---
title: "Locating phase-to-phase cable fault"
subject: "Power System Analysis I"
chapter: 2
key: "semester_4/power_system_analysis_i:phase-to-phase-cable-fault"
source: https://www.bctengineer.com/q/semester_4/power_system_analysis_i/phase-to-phase-cable-fault
site: BCT Engineering
---

# Locating phase-to-phase cable fault

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

- Asked in: 2073 Bhadra, 5 marks
- Video: [how to find underground cable fault location - electrical interview question](https://www.youtube.com/watch?v=SyPrTj93opg) — Electrical Dost
- 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/phase-to-phase-cable-fault
- Whole chapter: https://www.bctengineer.com/md/semester_4/power_system_analysis_i/chapter-2

## Question

Explain one of the techniques to locate phase to phase fault on underground power cable.

## Short answer

Use the Murray loop test with one sound core. Link the sound core and one faulty core at the far end, connect a Wheatstone bridge with ratio arms P and Q, and apply the battery between P–Q junction and the other faulty core. At balance, fault distance from test end is x = (Q/(P+Q)) × 2L.

## Answer

A phase-to-phase (short-circuit) fault between two cores of a multi-core cable can be located by the **Murray loop test**, a Wheatstone bridge method that needs one sound core.

#### Connections
```text
   +--------------(G)--------------+
   |                               |
   c ---/\/\------+------/\/\----- a
   |     P        |        Q       |
   |           battery             |
   |              |                |
   |           core 2              |
 sound core 3                faulty core 1
   |                               x  <- fault (core 1 to core 2)
   |                               |
   +====== link at far end ========+
```

1. Core 1 and core 2 are shorted together at the fault. Core 3 is sound.
2. At the far end, link core 1 to sound core 3 to form a loop.
3. Connect ratio arm $P$ to the test end c of core 3 and ratio arm $Q$ to the test end a of core 1, and connect the galvanometer across a and c.
4. Connect the battery between the junction of $P$ and $Q$ and core 2 (the other shorted core). Core 2 takes the place of earth in the earth-fault test. Current then flows through the fault into the loop.
5. Adjust $P$ and $Q$ for zero galvanometer deflection.

#### Calculation
Let $R_x$ be the resistance of core 1 from the test end to the fault, and $R_L$ the whole loop resistance (core 1 + core 3). The arm next to $P$ is $R_L - R_x$ and the arm next to $Q$ is $R_x$. At balance:

$$
\frac{P}{Q} = \frac{R_L - R_x}{R_x}
\;\Rightarrow\; R_x = \frac{Q}{P+Q}R_L
$$

For cores of equal size and cable length $L$:

$$
x = \frac{Q}{P+Q}\times 2L
$$

#### Example
A 3 km cable balances at $P = 2.5\ \Omega$ and $Q = 1\ \Omega$:

$$
x = \frac{1}{3.5}\times 6 = 1.714\ \text{km}
$$

The fault resistance lies in the battery circuit, so it does not affect the balance. The Varley loop test can be used in the same way when fine adjustment by a series resistor is preferred.

## Check yourself

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

1. Which test locates a phase-to-phase fault described here?
   A. Megger test only
   B. Pulse-echo test only
   C. Murray loop test
   D. Capacitance comparison
   Answer: C. A short between two cores is located using the resistance Murray loop. (Key point: Technique)

2. Where is the battery connected?
   A. To earth
   B. Between the P-Q junction and the other shorted core (core 2), which replaces earth
   C. Across the sound core
   D. Across the galvanometer
   Answer: B. Core 2 provides the return path through the fault. (Key point: Role of other shorted core)

3. What is done at the far end?
   A. Cores 1 and 2 are linked
   B. All three cores are earthed
   C. Faulty core 1 is linked to sound core 3
   D. The cores are left open
   Answer: C. The loop of faulty and sound cores is needed for the bridge. (Key point: Loop connection)

4. Why does the fault resistance not affect the balance?
   A. It is zero
   B. It is in the galvanometer arm
   C. It is much larger than the loop
   D. It lies in the battery circuit
   Answer: D. Only battery current flows through it, so the bridge null is unaffected. (Key point: Fault resistance)

## 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
- [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×
- [Murray loop test for cable faults](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Amurray-loop-test) — Power System Analysis I, chapter 2, asked 5×
- [What a power cable is](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Apower-cable-brief) — 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
- [Underground cables vs overhead lines](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Acables-vs-overhead-lines) — Power System Analysis I, chapter 2

## Related in other subjects

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- [Splicing techniques of HV cable](https://www.bctengineer.com/question.md?key=semester_6%2Findustrial_power_distribution_and_illumination%3Ahv-cable-splicing) — Industrial Power Distribution and Illumination, chapter 3
- [Single-phase Cu cable for three loads](https://www.bctengineer.com/question.md?key=semester_6%2Findustrial_power_distribution_and_illumination%3Asingle-phase-cable-three-loads) — Industrial Power Distribution and Illumination, chapter 5
- [Aluminium cable for 25 kW single-phase load](https://www.bctengineer.com/question.md?key=semester_6%2Findustrial_power_distribution_and_illumination%3Aaluminium-cable-25kw) — Industrial Power Distribution and Illumination, chapter 5