File:Murray loop bridge.svg

English: Murray loop bridge for locating faults in underground cables. One end of the faulted cable is connected through a pair of resistors to the voltage source. Also a null detector is connected. The other end of the cable is shorted. The bridge is brought to balance by changing the values of R_B1 and R_B2, which is achieved when:

${\displaystyle {\frac {R_{x}}{R_{g}+R_{y}}}={\frac {R_{B1}}{R_{B2}}}}$

which is equivalent to:

${\displaystyle R_{x}=(R_{g}+R_{y})\cdot {\frac {R_{B1}}{R_{B2}}}}$

The value of resistance R_x is proportional the the length L_x, thus the location of the fault can be calculated:

${\displaystyle L_{x}=2\cdot L\cdot {\frac {R_{B1}}{R_{B2}}}}$

where L is the total lenght of the cable under test - a value proportional to R_g.