' vol. ii. p. 442. 



Phil. Mag. S. 5. Vol. 42. No. 257. Oct. 1896. Z 



