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

# Murray loop test for open and short circuit faults

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

- Asked in: 2080 Chaitra, 6 marks
- Video: [Underground Cable Faults Explained | Murray & Varley Loop Test with Numerical Insight](https://www.youtube.com/watch?v=DQ9kt5wLWQ0) — Electrology
- 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-open-short-circuit
- Whole chapter: https://www.bctengineer.com/md/semester_4/power_system_analysis_i/chapter-2

## Question

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

## Short answer

For short-circuit faults, the Murray loop test uses a Wheatstone bridge with a sound core linked at the far end. Distance from test end is x = (Q/(P+Q)) * 2L. For open-circuit faults, capacitance comparison gives x = L * (Q/P) with P connected to the broken core.

## Answer

The Murray loop test is a bridge method for locating faults in underground cables. For a short-circuit or earth fault it compares the resistance of the faulty core with the resistance of a sound core (Wheatstone bridge). For an open-circuit fault it compares capacitances.

#### Murray loop test (short-circuit or earth fault)
This is a Wheatstone bridge method. It needs one sound core running alongside the faulty core.

```text
   +--------------(G)--------------+
   |                               |
   B ---/\/\------+------/\/\----- A
   |     P        |        Q       |
   |           battery             |
   |              |                |
   |            earth              |
 sound core                   faulty core
   |                               x  <- fault to earth
   |                               |
   +====== loop at far end ========+
```

1. At the far end, connect the faulty core to the sound core with a low-resistance link, so the two cores form a loop.
2. Connect ratio arm $P$ (a variable resistor) to the test end B of the sound core and ratio arm $Q$ to the test end A of the faulty core, and connect the galvanometer across A and B. Connect the battery between the junction of $P$ and $Q$ and earth (for an earth fault). For a short circuit between two cores, connect the battery to the other shorted core instead of earth.
3. Adjust $P$ and $Q$ until the galvanometer reads zero.

Let $R_x$ be the resistance of the faulty core from the test end to the fault, and $R_L$ the resistance of the whole loop. The arm next to $P$ is the rest of the loop, $R_L - R_x$, and the arm next to $Q$ is $R_x$. At balance:

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

If both cores have the same cross-section and the cable length is $L$, resistance is proportional to length:

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

Here $x$ is the distance from the test end to the fault. The fault resistance carries only battery current, so it does not affect the balance.

#### Murray loop test for an open-circuit (broken-conductor) fault
A broken core gives no resistance loop, so capacitance is compared instead (the Murray capacitance loop). The capacitance of a core to the sheath is proportional to its length.

1. At the far end, leave the broken core and the sound core open (insulated).
2. Connect ratio arm $P$ to the broken core and ratio arm $Q$ to the sound core. Connect an AC source (or a battery with a key and a ballistic galvanometer) between the junction of $P$ and $Q$ and the sheath, and connect a detector between the two cores at the test end.
3. Adjust $P$ and $Q$ for a null. The arm impedances are $1/\omega C_x$ (broken core up to the break, length $x$) and $1/\omega C_L$ (sound core, full length $L$). At balance:

$$
\frac{P}{Q} = \frac{1/\omega C_x}{1/\omega C_L} = \frac{C_L}{C_x}
\;\Rightarrow\; x = L\,\frac{C_x}{C_L} = L\,\frac{Q}{P}
$$

($P$ is the arm joined to the broken core.)

#### Points to note
- The method needs at least one sound core of the same size.
- It is accurate when the fault resistance is low enough for a sensitive galvanometer reading.
- Fault-to-earth resistance does not affect the result, because it lies in the battery circuit.

## Check yourself

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

1. What does the Murray loop test compare to locate an earth or short-circuit fault?
   A. The capacitance of the two cores
   B. The resistance of the faulty core with that of a sound core, in a Wheatstone bridge
   C. The inductance of the faulty core
   D. The travel time of a pulse
   Answer: B. The resistive Murray loop is a Wheatstone bridge using the loop of faulty and sound cores. (Key point: Principle for short circuit)

2. What is done at the far end of the cable for the resistance test?
   A. Both cores are left open
   B. Both cores are earthed separately
   C. The faulty and sound cores are joined by a low-resistance link to form a loop
   D. The sound core is disconnected
   Answer: C. The link forms a loop through the fault point so the bridge can measure. (Key point: Far-end connection)

3. If P and Q are the ratio arms at balance and cable length is L, what is the fault distance x from the test end?
   A. x = P/(P+Q) x 2L
   B. x = Q/P x L
   C. x = (P+Q)/Q x L
   D. x = Q/(P+Q) x 2L
   Answer: D. From P/Q = (R_L - Rx)/Rx, Rx = Q R_L/(P+Q), and the loop length is 2L. (Key point: Location formula)

4. How is an open (broken conductor) fault located?
   A. By comparing capacitances: x = L Cx/CL
   B. By comparing resistances in the same loop as for a short circuit
   C. By measuring insulation resistance only
   D. By the fault resistance value
   Answer: A. A break gives no resistance loop; capacitance to the sheath is proportional to length, so capacitances are compared. (Key point: Open-circuit fault)

## Close variants set in other exams

- [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×

## 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

## Related in other subjects

- [Two-conductor open circuit fault](https://www.bctengineer.com/question.md?key=semester_5%2Fpower_system_analysis_ii%3Aopen-conductor-fault-series) — Power System Analysis II, chapter 5