4-A] 



SERIES AND PARALLEL CIRCUITS. 



119 



The main current / is laid off, in Fig. n, as the diagonal of a 

 parallelogram with sides equal to the branch currents 7 t and 7 2 . 

 The electromotive force E is laid off in the direction of I lf since 



Adjusting 

 Resistance 



FIG. 10. 



Resistance and coil in parallel. 



the current and electromotive force in the non-inductive branch 

 are in phase. E is the common terminal electromotive force and 

 is the same for both branches. 



For the inductive branch, the electromotive force triangle OCA 

 is constructed, as in (b). For this branch, the power electro- 

 motive force is OC, in phase with 7 2 ; the wattless electromotive 

 force is CA in quadrature with 7 2 . Fig. 1 1 is seen to be the same 

 as Figs. 5 and 7, drawn with a common E and combined. In 

 Fig. 9, these figures were combined with a common 7. 



52. The right triangle OC'A is the electromotive force tri- 

 angle for an equivalent* single circuit, R'L\ which could be sub- 

 stituted for the two parallel circuits. Since OC' = R'I, and 



is the vector sum of the admittance of the separate branches. In parallel 

 circuit's we may add as vectors either currents or admittances; while in 

 series circuits we may add as vectors either electromotive forces or im- 

 pedances, .19 and 20. 



* (52a). For a more complete discussion of equivalent resistance and 

 inductance, see Bedell and Crehore's Alternating Currents, pp. 238-41. 

 Both R' and L' depend upon frequency and are not constants of the 

 circuits; the equivalent resistance of parallel circuits is not the same for 

 alternating as for direct current. 



