---
title: "Murray loop test for cable faults"
subject: "Power System Analysis I"
chapter: 2
key: "semester_4/power_system_analysis_i:murray-loop-test"
source: https://www.bctengineer.com/q/semester_4/power_system_analysis_i/murray-loop-test
site: BCT Engineering
---

# Murray loop test for cable faults

Power System Analysis I · Chapter 2: Overhead and Underground Transmission

- Asked in: 2078 Chaitra, 6 marks; 2076 Bhadra, 4 marks; 2072 Magh, 4 marks; 2071 Magh, 6 marks (asked 4 times)
- Video: [How to Locate Cable Faults with the Murray Loop Test](https://www.youtube.com/watch?v=IbeTNogACYQ) — The Learning Curve
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/power_system_analysis_i/murray-loop-test
- Whole chapter: https://www.bctengineer.com/md/semester_4/power_system_analysis_i/chapter-2

## Question

Explain Murray Loop test for locating short circuit fault in underground cable.

## Short answer

The Murray loop test locates a cable fault by forming a Wheatstone bridge with a sound core and the faulty core linked at the far end. At balance, fault distance from test end is x = [Q/(P+Q)] × 2l, where l is cable length. Fault resistance in the battery arm does not affect the result.

## Answer

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.

```text
     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.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. The Murray loop test uses
   A. A capacitance bridge
   B. Pulse reflection
   C. A Wheatstone bridge with a sound core
   D. Acoustic thumper
   Answer: C. The loop forms a bridge. (Key point: Murray principle)

2. The fault distance x from test end is
   A. Q/(P+Q) x 2l
   B. P/(P+Q) x l
   C. (P+Q)/Q x 2l
   D. Q/P x l
   Answer: A. x = Q/(P+Q) x 2l. (Key point: Fault distance)

3. With P=3, Q=1 and 500 m cable, x is
   A. 750 m
   B. 500 m
   C. 125 m
   D. 250 m
   Answer: D. 1/4 x 1000 = 250 m. (Key point: Example)

4. Fault resistance
   A. Changes balance directly
   B. Doubles x
   C. Is in the battery arm, so does not affect balance
   D. Must be zero
   Answer: C. It affects only sensitivity. (Key point: Fault resistance)

## Close variants set in other exams

- [Murray loop test for open and short circuit faults](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Amurray-loop-open-short-circuit) — Power System Analysis I, chapter 2, asked 5×

## Related in Power System Analysis I

- [Cable fault location techniques and Murray loop](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Acable-fault-techniques-murray) — Power System Analysis I, chapter 2
- [Varley loop test for cable faults](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Avarley-loop-test) — Power System Analysis I, chapter 2
- [Locating faults in underground cables](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Acable-fault-location-method) — Power System Analysis I, chapter 2, asked 3×
- [Locating phase-to-phase cable fault](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Aphase-to-phase-cable-fault) — Power System Analysis I, chapter 2