BRIDGE METHODS FOR LOCATING RESISTANCE FAULTS 405 



The network of Fig. 17 can be replaced by the equivalent network 

 of Fig. 18. The values of the impedances //, k and p of Fig. 18 are: 



h='-^-\- 



jcoC: 



(r+ F) 



1 



+ 



1 



jcoCi jw{2Ci + Ci) 



+ r-\- F 



k = 



1 



1 



JC0(2C2 + Ci) 



+ 



1 



jcoCi Jw(2C2 + Ci) 



+ r + F 



^ = L+f + i?o + 



1 



jw(2C2 + Ci) 



(r + F) 



+ . 



1 



JCoCl 7C0(2C2 + Cl) 



+ r+ F 



AAA/WW^ 



k 

 M/WWV*- 



-WWVW 



P 



Fig. 18— Third equivalent circuit— long cable method for locating a series 

 resistance unbalance. 



It is evident from inspection of Fig. 18 that if h equals p the net- 

 work is balanced so that there is no current through the detector. 

 Equating the values of h and p, and solving gives: 



F 



+ 



jcoCi JCC{2C2 + Cl) 



-j- r -\- F 



X 



F 



If the capacitive reactances of the wires are very high compared to 

 the conductor resistances and the fault resistance, this last equation 

 can be reduced to: 



Ro 

 F 



a 



+ 



Cl + C2 ' F 



C2 



Ci4- C2 



X 



J' 



