Equivalent Resistance 8fc. of Parallel Circuits. 273 

 in advance of the impressed E.M.F. in this particular case, in 

 which r-^— is taken as greater than L«. 



In fig. 5, OB A, OCA, OD A are the E.M.F. triangles 

 for the several branches of a divided circuit (see fig. 4), with 



Fig. 5. 



sin impressed E.M.F. equal to OA. The main current, I m , is 

 the vector sum of the currents I 1? I 2 , I 3 in the branches. By 

 taking the projections of the currents upon the line OA, and 

 then upon a line perpendicular to OA, we obtain the equations 



I wt cos^ = I 1 cos^ 1 + I 2 cos # 2 + - • . = ^1 cos 0. . . (1) 

 I m sin0=I 1 sin0 1 +I,sin0 2 + ...=2lBin0. . . (2) 

 In the right triangle F A, 



E 



L. = 



\A 2+ (rfc- L, "J 



(3) 



