28 



ELEMENTS OF ELECTRICAL ENGINEERING. 



in sign, its actual direction will be opposite to the direction indi- 

 cated by the arrow. Let it be required to find the currents i v t' 2 , 



iy z* 4 , i & , and z' 6 in the respective branches 

 /, 2, 3, 4, 5 and <5, having given the re- 



sistances r v r 2 , r y 



and r of the 



respective branches, and the electro- 

 motive forces E and e. The direc- 

 tions of these given electromotive 

 forces are indicated by the short ar- 

 rows. This problem is to be solved 

 with the help of two distinct principles 

 as follows : 



(a) The algebraic sum of all the currents flowing towards a 

 branch point is equal to zero. (Kirchhorf.) 



(b) The algebraic sum of all the electromotive forces acting 

 around a closed circuit, or a mesh of a network of conductors, is 

 equal to the sum of the products ri around the mesh. (Kirch- 

 hofif.) 



Applying the first principle to the branch points, a y b, c, and 

 d, Fig. 13, in succession, with due consideration of algebraic 

 signs, we have the following four equations : 



o 



Consider any mesh, for example the one formed by the 

 branches I, 2 and 4, Fig. 13. The sum of the products ri taken 

 in a clock-wise direction around this mesh is equal to the sum of 

 all the electromotive forces acting in a clock-wise direction around 

 the mesh, a counter-clock-wise electromotive force being reckoned 

 as negative. Applying the second principle in this way to the 

 mesh formed by branches 1 , 2 and 4, we have : 



r r r = E v 



