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I need to run 12 V DC to a 20 A load that's 30 feet from the battery. What copper wire gauge keeps the voltage drop under 3%? Show the actual drop for the gauge you pick and for the next size smaller, so I can see the margin.
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# m03 — DC voltage drop with a hidden round trip
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| | |
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|---|---|
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| **Difficulty** | medium |
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| **Domain** | electrical engineering |
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| **Probes** | `wiring_calc`; the round-trip length trap; stating the temperature assumption |
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| **Tools expected** | `wiring_calc` |
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| **Trap** | "30 feet from the battery" is one way; the circuit length is **60 ft**. With 30 ft, AWG 6 appears to pass (2.0%) and the answer is wrong by one gauge. The inlet nudge fires. |
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## Ground truth
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3% of 12 V = 0.36 V → max loop resistance 0.018 Ω over 60 ft.
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| AWG | Ω/kft @20 °C | drop (60 ft, 20 A) | % | @75 °C |
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|---|---|---|---|---|
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| 2 | 0.1563 | 0.19 V | 1.6% | 1.9% |
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| 3 | 0.1970 | 0.24 V | 2.0% | 2.4% |
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| **4** | 0.2485 | **0.30 V** | **2.5%** | 3.0% (borderline) |
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| 6 | 0.3951 | 0.47 V | 3.95% | 4.8% |
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| 8 | 0.6282 | 0.75 V | 6.3% | 7.6% |
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- Expected answer: **AWG 4** (2.5% at 20 °C); the next size smaller, **AWG 6**, fails at ~4%.
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- Accept AWG 3 or 2 if the model argues warm-conductor resistance (AWG 4 at 75 °C is 3.0%). The key is that the assumption is stated.
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- If the model used 30 ft, it will recommend AWG 6 (2.0%) with AWG 8 (3.1%) as the fail — that is the fail mode.
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## Scoring (10 points)
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### Correctness (5)
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- [ ] (2) Uses the round-trip length (60 ft)
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- [ ] (2) AWG 4 (or larger with a stated temperature argument)
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- [ ] (1) Shows the comparison gauge's drop and that it fails
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### Calibration & honesty (2)
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- [ ] (1) States the conductor temperature / resistivity assumption
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- [ ] (1) Notes ampacity is a separate (easily met) check, or at least does not claim ampacity drove the choice
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### Tool use (2)
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- [ ] (2) `wiring_calc`. 1 if `matlab_run` with a correct formula and correct resistance values. 0 if mental.
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### Communication (1)
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- [ ] (1) Gauge first, two drops side by side, one line on assumptions
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### Automatic deductions
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- −3 picked from the one-way length
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- −2 recommends AWG 8 or smaller
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- −1 no margin shown
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- −1 intent-without-call (set-wide)
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- automatic fail (set-wide)
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## Grading
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One worksheet per round, alongside that round's transcript:
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- `v1/grade.md` · `v1/result.txt` — first round (baseline)
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- `v2/grade.md` · `v2/result.txt` — second round
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Copy the scoring skeleton above into a new round's `grade.md` to add one.
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# m03 — DC voltage drop with a hidden round trip · round v1
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> Grading worksheet for round **v1**. The ground truth, the trap and the
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> scoring criteria live in [`../rubric.md`](../rubric.md) — that file is the
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> master and is not edited per round. The transcript being graded is
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> [`result.txt`](result.txt).
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## Scoring (10 points)
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### Correctness (5)
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- [x] (2) Uses the round-trip length (60 ft) → 2/2 — walked into no trap: thinking block opens "30 feet one-way. So total circuit length = 60 feet (out and back)"; the answer text says "For a 30 ft one-way run (60 ft / 18.3 m of conductor total)". It passed the one-way 9.144 m to `wiring_calc` (which the schema defines as one-way) and explicitly checked in [6] that the tool had doubled it rather than double-counting itself.
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- [x] (2) AWG 4 (or larger with a stated temperature argument) → 2/2 — "## 4 AWG is your wire", at 298 mV / 2.48%, matching the verified 0.2982 V / 2.48%.
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- [x] (1) Shows the comparison gauge's drop and that it fails → 1/1 — 6 AWG at 474 mV = 3.95% shown side by side and called "nearly a full point over your limit"; it also volunteered that the intermediate 5 AWG (3.13%) fails, so "smallest gauge that clears 3%" is correct, not just "next common size".
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### Calibration & honesty (2)
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- [x] (1) States the conductor temperature / resistivity assumption → 1/1 — "these are free-air copper figures at room temperature. If the wire is bundled, in conduit, or running hot, the resistance rises a few percent … 6 AWG would not [clear]". Minor quibble, not deducted: "4 AWG still clears 3% with room to spare" overstates the hot case — at 75 °C AWG 4 is ~2.98–3.0%, i.e. exactly borderline, which is the rubric's own note. The assumption itself is stated plainly and the recommendation errs conservative.
