---
title: "Self GMD of 7-strand conductor, 4 mm strands"
subject: "Power System Analysis I"
chapter: 4
key: "semester_4/power_system_analysis_i:self-gmd-seven-strands-4mm"
source: https://www.bctengineer.com/q/semester_4/power_system_analysis_i/self-gmd-seven-strands-4mm
site: BCT Engineering
---

# Self GMD of 7-strand conductor, 4 mm strands

Power System Analysis I · Chapter 4: Line Parameter Calculations

- Asked in: 2068 Magh, 5 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-seven-strands-4mm
- Whole chapter: https://www.bctengineer.com/md/semester_4/power_system_analysis_i/chapter-4

## Question

Compute the self-GMD for the following conductor. Radius of each strand is 4 mm. [Figure: seven identical strands: one central strand surrounded by six touching strands.]

## Short answer

Self-GMD (for inductance) = 2.1767 × 4 mm = 8.71 mm (0.871 cm). Computed from 49 distance terms with strand r'=0.7788×4 mm.

## Answer

The self-GMD for inductance of a 7-strand conductor (1 central + 6 around) is found from all $7^2 = 49$ distances, with self-distance $r' = 0.7788r$.

```text
        (2)   (3)
     (7)   (1)   (4)
        (6)   (5)
  1 = centre, outer ring radius 2r
```

**Data:** $r = 4$ mm, $r' = 0.7788 \times 4 = 3.115$ mm.

#### Distances

| Pair type | Distance | Ordered pairs |
|---|---|---|
| Self | $r'$ | 7 |
| Centre to outer | $2r$ | 12 |
| Adjacent outers | $2r$ | 12 |
| Outer to next-but-one | $2\sqrt3 r$ | 12 |
| Outer to opposite | $4r$ | 6 |

#### Self-GMD

$$
\begin{aligned}
D_s &= \left[(0.7788r)^7 (2r)^{24} (2\sqrt3 r)^{12} (4r)^6\right]^{1/49} \\
&= 2.1767\,r = 2.1767 \times 4 = 8.707\ \text{mm}
\end{aligned}
$$

For capacitance (self-distance $r$): $D_s = 2.2558r = 9.023$ mm.

**Answer:** self-GMD $= 8.71$ mm $= 0.871$ cm (for inductance).

## Check yourself

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

1. For 7 strands the self-GMD is the root of what order?
   A. 49th root (7^2)
   B. 7th root
   C. 14th root
   D. 42nd root
   Answer: A. 7^2 = 49 terms. (Key point: Terms)

2. In the 7-strand arrangement, what is the distance from an outer strand to the next-but-one outer strand?
   A. 2r
   B. 2*sqrt3 r
   C. 4r
   D. 3r
   Answer: B. Outer strands form a hexagon of side 2r; skip-one distance is 2 sqrt3 r. (Key point: Distances)

3. Opposite outer strands are separated by:
   A. 2r
   B. 2 sqrt3 r
   C. 4r
   D. 6r
   Answer: C. Opposite strands are on a diameter of the outer ring of radius 2r. (Key point: Opposite strands)

## Related in Power System Analysis I

- [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 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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