---
title: "T/F: capability curve inversely proportional to length"
subject: "Transmission and Distribution System Design"
chapter: 2
key: "semester_8/transmission_and_distribution_system_design:tf-capability-curve-inverse-length"
source: https://www.bctengineer.com/q/semester_8/transmission_and_distribution_system_design/tf-capability-curve-inverse-length
site: BCT Engineering
---

# T/F: capability curve inversely proportional to length

Transmission and Distribution System Design · Chapter 2: Transmission Voltage Level and Number of Circuits

- Asked in: 2067 Mangsir (old course), 1+3 marks
- 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-capability-curve-inverse-length
- Whole chapter: https://www.bctengineer.com/md/semester_8/transmission_and_distribution_system_design/chapter-2

## Question

For a given amount of power to be transmitted over a given distance, state whether the following statement is TRUE or FALSE. Justify your answer with a brief explanation: The power transfer capability curve of an EHV transmission line as a function of multiple of surge impedance loading is inversely proportional to the line length.

## Short answer

False. The power transfer capability decreases non-linearly with line length, not in inverse proportion. The multiplying factor times length is not constant, and the drop arises from thermal, voltage-drop, and stability limits.

## Answer

**FALSE** (strictly). The capability (in multiples of SIL) **decreases** with line length, but **not in inverse proportion**.

- If it were inversely proportional, m.f. × length would be constant. From the capability curve: $80 \times 2.75 = 220$, $160 \times 2.25 = 360$, $320 \times 1.35 = 432$, $640 \times 0.75 = 480$; the product is not constant.
- The curve has three regions: short lines (thermal limit, about 3 × SIL, nearly independent of length), medium lines (voltage-drop limit), long lines (stability limit, $P \propto 1/\sin\beta l$).

So the correct statement is: power transfer capability falls non-linearly as length increases.

## Check yourself

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

1. Is the capability curve (in multiples of SIL) inversely proportional to line length?
   A. True
   B. False, it falls with length but not inversely
   C. False, it rises with length
   D. True only above 320 km
   Answer: B. It decreases with length, but not in inverse proportion. (Key point: Verdict)

2. How can inverse proportionality be checked from the curve?
   A. Check whether m.f. x length is constant
   B. Check whether m.f. + length is constant
   C. Check whether m.f. / length is constant
   D. Check whether m.f. is above 1
   Answer: A. If inversely proportional, m.f. x length would be constant. Products are 220, 360, 432, 480, so not constant. (Key point: Test of proportionality)

3. What limits the capability of short lines in the curve?
   A. Stability
   B. Thermal rating
   C. Corona
   D. Voltage regulation only
   Answer: B. Short lines (< 80 km) are thermally limited at about 3 x SIL, nearly independent of length. (Key point: Three regions)

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