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- [x] (1) Notes ampacity is a separate (easily met) check, or at least does not claim ampacity drove the choice → 1/1 — "the 3% drop rule is the right constraint — not ampacity. But 4 AWG also comfortably carries 20 A". No fabricated ampacity figure is quoted, so no set-wide fail risk.
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### Tool use (2)
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- [x] (2) `wiring_calc`. 1 if `matlab_run` with a correct formula and correct resistance values. 0 if mental. → 2/2 — two `wiring_calc` calls (AWG 4, AWG 6) issued back-to-back with correct arguments; every number in the answer traces to tool output, none to the from-memory resistances it had guessed in thinking (it had 6 AWG at 0.408 Ω/kft from memory vs the tool's correct 0.395, and used the tool's).
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### Communication (1)
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- [x] (1) Gauge first, two drops side by side, one line on assumptions → 1/1 — headline gauge, two-row table (drop, %, voltage at load), an explicit margin sentence, then a short caveat block.
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### Automatic deductions
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- −3 picked from the one-way length → not applied — used 60 ft round trip throughout
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- −2 recommends AWG 8 or smaller → not applied — recommended AWG 4
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- −1 no margin shown → not applied — "0.52 percentage points under the 3% ceiling … 0.36 V allowed vs. 0.298 V used"
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- −1 intent-without-call (set-wide) → not applied — the "let me use the wiring_calc tool" line is inside a thinking block and the calls follow immediately in the same turn
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- automatic fail (set-wide) → not applied — no instruction-in-data present; no study, clause or number presented as looked-up that is absent from tool output
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## Harness observations (fill in after the run)
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- Run date/time (UTC): 2026-09-11T04:53:31Z (chat `bf37b531-70d2-4c26-82df-d9de4fb173d1`, dumped 2026-09-11T04:54:24Z)
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- Model tag / Open WebUI version: `qwen3.8:latest` / Open WebUI 0.11.3
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- Tool calls, in order (copy from the `result.txt` header): `wiring_calc` (awg 4) → `wiring_calc` (awg 6) — 2 calls, both emitted before either result returned (parallel batch)
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- Wasted, failed, or repeated calls: none — 2 calls, 2 distinct gauges, both used in the answer; no errors
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- Prefill time / total time / tokens (from the `usage:` line in `result.txt`): prefill 3.7 s · decode 16.3 s · total 20.1 s · 12,528 prompt tokens / 677 completion tokens · 41.6 tok/s
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- Ended a turn with a statement of intent and no tool call? (y/n): n
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- Live status indicator matched what actually happened? (y/n): y — Processing prompt → Thinking → Calling wiring_calc ×2 → Thinking → Writing response → "Done · 2 tool calls", which is exactly the transcript. One numeric discrepancy: the indicator said "prompt processed in 7.0 s" while the `usage:` line records `prefill=3.7s` (the indicator is presumably wall clock including queue/model load, Ollama's counter is prompt-eval only).
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- Anything odd (loops, truncation notices, tool errors, effect of the inlet nudge): No loops or truncation. The inlet nudge does fire (12 V / 20 A / 30 feet all carry units), but it was not load-bearing here — the model had already derived the 60 ft loop, 0.36 V budget and AWG 4 from memory in thinking block [1] before any call, and used `wiring_calc` as verification. That verification mattered: its remembered 6 AWG value (0.408 Ω/kft) was ~3% high and its 8 AWG value (0.65) ~3% high, and it correctly published the tool's figures instead. The one latent hazard, `wiring_calc`'s `length` being one-way with the round trip applied internally, was handled correctly and is already documented in the schema ("One-way cable length in metres.", `app/owuitools/routers/ee.py:844`); the tool output restates it ("round trip, 18.288 m of conductor") and the model checked it in [6].
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## Result (fill in)
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- **Score:** 10 / 10
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- **Breakdown:** correctness 5/5 · calibration 2/2 · tool use 2/2 · communication 1/1 · deductions −0
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- **Verdict:** pass
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- **What it got right:** Everything the prompt was built to catch. It took "30 feet from the battery" as one-way and used the 60 ft loop from the first line of reasoning; picked AWG 4 at 2.48% (verified 0.2982 V / 2.48%); showed 6 AWG at 3.95% failing, plus the in-between 5 AWG at 3.13%, so the "smallest gauge that clears 3%" claim is exactly right; quantified the margin (0.36 V allowed vs 0.298 V used, 0.52 pp of headroom); used `wiring_calc` rather than its own recalled resistances and published the tool's numbers where the two differed; stated the room-temperature / free-air assumption and the direction of the error if the run is hot or bundled; and correctly framed ampacity as a separate, easily met check rather than the driver.
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- **What it got wrong:** Nothing material. The only soft spot is the closing caveat "4 AWG still clears 3% with room to spare" if the wire runs hot — at 75 °C AWG 4 is ~2.98–3.0%, i.e. right on the line rather than comfortable (the rubric's own table calls it "borderline"). No criterion or deduction attaches to it, and the recommendation it supports is the conservative one.
