---
title: "Inductance of 4-conductor bundle line, 6 m spacing"
subject: "Power System Analysis I"
chapter: 4
key: "semester_4/power_system_analysis_i:quad-bundle-200km-12mm-6m"
source: https://www.bctengineer.com/q/semester_4/power_system_analysis_i/quad-bundle-200km-12mm-6m
site: BCT Engineering
---

# Inductance of 4-conductor bundle line, 6 m spacing

Power System Analysis I · Chapter 4: Line Parameter Calculations

- Asked in: 2071 Magh, 5 marks
- Video: [Bundled Conductors for Inductance - Transmission Line Parameters - Power System Engineering 1](https://www.youtube.com/watch?v=qrT9DibTed0) — Ekeeda
- 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/quad-bundle-200km-12mm-6m
- Whole chapter: https://www.bctengineer.com/md/semester_4/power_system_analysis_i/chapter-4

## Question

Compute the inductance per phase for a 200 km line. Each sub-conductor is of 12 mm radius and configured as given below. [Figure: horizontal single-circuit line; each phase is a square bundle of four sub-conductors with 45 cm sides; centres of adjacent phases 6 m apart.]

## Short answer

Using Deq = 7.56 m and square bundle self-GMD = 0.1863 m, inductance = 0.741 mH/km, yielding 148 mH per phase for 200 km.

## Answer

Each phase is a square 4-conductor bundle. For inductance, its self-GMD is $D_s = (r' \cdot d \cdot d \cdot \sqrt2 d)^{1/4} = 1.09\sqrt[4]{r'd^3}$. The line is taken as transposed.

```text
   o o        o o        o o
   o o        o o        o o
    A    6 m   B    6 m   C
   d = 45 cm, r = 12 mm
```

**Data:** $r = 0.012$ m, $r' = 0.7788 \times 0.012 = 0.009346$ m, $d = 0.45$ m, $D = 6, 6, 12$ m, 200 km.

#### Mutual GMD

$$
D_m = \sqrt[3]{6 \times 6 \times 12} = 7.5595\ \text{m}
$$

#### Self GMD of bundle

$$
D_s = 1.09\sqrt[4]{0.009346 \times 0.45^3} = 0.18629\ \text{m}
$$

#### Inductance

$$
\begin{aligned}
L &= 2\times10^{-7}\ln\frac{7.5595}{0.18629} = 2\times10^{-7}\times3.7033 \\
&= 7.4065\times10^{-7}\ \text{H/m} = 0.7407\ \text{mH/km} \\
L_{200} &= 0.7407 \times 200 = 148.13\ \text{mH}
\end{aligned}
$$

**Answer:** $L = 148.1$ mH per phase for 200 km (0.7407 mH/km).

## Check yourself

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

1. For a square 4-conductor bundle with side d, the inductance self-GMD is:
   A. 1.09 x fourth root of (r' d^3)
   B. 1.09 x fourth root of (r d^3)
   C. 1.09 x cube root of (r' d^2)
   D. square root of (r' d)
   Answer: A. Distances are d, d and sqrt2*d, giving 1.09*(r'd^3)^(1/4) using r' for inductance. (Key point: Quad bundle self-GMD)

2. For phase spacings 6 m, 6 m and 12 m in a transposed line, D_m is:
   A. 6 m
   B. cube root of (6 x 6 x 12) = 7.56 m
   C. 9 m (mean)
   D. 12 m
   Answer: B. D_m is the geometric mean of the three spacings. (Key point: Mutual GMD)

3. The inductance per phase is:
   A. L = 2e-7 ln(D_s / D_m) H/m
   B. L = 4e-7 ln(D_m / D_s) H/m
   C. L = 2e-7 ln(D_m / D_s) H/m
   D. L = 2e-7 (D_m / D_s) H/m
   Answer: C. L = 2e-7 ln(GMD/GMR); here 2e-7 x ln(7.5595/0.18629) = 0.7407 mH/km. (Key point: Inductance formula)

## Close variants set in other exams

- [Inductance of twin-bundle line, 16 mm radius](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Atwin-bundle-150km-16mm) — Power System Analysis I, chapter 4, asked 3×

## Related in Power System Analysis I

- [Inductance and capacitance of 4-conductor bundle line](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Aquad-bundle-220kv-l-c) — Power System Analysis I, chapter 4
- [Inductance of 3-conductor bundled line, 6.1 m spacing](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Ainductance-three-subconductor-bundle-6-1m) — Power System Analysis I, chapter 4
- [400 kV quadruple bundle line, 20 m spacing](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Aquad-bundle-400kv-20m) — Power System Analysis I, chapter 4
- [L and C of triple-bundle line, D=8 m](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Atriple-bundle-18mm-45cm-8m) — Power System Analysis I, chapter 4, asked 2×
- [Inductance of composite-conductor single-phase line](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Asingle-phase-composite-conductors) — Power System Analysis I, chapter 4
- [Inductance of transposed double circuit, 0.9 cm radius](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Adouble-circuit-inductance-0-9cm) — Power System Analysis I, chapter 4

## Related in other subjects

- [Inductance matrix of 500 kV bundled line](https://www.bctengineer.com/question.md?key=semester_8%2Fhigh_voltage_engineering%3Ainductance-matrix-500kv) — High Voltage Engineering, chapter 5, asked 3×
- [Initial line design for 200 MW over 120 km](https://www.bctengineer.com/question.md?key=semester_8%2Ftransmission_and_distribution_system_design%3Aline-design-200mw-120km) — Transmission and Distribution System Design, chapter 2
- [Insulator discs per string, 180 MW over 200 km](https://www.bctengineer.com/question.md?key=semester_8%2Ftransmission_and_distribution_system_design%3Ainsulator-discs-180mw-200km) — Transmission and Distribution System Design, chapter 3
- [Minimum spacing for 30 mm conductors (m = 0.95)](https://www.bctengineer.com/question.md?key=semester_8%2Fhigh_voltage_engineering%3Acorona-spacing-30mm-0-95) — High Voltage Engineering, chapter 5, asked 4×