---
title: "Effect of earth on line capacitance"
subject: "Power System Analysis I"
chapter: 4
key: "semester_4/power_system_analysis_i:earth-effect-capacitance"
source: https://www.bctengineer.com/q/semester_4/power_system_analysis_i/earth-effect-capacitance
site: BCT Engineering
---

# Effect of earth on line capacitance

Power System Analysis I · Chapter 4: Line Parameter Calculations

- Asked in: 2072 Asoj, 4 marks; 2071 Bhadra, 4 marks (asked 2 times)
- Video: [PS21 Effect of Earth on Capacitance of Transmission Line](https://www.youtube.com/watch?v=c8F2M1F4FtE) — Lectures in Electrical Engineering
- 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/earth-effect-capacitance
- Whole chapter: https://www.bctengineer.com/md/semester_4/power_system_analysis_i/chapter-4

## Question

What is the effect of earth on the capacitance of an overhead line? Explain.

## Short answer

Earth acts as a conducting plane, increasing line capacitance slightly by introducing image charges. The method of images places opposite-charge images below ground, reducing the effective distance between conductors and their images, which raises capacitance. The effect is usually small for overhead lines but important for zero-sequence calculations.

## Answer

The earth is a conductor at zero potential. Its presence changes the electric field of an overhead line and so **increases the line capacitance slightly**.

#### Method of images
The earth's surface is an equipotential plane. Its effect can be modelled by removing the earth and placing an **image conductor** as far below the ground surface as the real conductor is above it, carrying an equal and opposite charge. For a conductor at height h with charge +q, the image is at depth h with charge −q. The field above ground is then calculated from the real and image charges together.

```text
     a (+qa)  <-- D -->  b (+qb)
     |                   |
     h                   h
 ====|======= earth =====|======
     h                   h
     |                   |
     a' (-qa)            b' (-qb)
  distance a to b' = H = sqrt(D^2 + 4h^2)
```

#### Single-phase line
Without earth:
$$
C_{ab} = \frac{\pi\varepsilon_0}{\ln(D/r)}\ \text{F/m}
$$

With earth effect (images included):
$$
C_{ab} = \frac{\pi\varepsilon_0}{\ln\left(\dfrac{D}{r}\cdot\dfrac{2h}{\sqrt{D^2 + 4h^2}}\right)}
$$

Because $\frac{2h}{\sqrt{D^2+4h^2}} < 1$, the denominator is smaller and the capacitance is **larger**.

#### Three-phase transposed line
$$
C_n = \frac{2\pi\varepsilon_0}{\ln\dfrac{D_{eq}}{r} - \ln\dfrac{\sqrt[3]{H_{12}H_{23}H_{31}}}{\sqrt[3]{H_1H_2H_3}}}\ \text{F/m to neutral}
$$

Here $H_{ij}$ is the distance from conductor i to the image of conductor j, and $H_i = 2h$ is the distance to its own image.

#### Points to note
- The earth brings charge of the opposite sign closer to the conductor, which raises the capacitance.
- The effect is **small** for normal overhead lines, because $h \gg D$, so it is usually neglected. It becomes important for low-height lines, large spacings, and in unbalanced-fault (zero-sequence) calculations.
- Earth has a negligible effect on line inductance under balanced conditions.
- Higher capacitance means slightly more charging current and charging kVAR.

## Check yourself

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

1. What is the effect of earth on line capacitance?
   A. It slightly increases capacitance
   B. It slightly decreases capacitance
   C. It has no effect at all
   D. It doubles capacitance
   Answer: A. The earth acts as an equipotential plane bringing opposite charge closer, raising capacitance slightly. (Key point: Effect on capacitance)

2. In the method of images, what replaces the earth for a conductor at height h with charge +q?
   A. An image conductor at depth h with charge -q
   B. An image conductor at height 2h with charge +q
   C. An image at depth h with charge +q
   D. A grounded wire at height h
   Answer: A. The earth plane is replaced by an equal and opposite image charge at the same depth below ground. (Key point: Method of images)

3. Why is the earth effect usually neglected for overhead lines?
   A. Because h is much greater than D, so the effect is small
   B. Because earth has high resistivity
   C. Because it affects inductance only
   D. Because lines are always underground
   Answer: A. For normal heights the factor 2h/sqrt(D^2+4h^2) is near 1, so the change is small; it matters for low lines and zero-sequence calculations. (Key point: Negligible in practice)

## 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
- [Single-phase line capacitance, 6 mm, 1.3 m](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Asingle-phase-capacitance-6mm-1-3m) — 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
- [Proximity effect in overhead lines](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Aproximity-effect) — Power System Analysis I, chapter 4
- [Proximity effect in cables vs overhead lines](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Aproximity-effect-cables-vs-lines) — Power System Analysis I, chapter 4

## Related in other subjects

- [Voltage rise at cable–overhead line junction](https://www.bctengineer.com/question.md?key=semester_8%2Fhigh_voltage_engineering%3Asurge-cable-overhead-junction) — High Voltage Engineering, chapter 3, asked 2×
- [Surge from overhead line into cable and transformer](https://www.bctengineer.com/question.md?key=semester_8%2Fhigh_voltage_engineering%3Aoverhead-line-cable-transformer-surge) — High Voltage Engineering, chapter 3
- [Fault at load end of overhead line](https://www.bctengineer.com/question.md?key=semester_5%2Fpower_system_analysis_ii%3Afault-load-end-33kv-line) — Power System Analysis II, chapter 3
- [Capacitance matrix of 400 kV bundled line](https://www.bctengineer.com/question.md?key=semester_8%2Fhigh_voltage_engineering%3Acapacitance-matrix-400kv-15m) — High Voltage Engineering, chapter 5, asked 2×