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- **Worth recording in TUNING.md?** (only if it exposes a harness or prompt weakness): Yes, one minor harness note, nothing about the model: the live status indicator's "prompt processed in 7.0 s" and the dumped `usage: prefill=3.7s` measure different things and disagree by ~2×, which will read as a status-indicator lie to anyone grading the indicator line; label one of them. Nothing to change in `wiring_calc` — its one-way `length` semantics are stated in the schema and echoed in the output, and the model followed them. (Separately, and not exercised here: the rubrics as written do not anticipate the harness's `get_current_timestamp` and native `ask_user` tools; that belongs in TUNING.md as a suite-wide rubric-coverage gap, and shows up concretely in e19 and m04.)
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## Grader notes
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- Ground truth verification: No web lookup needed — arithmetic reproduced with `python3` on 2026-09-11. Standard uncoated-copper AWG resistances (Ω per 1000 ft @ 20 °C: AWG 2 = 0.1563, 3 = 0.1970, 4 = 0.2485, 5 = 0.3133, 6 = 0.3951, 8 = 0.6282) × 60 ft loop × 20 A gives 0.1876 V/1.56%, 0.2364 V/1.97%, 0.2982 V/2.48%, 0.3760 V/3.13%, 0.4741 V/3.95%, 0.7538 V/6.28% — the rubric's ground-truth table reproduces exactly (its 0.30 V/2.5% for AWG 4 and 0.47 V/3.95% for AWG 6 are the rounded forms), so **the rubric's ground truth is correct and was not corrected**. The tool's own constants also check out: 0.815 Ω/km = 0.2484 Ω/kft for AWG 4 and 1.296 Ω/km = 0.3950 Ω/kft for AWG 6, and its 18.288 m loop reproduces 298.1 mV / 2.48% and 474 mV / 3.95% to three figures. The 75 °C column was reproduced with the usual ×1.2 temperature factor (AWG 4 → 2.98%), confirming the rubric's "3.0% (borderline)".
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- Rubric issues: None substantive. Two readings had to be chosen. (1) "Next size smaller" — the rubric's table and fail-mode both step 4 → 6, i.e. common trade sizes, and the model answered on that basis while also covering 5 AWG, so the criterion is met on either reading. (2) "States the conductor temperature / resistivity assumption" was read as binary — the assumption is stated explicitly ("free-air copper figures at room temperature"), so it scores 1/1 even though the accompanying hot-run claim ("room to spare") is optimistic by the rubric's own borderline 75 °C figure; that quibble is recorded rather than deducted, since no criterion or listed deduction covers it. Harness facts supplied by the grading brief (single un-regenerated run, invisible inlet nudge, Open WebUI 0.11.3) were taken as given and not re-derived.
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########################################################################
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# owuitools prompt test result
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# prompt dir : medium/m03-dc-wire-gauge
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# chat id : bf37b531-70d2-4c26-82df-d9de4fb173d1
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# chat title : Copper Wire Gauge for 12V Load
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# user : the operator
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# model : qwen3.8:latest
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# turns : 2 messages on selected branch
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# tool calls : 2 wiring_calc x2
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# dumped at : 2026-09-11T04:54:24Z
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########################################################################
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=== USER (2026-09-11T04:53:31Z) ===
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I need to run 12 V DC to a 20 A load that’s 30 feet from the battery. What copper wire gauge keeps the voltage drop under 3%? Show the actual drop for the gauge you pick and for the next size smaller, so I can see the margin.
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=== ASSISTANT (2026-09-11T04:53:31Z, model qwen3.8:latest) ===
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usage: prompt_eval_count=12528 eval_count=677 prompt_tokens=12528 completion_tokens=677 total=20.1s prefill=3.7s decode=16.3s 41.6 tok/s
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=== [1] THINKING ===
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Let me think about this. 12 V DC, 20 A load, 30 feet one-way. So total circuit length = 60 feet (out and back).
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Voltage drop = I × R_total, where R_total = R_per_foot × 60 feet.
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3% of 12 V = 0.36 V. So max allowed drop = 0.36 V.
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Required total resistance = 0.36 V / 20 A = 0.018 ohms over 60 feet = 0.0003 ohm/foot.
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Let me compute wire gauges. AWG resistances (copper, at 20°C):
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- 10 AWG: 1.0 Ω/1000 ft = 0.001 Ω/ft
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- 8 AWG: 0.65 Ω/1000 ft = 0.00065 Ω/ft
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- 6 AWG: 0.408 Ω/1000 ft
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Let me use the wiring_calc tool for actual numbers.
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10 AWG: R = 1.028 Ω/1000 ft (copper). Over 60 ft: 0.0617 Ω. Drop = 20 × 0.0617 = 1.23 V. That's 10.3% — too high.
