394 





/^ fi-yfz ohms. 



Osc; Resistance 



ipQ, 



A 







Gi-i/'=K^u,-teH 



PROCEEDINGS OF THE AMERICAN ACADEMY. 



latory impedance of the circuit is 

 Z = p + jlw ohms, or Zq /_^; where 

 Zo is the impedance in the resistance- 

 less condition of Figure 4. The total 

 resistance r of the circuit is repre- 

 sented by A A'. The initial vector 

 potential difference has an ampli- 

 tude ^^0 = IqZq volts. The total ini- 

 tial drop of potential resistance is 

 indicated by DV. The undamped 

 maximum cyclic power is indicated 

 at F, and the undamped cyclic energy 

 at IF. The F and W diagrams to 

 standard current phase are inverted 

 with respect to those of standard p. d. 

 8i6-y phase, because the undamped power 



lags behind the p. d. but leads the 

 undamped current. 



The diagrams in Figures 7 and 12 

 of the oscillating-current circuit cor- 

 respond to similar diagrams in con- 

 nection with the alternating-current 

 circuit.2 The U, I, F, and W dia- 

 grams are stationary vector-diagrams, 

 but they may be converted into ro- 

 ^33} >. . .. tating vector-diagrams. Thus /may 

 G be made a rotating vector-diagram 

 by mounting it on the point d as 

 center, and giving a positive angular 

 velocity w to the triangle, starting 

 vnth df in the —j direction. The 

 projection of df ow. the real axis, after 

 applying the damping-factor c"-'', will 



l-lbOJ 



t 



DiSsltxitLve Enernu 



JooUs. 



Figure 12. Stationary vector-dia- 

 grams of impedance, vector potential 

 difference, maximum cyclic power and 

 energy in a simple o. c. circuit con- 

 taining resistance. Phase of current, 

 standard. 



' "Vector Power in Alternating-Current Circuits" by A. E. Kennelly. 

 Trans. American Inst. Elect. Engrs. June, 1910. Vol. 29. 



