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T/F: capability curve inversely proportional to 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.

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.

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: 80×2.75=22080 \times 2.75 = 220, 160×2.25=360160 \times 2.25 = 360, 320×1.35=432320 \times 1.35 = 432, 640×0.75=480640 \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∝1/sin⁡βlP \propto 1/\sin\beta l).

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

✓ Answer checked by Claude Opus 5.5 (high effort)

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