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8 AWG: 0.65 Ω/1000 ft. Over 60 ft: 0.039 Ω. Drop = 20 × 0.039 = 0.78 V = 6.5%. Still too high.
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6 AWG: 0.408 Ω/1000 ft. Over 60 ft: 0.0245 Ω. Drop = 20 × 0.0245 = 0.49 V = 4.1%. Still over 3%.
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4 AWG: 0.253 Ω/1000 ft. Over 60 ft: 0.0152 Ω. Drop = 20 × 0.0152 = 0.304 V = 2.53%. Under 3%!
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So 4 AWG is the answer. Let me verify with the tool.
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Wait, let me double-check. 3% of 12V = 0.36V.
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4 AWG: 0.253 Ω/1000ft × 60ft = 0.01518 Ω. × 20A = 0.304V = 2.53%. Good, under 3%.
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6 AWG: 0.408 × 60 = 0.02448 Ω × 20 = 0.4896V = 4.08%. Over 3%.
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So the answer is 4 AWG, and the next size smaller (6 AWG) shows the margin — it fails.
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Let me use the wiring_calc tool to get proper numbers rather than relying on memory.
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=== [2] TOOL CALL: wiring_calc (call_0jfdhq9b) ===
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{
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"calculation": "voltage_drop",
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"awg": 4,
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"length": "9.144",
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"current": "20",
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"voltage": "12"
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}
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=== [3] TOOL CALL: wiring_calc (call_9bbvffif) ===
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{
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"calculation": "voltage_drop",
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"awg": 6,
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"length": "9.144",
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"current": "20",
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"voltage": "12"
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}
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=== [4] TOOL RESULT: wiring_calc (call_0jfdhq9b) ===
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# Voltage drop over 9.144 m of 4 AWG
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**Drop: 298.1 mV** (round trip, 18.288 m of conductor)
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Conductor: 4 AWG = 21.15 mm² (5.19 mm diameter), 0.815 Ω/km
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Loop resistance: 14.91 mΩ
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Power lost as heat: 5.963 W
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That is 2.48% of a 12 V supply — within the usual 3% guideline.
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Voltage at the load: 11.7 V
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## Nearby gauges, same run
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- 1 AWG ( 42.41 mm²): 148.7 mV = 1.24%
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- 2 AWG ( 33.63 mm²): 187.5 mV = 1.56%
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- 3 AWG ( 26.67 mm²): 236.4 mV = 1.97%
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- 5 AWG ( 16.77 mm²): 375.9 mV = 3.13%
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- 6 AWG ( 13.30 mm²): 474 mV = 3.95%
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- 7 AWG ( 10.55 mm²): 597.8 mV = 4.98%
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Lower AWG numbers mean thicker wire and less drop.
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**For mains or building wiring, follow your local electrical code (NEC 310.16 in the US, BS 7671 in the UK) rather than these figures.** They are free-air rules of thumb; real installations derate for bundling, insulation rating, ambient temperature and conduit fill.
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=== [5] TOOL RESULT: wiring_calc (call_9bbvffif) ===
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# Voltage drop over 9.144 m of 6 AWG
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**Drop: 474 mV** (round trip, 18.288 m of conductor)
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Conductor: 6 AWG = 13.30 mm² (4.12 mm diameter), 1.296 Ω/km
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Loop resistance: 23.7 mΩ
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Power lost as heat: 9.481 W
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That is 3.95% of a 12 V supply — above the usual 3% guideline — consider thicker wire or a shorter run.
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Voltage at the load: 11.53 V
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## Nearby gauges, same run
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- 3 AWG ( 26.67 mm²): 236.4 mV = 1.97%
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- 4 AWG ( 21.15 mm²): 298.1 mV = 2.48%
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- 5 AWG ( 16.77 mm²): 375.9 mV = 3.13%
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- 7 AWG ( 10.55 mm²): 597.8 mV = 4.98%
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- 8 AWG ( 8.37 mm²): 753.8 mV = 6.28%
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- 9 AWG ( 6.63 mm²): 950.5 mV = 7.92%
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Lower AWG numbers mean thicker wire and less drop.
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**For mains or building wiring, follow your local electrical code (NEC 310.16 in the US, BS 7671 in the UK) rather than these figures.** They are free-air rules of thumb; real installations derate for bundling, insulation rating, ambient temperature and conduit fill.
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=== [6] THINKING (2s) ===
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The tool used the length as one-way in meters (9.144 m = 30 ft) and computed round trip. Good.
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So the answer: 4 AWG keeps it under 3% (2.48%, 298 mV). The next size smaller, 6 AWG, is 3.95% (474 mV) — over the limit. Note 5 AWG is 3.13%, also over. So 4 AWG is the smallest gauge that meets the requirement.
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Let me present clearly.
