352, 353] 



Currents in a Network 



307 



353. 



II. Telegraph wire with faults. 

 As a more complex example of the flow of electricity in a system 



of linear conductors, we may examine the case of a telegraph wire, in which 

 there are a number of connexions through which the current can leak to 

 earth. Such leaks are technically known as " faults." 



F 3 



FIG. 100. 



Let AB be the wire, and let F l} F 2 , ...F n _ l} F n be the points on it at 

 which faults occur, the resistances through these faults being R lt R Zy ... 

 Rn-!, R n , and the resistances of the sections AF l} F^F Z , ...Fn^Fn and F n B 

 being r lt r a , ... r n , r n+l . Let the end B be supposed put to earth, and let the 

 current be supposed to be generated by a battery of which one terminal is 

 connected to A while the other end is to earth. 



The equivalent resistance of the whole network of conductors from A to 

 earth can be found in a very simple way. Current arriving at F n from the 

 section F n _^F n passes to earth through two conductors arranged in parallel, 

 of which the resistances are R n and r n+1 . Hence the resistance from F n to 

 earth is 



and the resistance from 



n r n+l 



n-i to earth, through F 



s 



(279). 



Current reaching F nr . 1 can, however, pass to earth by two paths, either 

 through the fault at F n _ lt or past F n . These paths may be regarded as 

 arranged in parallel, their resistances being R n -i and expression (279) re- 

 spectively. Thus the equivalent resistance from F n ^ is 



1 



1 1 



-- + 



or, written as a continued fraction, 



1 1 



202 



