The Murray loop test is
useful to find out location of underground fault for earth fault and short
circuit.

__Earth fault__

Figure shows the circuit diagram for location of
underground fault in the cable.

Let

AB = Sound cable ( without fault )

CD = Faulty cable

P = Variable resistance

Q = Variable resistance

B = Battery ( DC Voltage )

G = Galvanometer

l = length of each cable

2r = Total resistance of sound cable and faulty cable

K1 = Switch

d = Distance of faulty cable from point E = ?

- Let us consider that the earth fault occurs at a distance x from point E.
- The far end C of faulty cable is joined in series with the sound cable by low resistance link.
- There are two variable resistance P and Q connected to cable end A and E respectively.
- This forms PQXR Wheatstone bridge. The four arm of the Wheatstone bridge is

P = Variable resistance

Q = Variable resistance

X = Resistance of cable from point E to point D

R = Resistance of the cable from test end to point D

- The variable resistance P and Q are varied till the galvanometer shows zero deflection after switch K and K1 is closed. For balance conditions

PX = RQ

P / Q = R / X

( P + Q ) / Q = ( R + X ) / X

Here R + x = 2r

( P + Q ) / Q = 2r / X

X = 2r ( P + Q ) / Q …….. ( 1 )

If l is the length of each cable, the resistance per
meter length of cable = r / l

Distance of faulty cable from point E is

d = X / ( r / l ) ……… ( 2 )

From equation ( 1 ) and ( 2 )

d = { 2r ( P + Q ) / Q } / ( r / l )

d = { 2r ( P + Q ) l / r Q }

d = { 2( P + Q ) l /
Q }

d = 2l { ( P + Q )
/ Q }

d = { ( P + Q )
/ Q } × 2l

d = { ( P + Q )
/ Q } × Loop length

d = { ( P + Q )
/ Q } × Length of faulty cable
and length of sound cable

- The fault resistance does not affect the balancing of the bridge circuit.
- If the fault resistance is high, the sensitivity of the bridge is reduced.

__Short circuit fault__

- The Murray loop test is used to find out location of fault point in the underground cable for short circuit fault.
- Let the P, Q , R and X are the arms of the Wheatstone bridge.
- Note that the fault resistance is in the battery B circuit not in the bridge circuit.
- The balancing of bridge is done by vary the ratio arms P and Q till the galvanometer shows zero reading after closing the switch K and K1.

Let

P = Variable resistance

Q = Variable resistance

X = Resistance of cable from point E to point D

R = Resistance of the cable from test end to point D

PX = RQ

P / Q = R / X

( P + Q ) / Q = ( R + X ) / X

Here R + x = 2r

( P + Q ) / Q = 2r / X

X = 2r ( P + Q ) / Q

X = { ( P + Q )
/ Q } × Loop length

X = { ( P + Q )
/ Q } × Length of faulty cable
and length of sound cable

- The location of fault is find out by adjusting ratio arms P and Q.

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