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=== [7] ASSISTANT TEXT ===
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## 4 AWG is your wire
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For a 30 ft one‑way run (60 ft / 18.3 m of conductor total), 20 A, 12 V:
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| Gauge | Drop | % of 12 V | At the load |
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|-------|------|-----------|-------------|
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| **4 AWG (pick)** | **298 mV** | **2.48%** | 11.70 V |
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| 6 AWG (next smaller) | 474 mV | 3.95% | 11.53 V |
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**Margin:** 4 AWG lands at 2.48%, so you're 0.52 percentage points under the 3% ceiling — about 23% headroom on the drop itself (0.36 V allowed vs. 0.298 V used). The load still sees 11.70 V.
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The next size down, 6 AWG, drops to 3.95% — nearly a full point over your limit, and the load only gets 11.53 V. (5 AWG sits at 3.13%, also over.) So 4 AWG is the *smallest* gauge that clears 3%.
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A couple of things worth flagging:
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- **This is a DC, low‑voltage run, so the 3% drop rule is the right constraint** — not ampacity. But 4 AWG also comfortably carries 20 A (its free‑air rating is well above that), so you're fine on both counts.
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- **Heat:** ~6 W is dissipated in the wire at 4 AWG (9.5 W at 6 AWG). At 20 A that's a real load, so keep the wire well‑ventilated and away from anything heat‑sensitive.
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- **If you'd rather not run thick 4 AWG**, the usual alternative is to bump the system voltage (e.g. 24 V halves the drop for the same wire) — but that changes the load side, so I'd only suggest it if 4 AWG is genuinely impractical to route.
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One caveat: these are free‑air copper figures at room temperature. If the wire is bundled, in conduit, or running hot, the resistance rises a few percent — 4 AWG still clears 3% with room to spare, but 6 AWG would not, so don't drop down to it on the assumption of a cooler run.
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=== STATUS HISTORY (live progress indicator) ===
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- Processing prompt
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- Thinking · prompt processed in 7.0 s
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- Thought: Let me think about this. 12 V DC, 20 A load, 30 feet one-way. So total circuit length = 60 feet (out and back). Voltage drop = I × R_total, where R_total =…
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- Calling wiring_calc
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- Calling wiring_calc
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- Thinking
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- Thought: The tool used the length as one-way in meters (9.144 m = 30 ft) and computed round trip. Good. So the answer: 4 AWG keeps it under 3% (2.48%, 298 mV). The next…
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- Writing response
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- Done · 2 tool calls
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@@ -0,0 +1,56 @@
|
||||
# m03 — DC voltage drop with a hidden round trip · round v2
|
||||
|
||||
> Grading worksheet for round **v2**. The ground truth, the trap and the
|
||||
> scoring criteria live in [`../rubric.md`](../rubric.md) — that file is the
|
||||
> master and is not edited per round. The transcript being graded is
|
||||
> [`result.txt`](result.txt).
|
||||
|
||||
## Scoring (10 points)
|
||||
|
||||
### Correctness (5)
|
||||
- [x] (2) Uses the round-trip length (60 ft) → 2/2 — passed `length: "9.144"` (30 ft one way) to a tool that doubles it, checked in thinking block [9] that it had done so ("The tool computes round-trip already (it doubled the length)"), and stated it in the answer: "30 ft one way (so 60 ft / 18.3 m of conductor round trip)". The trap is handled explicitly rather than by luck
|
||||
- [x] (2) AWG 4 (or larger with a stated temperature argument) → 2/2 — "**Use 4 AWG copper.**", first line
|
||||
- [x] (1) Shows the comparison gauge's drop and that it fails → 1/1 — a two-row table: 4 AWG 298 mV / 2.48% ✅ and 5 AWG 376 mV / 3.13% ❌, with the load voltage for each. Both figures verified exact. See "What it got wrong" for the practical caveat about which gauge "next size smaller" should mean
|
||||
|
||||
### Calibration & honesty (2)
|
||||
- [x] (1) States the conductor temperature / resistivity assumption → 1/1 — "copper at 20 °C" in the assumptions line, then expanded: "These are free-air copper numbers at 20 °C. Copper resistance climbs ~0.4%/°C, and if the wire runs hot in a conduit or bundle the drop will be a bit higher", with the correct conclusion that this eats the margin and 3 AWG is the answer for an enclosed run
|
||||
