4-A] 



SERIES AND PARALLEL CIRCUITS. 



109 



are shown by the electromotive force triangle, Fig. 2, and by the 

 following equations : 



E = 1EJ -f 



-f 



The impedance triangle, Fjg. 3, is derived by dividing the elec- 

 tromotive forces, Fig. 2, by /. 



19. It is seen that the electromotive forces XI and RI are 

 added as vectors. If, instead of a single X and R, there were 



Resistance 



O / D RI G 



FIG. 2. Electromotive force triangle. 



O R G 



FIG. 3. Impedance triangle. 



several, the same procedure could be followed: RJ, RJ, RJ, 

 etc., would be laid off in phase with / ; and XJ, X Z I, XJ, etc., in 

 quadrature with /. 



Electromotive forces in a series circuit are added as vectors. 

 Impedances, resistances and reactances in a series circuit are 

 added as vectors. 



20. The total drop in phase with / is 2RI ; the total drop in 

 quadrature with / is 2X1. Hence, for any series circuit, 



, and Z = 



The total resistance of a series circuit is seen to be the arith- 

 metical sum of the separate resistances; the total reactance is the 

 arithmetical sum of the separate reactances. 



For further discussion of series circuits, see 38-50; for par- 

 allel circuits see 5i~53- 



