---
title: "Single-phase line capacitance, 6 mm, 1.3 m"
subject: "Power System Analysis I"
chapter: 4
key: "semester_4/power_system_analysis_i:single-phase-capacitance-6mm-1-3m"
source: https://www.bctengineer.com/q/semester_4/power_system_analysis_i/single-phase-capacitance-6mm-1-3m
site: BCT Engineering
---

# Single-phase line capacitance, 6 mm, 1.3 m

Power System Analysis I · Chapter 4: Line Parameter Calculations

- Asked in: 2069 Bhadra, 6 marks
- Video: [Capacitance of Single Phase Line - Transmission Line Parameters - Power System Engineering 1](https://www.youtube.com/watch?v=RN9OmWwx9kk) — 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/single-phase-capacitance-6mm-1-3m
- Whole chapter: https://www.bctengineer.com/md/semester_4/power_system_analysis_i/chapter-4

## Question

For a single phase overhead line having both conductors of 6 mm, calculate the capacitance between the conductors and capacitance of each conductor to ground. The conductors are separated from each other by 1.3 m. Assume flat horizontal configuration and effect of earth is negligible.

## Short answer

Capacitance between conductors is 5.17 nF/km; each conductor to ground is 10.34 nF/km.

## Answer

For a single-phase line with ground effect neglected, the capacitance between the conductors is $C_{ab} = \pi\varepsilon_0/\ln(D/r)$, and the capacitance of each conductor to ground (neutral) is $C_n = 2C_{ab}$, since the neutral plane lies midway and $V_{an} = V_{ab}/2$.

"Conductors of 6 mm" is read as **radius 6 mm**.

```text
   a o<-------- 1.3 m -------->o b
           (neutral plane midway)
```

**Data:** $r = 0.006$ m, $D = 1.3$ m.

$$
\ln\frac{D}{r} = \ln\frac{1.3}{0.006} = \ln 216.67 = 5.3784
$$

#### Capacitance between conductors

$$
\begin{aligned}
C_{ab} &= \frac{\pi\varepsilon_0}{\ln(D/r)} = \frac{\pi \times 8.854\times10^{-12}}{5.3784} \\
&= 5.172\times10^{-12}\ \text{F/m} = 5.172\ \text{nF/km}
\end{aligned}
$$

#### Capacitance of each conductor to ground (neutral)

$$
C_n = 2C_{ab} = \frac{2\pi\varepsilon_0}{\ln(D/r)} = 10.344\times10^{-12}\ \text{F/m} = 10.344\ \text{nF/km}
$$

```text
  a o--||--o--||--o b      C_ab = C_n/2
       C_n  |  C_n         (two C_n in series)
           ground
```

**Answer:** $C_{ab} = 5.17$ nF/km; $C_n = 10.34$ nF/km. (If 6 mm were the diameter, $r = 3$ mm, giving $C_{ab} = 4.58$ nF/km and $C_n = 9.16$ nF/km.)

## Check yourself

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

1. For a single-phase line, capacitance between the two conductors is:
   A. pi*eps0 / ln(D/r)
   B. 2*pi*eps0 / ln(D/r)
   C. pi*eps0 * ln(D/r)
   D. 4*pi*eps0 / ln(D/r)
   Answer: A. The line-to-line capacitance is half the capacitance to neutral. (Key point: C between conductors)

2. The capacitance of each conductor to ground (neutral) is:
   A. C_n = C_ab / 2
   B. C_n = 2 C_ab
   C. C_n = C_ab
   D. C_n = C_ab^2
   Answer: B. Two C_n in series make C_ab, so C_n = 2 C_ab (since V_an = V_ab/2). (Key point: C to neutral)

3. Why is there a neutral plane midway between the conductors?
   A. The earth is at midpoint
   B. Both conductors carry the same charge
   C. The conductors carry equal and opposite charges
   D. The conductors have different radii
   Answer: C. Equal and opposite charges produce a zero-potential plane halfway between. (Key point: Neutral plane)

4. If 6 mm were taken as diameter instead of radius, C_ab would:
   A. Decrease, because r becomes smaller
   B. Increase
   C. Stay the same
   D. Become zero
   Answer: A. Smaller r increases ln(D/r), so capacitance falls (4.58 vs 5.17 nF/km). (Key point: Interpretation of 6 mm)

## Related in Power System Analysis I

- [Effect of neglecting earth on capacitance](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Aearth-effect-horizontal-13m) — Power System Analysis I, chapter 4
- [Capacitance with and without earth effect](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Acapacitance-with-earth-effect-13m) — Power System Analysis I, chapter 4
- [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
- [Transposition; single-phase capacitance with earth](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Atransposition-single-phase-earth-capacitance) — Power System Analysis I, chapter 4
- [Effect of earth on line capacitance](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Aearth-effect-capacitance) — 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

## Related in other subjects

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- [Capacitance matrices, untransposed and transposed (15 m)](https://www.bctengineer.com/question.md?key=semester_8%2Fhigh_voltage_engineering%3Acapacitance-matrix-transposed-15m) — High Voltage Engineering, chapter 5, asked 3×
- [Capacitance and charge matrices (9.81 m clearance)](https://www.bctengineer.com/question.md?key=semester_8%2Fhigh_voltage_engineering%3Acapacitance-charge-matrix-9-81m) — High Voltage Engineering, chapter 5, asked 3×
- [Capacitance and charge matrices, transposed and untransposed](https://www.bctengineer.com/question.md?key=semester_8%2Fhigh_voltage_engineering%3Acapacitance-charge-matrix-midspan) — High Voltage Engineering, chapter 5