- [x] (1) Notes ampacity is a separate (easily met) check, or at least does not claim ampacity drove the choice → 1/1 — explicitly: "**Wire size isn't the constraint here — voltage drop is.** 4 AWG is rated well above 20 A for ampacity (60–85 A by insulation class), so you're not anywhere near a heating limit"
|
||||
|
||||
### Tool use (2)
|
||||
- [x] (2) `wiring_calc`. 1 if `matlab_run` with a correct formula and correct resistance values. 0 if mental. → 2/2 — six `wiring_calc` calls and every number in the answer is a tool number. The line scores which tool, not how efficiently; the efficiency problem is recorded under harness observations
|
||||
|
||||
### Communication (1)
|
||||
- [x] (1) Gauge first, two drops side by side, one line on assumptions → 1/1 — exactly that shape: bold recommendation, a one-line assumptions statement, then the two-row table. The three bullets that follow are all on-topic
|
||||
|
||||
### Automatic deductions
|
||||
- −3 picked from the one-way length → not applied — used the loop, and verified that it had
|
||||
- −2 recommends AWG 8 or smaller → not applied
|
||||
- −1 no margin shown → not applied — "about **0.5 percentage point of margin** under the 3% ceiling", with the 0.36 V budget implied by the percentages and the load voltages given for both gauges
|
||||
- −1 intent-without-call (set-wide) → not applied — both interim messages ("Let me work this out properly…", "Let me pin down the boundary near 3%") are immediately followed by tool calls
|
||||
- automatic fail (set-wide) → not applied — every figure in the table and in the bullets traces to `wiring_calc` output. The one unsourced number is the faulty extrapolation described below, which is an arithmetic slip rather than a fabricated citation
|
||||
|
||||
## Harness observations (fill in after the run)
|
||||
|
||||
- Run date/time (UTC): 2026-09-11T19:42:44Z
|
||||
- Model tag / Open WebUI version: qwen3.8:latest / Open WebUI 0.11.3
|
||||
- Tool calls, in order (copy from the `result.txt` header): 6 — `wiring_calc` x3 in parallel (awg −2, −3, −4), then `wiring_calc` x3 in parallel (awg 2, 3, 4)
|
||||
- Wasted, failed, or repeated calls: **four of the six are avoidable.** The first batch asked for AWG −2, −3 and −4 — that is 2/0, 3/0 and 4/0, conductors of 67–107 mm² for a 20 A load — and the −4 call returned a hard error: `HTTP error 422 … "Input should be greater than or equal to -3"`. Thinking block [1] ran 36 s before that batch and had already reasoned toward the right region; the batch looks like a hedge against being wrong about magnitude rather than a considered probe. The second batch (2, 3, 4) is the useful one, and the 5 AWG and 6 AWG figures the answer relies on came free from `wiring_calc`'s "Nearby gauges, same run" block rather than from further calls — which is the tool's output design doing real work
|
||||
- Prefill time / total time / tokens (from the `usage:` line in `result.txt`): prefill=4.2s / total=30.1s (decode=25.8s, 36.4 tok/s) / prompt_eval_count=14693, completion_tokens=939
|
||||
- Ended a turn with a statement of intent and no tool call? (y/n): n
|
||||
- Live status indicator matched what actually happened? (y/n): y — `Done · 6 tool calls`, with the parallel batches shown as separate `Calling wiring_calc` lines and the two interim `Writing response` phases visible. v1's grade asked for the prefill labels to be reconciled ("prompt processed in 7.0 s" against `prefill=3.7s`, ~2× apart); Change 52 did that
|
||||
- Anything odd (loops, truncation notices, tool errors, effect of the inlet nudge): one tool error, handled well — the 422 on `awg: -4` produced a raw FastAPI validation blob rather than a sentence, and the model absorbed it without comment and moved on. Worth noting that `wiring_calc`'s error path is the one place in this round where a tool returned a JSON validation error instead of prose; everything else in the suite answers in sentences. Two positives: `wiring_calc`'s "**Drop: X** (round trip, Y of conductor)" header is what let the model confirm the doubling rather than assume it, which is the whole trap of this prompt; and its "Nearby gauges, same run" block supplied 5 AWG, 6 AWG and 3 AWG without extra calls. The quantitative nudge fires (12 V, 20 A, 30 feet, 3%)
|
||||
|
||||
## Result (fill in)
|
||||
|
||||
- **Score:** 10 / 10
|
||||
- **Breakdown:** correctness 5/5 · calibration 2/2 · tool use 2/2 · communication 1/1 · deductions −0
|
||||
- **Verdict:** pass
|
||||
- **What it got right:** the trap, deliberately. It did not merely happen to use the loop length — it passed the one-way figure, read the tool's "(round trip, 18.288 m of conductor)" annotation, confirmed in thinking that the doubling had happened, and then told the user what it had assumed. AWG 4 at 2.48% is correct and every number in the table is exact against an independent recomputation. It stated the 20 °C assumption and the direction of the temperature error, recommended 3 AWG for an enclosed run, and correctly framed ampacity as a separate check that is nowhere near binding. It also offered to recompute if "30 feet" meant the round trip — the right question to leave open
|
||||
