Murray loop test for cable faults

The Murray loop test is a bridge (Wheatstone principle) method to locate a short-circuit or earth fault in an underground cable. It needs one sound core running alongside the faulty core.

Connections

• At the far end, the faulty core and a sound core are joined by a low-resistance link, forming a loop.
• At the test end, the sound-core end (D) is connected to ratio arm $P$ and the faulty-core end (B) to ratio arm $Q$ (both variable resistors); a galvanometer G is connected across D and B.
• A battery is connected between the junction A of $P$ and $Q$ and earth (for an earth fault), or the other core in contact (for a short-circuit fault). The fault point completes the circuit.

     A o-----[Battery]------+  Earth (sheath)
       |                    :
   +---+---+                :  fault resistance
   P       Q                :
   |       |                :
 D o--(G)--o B              :
   |       |                :
   |       +== faulty core =X========+
   |        <------ x ----->         |
   +========= sound core ============+
 Test end                 Far end (cores joined)

Theory

The loop forms a Wheatstone bridge: $P$, $Q$, $R_x$ (faulty core from test end to fault) and $R$ (sound core plus faulty core from far end back to fault). At balance (G reads zero):

$$\frac{P}{Q} = \frac{R}{R_x} \quad\Rightarrow\quad \frac{P+Q}{Q} = \frac{R+R_x}{R_x}$$ $$R_x = \frac{Q}{P+Q}(R+R_x)$$

$(R+R_x)$ is the total loop resistance $= 2l\times r$ (r per unit length). If both cores have the same cross-section, resistance is proportional to length:

$$x = \frac{Q}{P+Q}\times2l$$

where $x$ is the distance of the fault from the test end and $l$ the cable length.

Example

For a 500 m cable balanced at $P = 3\ \Omega$, $Q = 1\ \Omega$: $x = \frac{1}{4}\times1000 = 250$ m from the test end.

Points to note

• Fault resistance appears in the battery arm, so it does not affect the balance (only sensitivity).
• Needs a sound core of known length; works best for low-resistance faults.
• If the cores differ in area, convert to equivalent lengths before using the formula.