---
title: "GMR of 6-strand triangular conductor"
subject: "Power System Analysis I"
chapter: 4
key: "semester_4/power_system_analysis_i:gmr-six-strand-triangle"
source: https://www.bctengineer.com/q/semester_4/power_system_analysis_i/gmr-six-strand-triangle
site: BCT Engineering
---

# GMR of 6-strand triangular conductor

Power System Analysis I · Chapter 4: Line Parameter Calculations

- Asked in: 2072 Asoj, 4 marks
- Video: [8.13 GATE 2022: How to Solve Geometric Mean Radius of Conductor Based Problems | GMR | Power Systems](https://www.youtube.com/watch?v=94uw1lX91gU) — Mritunjay Lectures
- 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-six-strand-triangle
- 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 1 cm. [Figure: six identical touching strands arranged in a triangle: one on top, two in the middle row, three in the bottom row.]

## Short answer

For the six-strand equilateral triangle configuration with strand radius 1 cm, the GMR for inductance is 2.102 cm (2.102 r).

## 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 each strand's self-distance taken as $r' = 0.7788r$.

```text
            (1)
         (2)   (3)
      (4)   (5)   (6)
   touching strands, centre spacing 2r
```

The centres lie on a triangular grid of side $2r$. With $r = 1$ cm, $2r = 2$ cm.

#### Distances (in cm)

| Pair | Distance |
|---|---|
| 1-2, 1-3, 2-3, 2-4, 2-5, 3-5, 3-6, 4-5, 5-6 | 2 (touching) |
| 1-5, 2-6, 3-4 | $2\sqrt3 = 3.464$ |
| 1-4, 1-6, 4-6 | 4 |

Check: 9 + 3 + 3 = 15 pairs $= \binom{6}{2}$.

Product of mutual distances (each pair counted twice):

$$
\left[2^9 \times 3.464^3 \times 4^3\right]^2
$$

#### GMR

$$
\begin{aligned}
D_s &= \left[(r')^6 \times \left(2^9 \times (2\sqrt3)^3 \times 4^3\right)^2\right]^{1/36} \\
r' &= 0.7788 \times 1 = 0.7788\ \text{cm} \\
D_s &= 2.1023\ \text{cm}
\end{aligned}
$$

**Answer:** GMR $= 2.102r = 2.102$ cm (for capacitance, with $r$ in place of $r'$, it would be 2.192 cm).

## Check yourself

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

1. For a 6-strand conductor, GMR is the root of what order of the product of all distances (including self)?
   A. 6th
   B. 12th
   C. 36th
   D. 15th
   Answer: C. n^2 = 36 terms, so the 36th root is used. (Key point: GMR definition)

2. How many distinct strand pairs are there, and how are they counted in the product?
   A. 15 pairs, each counted twice
   B. 6 pairs, each counted once
   C. 15 pairs, each counted once
   D. 36 pairs
   Answer: A. C(6,2) = 15 pairs, each appearing twice (ij and ji), plus 6 self terms r'. (Key point: Number of pairs)

3. On the triangular grid of touching strands (centre spacing 2r), what is the distance between strands 1 and 4 (top to bottom-left)?
   A. 2 cm
   B. 3.464 cm
   C. 4 cm
   D. 6 cm
   Answer: C. They are two rows apart along the edge of the triangle: 2 x 2r = 4 cm. (Key point: Strand distances)

4. The GMR for inductance is 2.102 cm. If capacitance were found, the value would be:
   A. Smaller, since r < r'
   B. Larger, 2.192 cm, since r replaces r'
   C. Same
   D. Zero
   Answer: B. Using r in place of r' increases the self-distance terms, giving 2.192 cm. (Key point: Inductance vs capacitance)

## Close variants set in other exams

- [GMR of 5-strand conductor, 0.5 cm strands](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Agmr-five-strands-0-5cm) — Power System Analysis I, chapter 4, asked 2×

## Related in Power System Analysis I

- [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
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- [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
- [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
- [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