26 



ELEMENTS OF ELECTRICAL ENGINEERING. 



arranged in series as shown in Fig. 1 2. The electromotive force 

 of such an arrangement is equal to nE, where n is the number of 

 cells in series, and E is the electromotive force of a single cell. 

 The combined resistance of a number of resistances connected 

 in series is equal to their sum. 



HHHH>- 

 -MHH- 



Fig. 11. 



Fig. 12. 



The combined resistance of a number of resistances connected 

 in parallel is equal to the reciprocal of the sum of the reciprocals 

 of the individual resistances. 



19. To determine the current in each of two branches of a cir- 

 cuit when the total current and the resistance of each branch are 

 given. The solution of this problem depends upon two princi- 

 ples as follows : 



(a) The current in the undivided part of a circuit is equal to 

 the sum of the currents in the respective branches into which the 

 circuit divides. (KirchhorT's law.) 



(&) Let A and B be the two points at which two or more 

 branches of a circuit unite. The product of the resistance R of 

 any one of the branches into the current / flowing in that branch 

 is equal to the electromotive force between the branch points A 

 and B. Therefore the product RI has the same value for every 

 branch terminating in the points A and B. 



In the case of two branches we have from (a) 



and from (&) we have 



