---
title: "T/F: corona inception voltage and GMR"
subject: "Transmission and Distribution System Design"
chapter: 4
key: "semester_8/transmission_and_distribution_system_design:tf-corona-inception-gmr"
source: https://www.bctengineer.com/q/semester_8/transmission_and_distribution_system_design/tf-corona-inception-gmr
site: BCT Engineering
---

# T/F: corona inception voltage and GMR

Transmission and Distribution System Design · Chapter 4: Conductor and Support Selection

- Asked in: 2073 Magh, 1+3 marks
- Video: [Corona Effect in Overhead Transmission Lines | Theory, Formula, Advantages & Reduction Methods](https://www.youtube.com/watch?v=bDKnAmOTBEE) — Electrology
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_8/transmission_and_distribution_system_design/tf-corona-inception-gmr
- Whole chapter: https://www.bctengineer.com/md/semester_8/transmission_and_distribution_system_design/chapter-4

## Question

State whether the following statement is TRUE or FALSE. Justify your answer with a brief explanation: Corona inception voltage is inversely proportional to the GMR of conductor.

## Short answer

FALSE. Corona inception voltage depends on the conductor's physical outer radius r, not its GMR. It is roughly proportional to r (V_d ∝ r ln(D/r)), increasing as radius increases, so it is not inversely proportional.

## Answer

**FALSE.**

The corona inception (disruptive critical) voltage is

$$
V_d = 21.1\,m_0\,\delta\,r\ln\frac{D}{r}\ \text{kV}
$$

- $V_d$ depends on the **physical outer radius** $r$, which sets the surface field. It does not depend on the GMR.
- GMR (about $0.7788r$ for a solid conductor) is a fictitious radius used only for **inductance** calculations.
- $V_d$ **increases** with radius: it is nearly proportional to $r$, because $r\ln(D/r)$ rises with $r$ for $D \gg r$. It is not inversely proportional.

So a larger conductor, or a bundle with a larger equivalent radius, raises the corona inception voltage. The statement is wrong on both counts.

## Check yourself

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

1. Is corona inception voltage inversely proportional to GMR?
   A. True
   B. False, it depends on the physical radius and rises with it
   C. True for bundles only
   D. False, it is independent of conductor size
   Answer: B. Vd = 21.1 m δ r ln(D/r) depends on physical radius r and increases with it. (Key point: Verdict)

2. What is GMR used for?
   A. Corona calculations
   B. Inductance calculations, as a fictitious radius
   C. Sag calculation
   D. Thermal rating
   Answer: B. GMR (about 0.7788 r) models the internal flux linkage for inductance only. (Key point: Meaning of GMR)

3. What happens to critical voltage as conductor radius increases?
   A. It decreases since the surface field drops
   B. It increases (roughly proportional to r)
   C. It is unchanged
   D. It becomes zero
   Answer: B. A larger radius lowers the surface electric field, so a higher voltage is needed to start corona. (Key point: Effect of larger conductor)

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