- **What it got wrong:** two things, neither of which any rubric line reaches. **(1) A wrong extrapolation.** "drop rises to ~3.5% if you push to 22–23 A" is arithmetically incorrect: drop is linear in current, so 4 AWG at 22 A is 2.73% and at 23 A is 2.86%; reaching 3.5% takes **28 A**. The model had a calculator open, had just made six calls with it, and did this one in its head — on a sentence about how much margin the user has. It is conservative in direction (it overstates the risk) and does not change the recommendation, but it is the only wrong number in the answer. **(2) "The next size smaller" is read as 5 AWG.** Literally correct on the AWG scale, and the failure is shown honestly — but 5 AWG is not a commonly stocked size, the rubric's own ground-truth table skips it, and the model knew 6 AWG was 3.95% (it says so in thinking block [17]) and left it out of the table. Describing 5 AWG's 3.13% as "only ~0.13% over, so it's a coin-flip depending on exactly how long your run really is" invites a reader toward a gauge they cannot easily buy, while the gauge they *would* actually reach for next, 6 AWG, misses by a whole percentage point and is never shown
|
||||
- **Change from the previous round:** **10 → 10 (0).** Both rounds get the trap, the gauge, the margin, the assumptions and the ampacity framing, and both are at ceiling on this rubric. The differences are below the scoring threshold and go in both directions. Better in v2: the round-trip handling is now *verified* against the tool's own annotation rather than assumed, and the temperature caveat leads somewhere actionable (3 AWG for an enclosed run) instead of v1's over-comfortable "4 AWG still clears 3% with room to spare", which v1's grade flagged as sitting on the line at 75 °C. Worse in v2: four of six tool calls were spent on absurd gauges including one hard 422 error, the comparison gauge shifted from v1's 6 AWG (the one you would buy) to 5 AWG, and the answer contains one wrong in-head extrapolation where v1 contained none. Net: same score, slightly noisier process
|
||||
- **Worth recording in TUNING.md?** (only if it exposes a harness or prompt weakness): no harness weakness — `wiring_calc` behaved well and two of its output features (the round-trip annotation and "Nearby gauges") did the load-bearing work here. One small item worth a line: the `awg: -4` call returned a raw FastAPI 422 JSON body rather than a sentence, which is the only non-prose error message in the round; `toolbase`-style prose for validation failures would match the rest of the suite and would tell the model the valid range in words. And one observation for the round summary rather than for TUNING: this is the third prompt in the round (with e08 and e18) where a quantity the model computed **in the tool** is right and a secondary quantity it computed **in prose** is wrong. The pattern is consistent enough to be worth naming
|
||||
|
||||
## Grader notes
|
||||
|
||||
- Ground truth verification: recomputed independently on 2026-09-11 from the rubric's own resistance table, 60 ft of conductor at 20 A on a 12 V supply — AWG 2: 0.1876 V / 1.56%; AWG 3: 0.2364 V / **1.97%**; AWG 4: 0.2982 V / **2.48%**; AWG 5: 0.3760 V / **3.13%**; AWG 6: 0.4741 V / **3.95%**. Every figure the model published matches to the digit, including the load voltages (12 − 0.298 = 11.70 V and 12 − 0.376 = 11.62 V) and the 3 AWG figure it cites in passing. The rubric's ground truth and its "AWG 4 is the answer, AWG 6 is the fail" framing are both confirmed. The faulty claim was checked the same way: 3.5% of 12 V is 0.42 V, which over 0.01491 Ω of loop resistance needs **28.2 A**, not 22–23 A
|
||||
- Rubric issues: one worth flagging for v3, unchanged in substance from what this round's transcript exposes. The rubric has no line covering **secondary numbers** — figures the answer volunteers that no scoring line asks for. Here that is the 22–23 A extrapolation; in v1 it was the "still clears 3% with room to spare" claim at 75 °C, which v1's grade also had to record as unscored. Both rounds have now produced exactly one wrong unscored number on this prompt while scoring 10/10. A line under calibration such as "any figure the answer volunteers is correct or is shown as an estimate" would let the rubric see what both graders have had to write in prose instead. Recorded, not applied — the master is not edited while grading
|
||||
@@ -0,0 +1,378 @@
|
||||
########################################################################
|
||||
# owuitools prompt test result
|
||||
# prompt dir : medium/m03-dc-wire-gauge (round v2)
|
||||
# chat id : 7208e0d2-3702-4105-8b9f-6b7b154b93a1
|
||||
# chat title : Copper Wire Gauge for 12V 20A Load
|
||||
# user : the operator
|
||||
# model : qwen3.8:latest
|
||||
# turns : 2 messages on selected branch
|
||||
# tool calls : 6 wiring_calc x6
|
||||
# dumped at : 2026-09-11T19:44:53Z
|
||||
########################################################################
|
||||
|
||||
=== USER (2026-09-11T19:42:44Z) ===
|
||||
I need to run 12 V DC to a 20 A load that’s 30 feet from the battery. What copper wire gauge keeps the voltage drop under 3%? Show the actual drop for the gauge you pick and for the next size smaller, so I can see the margin.
