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BELL SYSTEM TECHNICAL JOURNAL 



containing F can be determined by inspection to be: 



1 



jcoC 



2 r 



2 ./C0C2 



o+^ + tV + tV 



2 jwCi 7C0C2 



where / is the operator /—I and w is 27r times the testing frequency. 

 Likewise, the impedance presented to the bridge terminals by the 

 network containing R is: 



1 



Z^ = R + 



X .jo)C 



2 jcoC-i 



r 1 1 



2 jijoCi jcjoCi 



When the bridge is balanced, these two impedances are equal, so that: 



- + 



2 JC0C2 



r 1 1 



2 J^^\ J0JL2 



= R,+'^^+^"^ 



2 JC0C2 J 



This equation reduces to: 



r 1 1 



2 ./'^L-i JC0C2 



1 



+ T 



1 



2 JwCi 7a;C2 



r 1 1 



--j--^^^ h ^ 



2 JojCi j(joC2 



2^ 



For a testing current of relatively low frequency the capacitive 

 reactances, l/jcoCi and I/JC0C2, are much larger than the resistances, 

 r and F, and the above equation can be written as follows, the symbol 

 = being used to denote "is practically equal to": 



' + ' 



jooCi JWC2 



'^0 

 F 



1 2^ 



jwC: J Rq ' 

 C2 



Ci + C2 



Since d is proportional to the length D and (Ci + Co) to the total 



length, T: 



/Ro ^ D 

 I F ' T 



When the bridge is balanced to the value R,, with the distant ends 

 of wires 1, 2, 3 and 4 connected together, the amount of unbalance 

 between wires 1 and 2 is measured. Assuming that F is the only 

 unbalance present, and that the conductor resistances of wires 1 and 2 



