Admittance and Impedance Loci. 303 



fig. 1 ; or they may be represented by different circles, as in 

 fig. 2. In the latter case, _„- > 



p x p 2 = 0Q X . 0G 2 = a constant. 



As the origin approaches the circle which represents the 

 locus of p p the centre of the reciprocal circle becomes more 

 distant and its radius becomes greater. When the origin 

 is a point in the circumference of the first circle, the centre 

 of the reciprocal circle is at an infinite distance ; that is, the 

 reciprocal locus is a straight line. 



Let us apply these principles to the transformer diagrams. 

 The locus of the primary impedance, as some particular quan- 

 tity is varied, is' a portion of a circle. For example, this may 

 be shown to be the case when the secondary resistance is 

 varied. Since the admittance of the primary is the reciprocal 

 of its impedance, the admittance may be represented by the 

 vector p 2 in the above construction, if the impedance is repre- 

 sented by p v These loci may be drawn to scale for actual 

 values. In a constant current transformer the primary elec- 

 tromotive force varies directly as the primary impedance. 

 In a constant potential transformer the primary current varies- 

 directly as the primary admittance. But the admittance is 

 the reciprocal of the impedance ; hence if we have an arc of a 

 circle for the locus of the primary electromotive force when 

 the primary current is maintained constant, we may employ 

 the above method to obtain the arc of a circle which will be 

 the locus for the primary current when the transformer is 

 supplied with a constant electromotive force. The converse 

 operation may likewise be performed. 



In fig. 3 let the circle C x represent the locus of the primary 

 electromotive force E 2 during some particular change of con- 

 dition, the primary current meanwhile being maintained 

 constant and in the direction OA. The difference in phase 

 between the current and electromotive force is the angle $ 1# 

 The locus of the primary current under the same change of 

 conditions, if the primary electromotive force is maintained 

 constant, is the dotted circle C 2 , which is reciprocal to G x . 

 If the constant electromotive force is drawn in the direction 

 OA, the locus of the primary current is the circle C 2 ', drawn 

 so that the angles AOCi and AOC 2 ' are equal. 



An application of the method of reciprocal vectors is shown 

 in fig. 4. Positive rotation is counter-clockwise. The semi- 

 circle JKN represents the locus of the primary electromotive 

 force of a transformer, when the primary current is constant 



