48 



ALTERNATING CURRENTS 



25. Polygon of Currents. Obviously, if the resistances, im- 

 pedances, etc. are in parallel, the voltage is the same for each 

 branch of the circuit, but the respective currents may differ. 

 Therefore, the polygon is composed of currents rather than of 

 voltages. Figure 45 (a) shows a circuit consisting of resistance, 

 inductive impedance and capacitance all in parallel. Assume 

 that the condenser current is in quadrature with its voltage. 

 Figure 45 (6) then represents the polygon of currents. The 

 voltage E, being common, is laid off horizontal. The current I R 

 is laid off in phase with E and the current I c leads E by 90. 



(a) 



FIG. 45. Parallel circuit, consisting of resistance, inductive impedance and 

 capacitance all in parallel, with vector diagram. 



These two are combined to obtain I'. From the outer end of I', 

 I z is swung to meet / which is swung from 0. This completes 

 the polygon, which is similar to those shown in Figs. 43 and 44, 

 except that the vectors are currents instead of voltages. 



26. Energy and Quadrature Currents. Figure 46 shows the 

 vector diagram for a load connected across alternating-current 

 mains. This load is typical of most commercial loads, except 

 incandescent lamps. It takes a current I, lagging the voltage E 

 by 6 degrees. The current I may be resolved into two com- 

 ponents, ii in phase with the voltage and t' 2 in quadrature with 

 the voltage. Obviously I is the vector sum of i\ and i*. 



The power taken by the load is 



P = El cos 6 

 but / cos 6 = ii 



Therefore 



P = 



