---
title: "GMR of 5-strand conductor, 0.5 cm strands"
subject: "Power System Analysis I"
chapter: 4
key: "semester_4/power_system_analysis_i:gmr-five-strands-0-5cm"
source: https://www.bctengineer.com/q/semester_4/power_system_analysis_i/gmr-five-strands-0-5cm
site: BCT Engineering
---

# GMR of 5-strand conductor, 0.5 cm strands

Power System Analysis I · Chapter 4: Line Parameter Calculations

- Asked in: 2070 Magh, 4 marks
- Video: [35.  GMR of a Conductor (Example 2)](https://www.youtube.com/watch?v=JhsEXR6jEJU) — Bright Engineers
- 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/gmr-five-strands-0-5cm
- Whole chapter: https://www.bctengineer.com/md/semester_4/power_system_analysis_i/chapter-4

## Question

Determine the GMR of the stranded conductor for calculation of inductance shown in figure below if the radius of each sub conductor is 0.5 cm. [Figure: five identical touching strands, two in the top row resting on three in the bottom row.]

## Short answer

GMR of the five-strand conductor is 0.956 cm.

## Answer

The GMR (self-GMD for inductance) of an $n$-strand conductor is the $n^2$-th root of the product of all inter-strand distances, with self-distance $r' = 0.7788r$.

```text
        (4)   (5)
     (1)   (2)   (3)
  touching strands, centre spacing 2r
```

**Data:** $r = 0.5$ cm, $2r = 1$ cm, $r' = 0.7788 \times 0.5 = 0.3894$ cm.

#### Distances (cm)

| Pair | Distance |
|---|---|
| 1-2, 2-3, 4-5, 1-4, 2-4, 2-5, 3-5 | $2r = 1$ |
| 1-3 | $4r = 2$ |
| 1-5, 3-4 | $2\sqrt3 r = 1.732$ |

Check: 7 + 1 + 2 = 10 pairs.

#### GMR

$$
\begin{aligned}
D_s &= \left[(r')^5 \times \left(1^7 \times 2 \times 1.732^2\right)^2\right]^{1/25} \\
&= \left[0.3894^5 \times 6^2\right]^{1/25} \\
&= 0.9557\ \text{cm}
\end{aligned}
$$

In terms of $r$: $D_s = 1.9114r$.

**Answer:** GMR $= 0.956$ cm.

## Check yourself

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

1. For a 5-strand conductor, the GMR is the root of what order?
   A. 5th root
   B. 10th root
   C. 25th root (5^2)
   D. 20th root
   Answer: C. There are 5^2 = 25 terms: 5 self terms r' and 20 ordered distances (10 pairs twice). (Key point: Number of terms)

2. How many distinct pairs of strands are there, and how many are at 2r?
   A. 10 pairs; 7 of them are at 2r
   B. 10 pairs; 5 at 2r
   C. 5 pairs; all at 2r
   D. 10 pairs; all at 2r
   Answer: A. Seven touching pairs are at 2r, one pair (1-3) at 4r, and two pairs (1-5, 3-4) at 2 sqrt3 r. (Key point: Pairs)

3. Which value is used for each strand's self term in inductance GMR?
   A. r = 0.5 cm
   B. r' = 0.7788r = 0.3894 cm
   C. 2r = 1 cm
   D. 0.5r
   Answer: B. Internal flux is accounted for by r' = r e^(-1/4) = 0.7788r. (Key point: Self distance)

## Close variants set in other exams

- [GMR of 6-strand triangular conductor](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Agmr-six-strand-triangle) — Power System Analysis I, chapter 4, asked 2×

## Related in Power System Analysis I

- [Self GMD of 5-strand conductor, 6 mm strands](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Aself-gmd-five-strands-6mm) — Power System Analysis I, chapter 4
- [GMR of 4-strand conductor in terms of r](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Agmr-four-strands-r) — Power System Analysis I, chapter 4
- [Self GMD of 4-strand conductor, 5 mm strands](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Aself-gmd-four-strands-5mm) — Power System Analysis I, chapter 4
- [Self GMD of 7-strand conductor, 4 mm strands](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Aself-gmd-seven-strands-4mm) — Power System Analysis I, chapter 4
- [Self GMD of 4-strand conductor in terms of r](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Aself-gmd-four-strands-r) — Power System Analysis I, chapter 4
- [Self GMD of 4-strand diamond conductor](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Aself-gmd-four-strands-diamond) — Power System Analysis I, chapter 4