Derivation of an Earth-Return Impedance of an Overhead Multi-Conductor Considering Displacement Currents
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Bibliographic record
Abstract
This paper explains an error involved in well-known formulas of the earth-return impedance of an overhead multi-conductor derived by Pollaczek, Carson and Sunde. It has been said that Pollaczek's infinite integral formula is numerically instable, and Carson's formula cannot deal with displacement currents. This paper has shown an accurate earth-return impedance formula considering the displacement currents, and Carson's formula is modified so as to be able to deal with the displacement currents. Also, an approximate formula considering the displacement currents is derived. The formula is of a simple closed form and is applicable to high frequencies.
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Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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