---
title: "Self GMD of 4-strand conductor, 5 mm strands"
subject: "Power System Analysis I"
chapter: 4
key: "semester_4/power_system_analysis_i:self-gmd-four-strands-5mm"
source: https://www.bctengineer.com/q/semester_4/power_system_analysis_i/self-gmd-four-strands-5mm
site: BCT Engineering
---

# Self GMD of 4-strand conductor, 5 mm strands

Power System Analysis I · Chapter 4: Line Parameter Calculations

- Asked in: 2069 Bhadra, 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/self-gmd-four-strands-5mm
- Whole chapter: https://www.bctengineer.com/md/semester_4/power_system_analysis_i/chapter-4

## Question

Compute the self GMD for inductance calculation for the stranded conductor as shown below. Radius of each strand is 5 mm. [Figure: four identical touching strands arranged in a 2 × 2 square.]

## Short answer

Self GMD is 8.61 mm (0.861 cm).

## Answer

The 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
     (1)   (2)
     (3)   (4)
  side of square = 2r, diagonal = 2(sqrt2)r
```

**Data:** $r = 5$ mm, $2r = 10$ mm, $r' = 0.7788 \times 5 = 3.894$ mm.

#### Distances

| Pair | Distance |
|---|---|
| 1-2, 1-3, 2-4, 3-4 (sides) | $2r = 10$ mm |
| 1-4, 2-3 (diagonals) | $2\sqrt2 r = 14.142$ mm |

Each strand: two distances of $2r$ and one of $2\sqrt2 r$.

#### Self-GMD

$$
\begin{aligned}
D_s &= \left[(r')^4 \times (2r)^8 \times (2\sqrt2 r)^4\right]^{1/16} \\
&= \left[r' \times (2r)^2 \times 2\sqrt2 r\right]^{1/4} \\
&= \left[3.894 \times 10^2 \times 14.142\right]^{1/4} \\
&= (5507.0)^{1/4} = 8.614\ \text{mm}
\end{aligned}
$$

In terms of $r$: $D_s = 1.7229r$.

**Answer:** self-GMD $= 8.61$ mm $= 0.861$ cm.

## Check yourself

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

1. In a 2 x 2 touching-strand square, the diagonal distance is:
   A. 2*sqrt2 r
   B. 2r
   C. 4r
   D. sqrt2 r
   Answer: A. Side = 2r, so diagonal = 2r x sqrt2. (Key point: Square geometry)

2. Each strand sees which set of distances?
   A. Three at 2r
   B. Two at 2r and one at 2*sqrt2 r (plus its own r')
   C. One at 2r and two at 2*sqrt2 r
   D. Two at 2*sqrt2 r only
   Answer: B. Two adjacent neighbours at side distance and one diagonal neighbour. (Key point: Distances per strand)

3. What value of self-GMD results for r = 5 mm?
   A. About 3.89 mm
   B. About 10 mm
   C. About 8.61 mm (1.723r)
   D. About 14.1 mm
   Answer: C. D_s = [r' (2r)^2 (2 sqrt2 r)]^(1/4) = 1.7229r = 8.61 mm. (Key point: Result)

## Related in Power System Analysis I

- [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 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
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- [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×
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