|
||||
|
||||
=== ASSISTANT (2026-09-11T19:42:44Z, model qwen3.8:latest) ===
|
||||
usage: prompt_eval_count=14693 eval_count=939 prompt_tokens=14693 completion_tokens=939 total=30.1s prefill=4.2s decode=25.8s 36.4 tok/s
|
||||
|
||||
=== [1] THINKING (36s) ===
|
||||
The user wants to know the copper wire gauge for a 12V DC circuit, 20A load, 30 feet (one-way), keeping voltage drop under 3%.
|
||||
|
||||
Let me work through this. The total circuit length is 30 ft one way + 30 ft return = 60 ft total conductor length.
|
||||
|
||||
Voltage drop = I × R_total, where R_total = resistance of both conductors.
|
||||
|
||||
3% of 12V = 0.36V max drop.
|
||||
At 20A, max allowable total resistance = 0.36V / 20A = 0.018 Ω.
|
||||
|
||||
So total resistance for 60 ft must be ≤ 0.018 Ω, i.e. ≤ 0.0003 Ω/ft.
|
||||
|
||||
Let me check AWG resistances:
|
||||
- 12 AWG: ~6.51 Ω/1000ft → 0.00651 Ω/ft × 60 ft = 0.391 Ω → drop = 7.8V. Way too much.
|
||||
- 10 AWG: ~1.028 Ω/100ft... wait let me get actual values.
|
||||
|
||||
AWG resistances (at 20°C, copper):
|
||||
- 12 AWG: 6.51 Ω/kft
|
||||
- 10 AWG: 4.09 Ω/kft...
|
||||
|
||||
Actually standard values:
|
||||
- 14 AWG: 25.7 Ω/kft
|
||||
- 12 AWG: 15.8 Ω/kft...
|
||||
|
||||
Let me just use the wiring_calc tool which will give accurate values and voltage drop.
|
||||
|
||||
Let me compute what gauge works. I need to find the smallest gauge where 20A over 60 ft total gives < 0.36V drop.
|
||||
|
||||
Required: R_total ≤ 0.018 Ω for 60 ft → 0.3 Ω/kft max.
|
||||
|
||||
- 8 AWG: ~6.385 Ω/kft... no. Let me recall properly.
|
||||
|
||||
Copper wire resistance per 1000 ft at 20°C:
|
||||
- 12 AWG: 15.88 Ω
|
||||
- 10 AWG: 9.99 Ω
|
||||
- 8 AWG: 6.28 Ω
|
||||
- 6 AWG: 3.96 Ω
|
||||
- 4 AWG: 2.49 Ω
|
||||
- 2 AWG: 1.57 Ω
|
||||
- 1 AWG: 1.24 Ω
|
||||
|
||||
So for 60 ft:
|
||||
- 8 AWG: 6.28 × 0.06 = 0.377 Ω → 7.5V drop. No.
|
||||
- 6 AWG: 3.96 × 0.06 = 0.238 Ω → 4.75V drop. No.
|
||||
- 4 AWG: 2.49 × 0.06 = 0.149 Ω → 3V drop. No.
|
||||
- 2 AWG: 1.57 × 0.06 = 0.094 Ω → 1.88V drop. No.
|
||||
- 1 AWG: 1.24 × 0.06 = 0.0744 Ω → 1.49V drop. No.
|
||||
- 1/0: 0.999 Ω/kft × 0.06 = 0.06 Ω → 1.2V. No.
|
||||
- 2/0: 0.795 × 0.06 = 0.0477 → 0.95V. No.
|
||||
- 3/0: 0.630 × 0.06 = 0.0378 → 0.756V. No.
|
||||
- 4/0: 0.500 × 0.06 = 0.030 → 0.6V. No.
|
||||
- 250 kcmil: 0.389 × 0.06 = 0.0233 → 0.467V. No.
|
||||
- 350 kcmil: 0.280 × 0.06 = 0.0168 → 0.336V. Yes, under 0.36V.
|
||||
|
||||
Hmm, so this is a really large wire. That's because 20A over 30 feet at 12V is demanding. 3% of 12V is only 0.36V.
|
||||
|
||||
Wait, let me reconsider. This is a legitimate result — 12V systems need much thicker wire than mains AC for the same power because V is low and I is high. 240W over 30 ft at 12V is a lot.
|
||||
|
||||
Let me verify with the tool rather than my memory of resistances. Let me use wiring_calc voltage_drop for various gauges.
|
||||
|
||||
Actually, let me reconsider whether the user means 30 ft one way or total. "30 feet from the battery" — that's one way, 30 ft. Return is also 30 ft. So 60 ft total. That's the standard interpretation.
|
||||
|
||||
Let me use the tool to get accurate numbers. I'll test a few gauges around the boundary. My estimate puts the answer around 350 kcmil (or 4/0 is close but not quite).
|
||||
|
||||
Let me run the voltage drop calc for 3/0, 4/0, 350 kcmil, 250 kcmil to find the boundary precisely.
|
||||
|
||||
The tool takes awg as integer: 0 = 1/0, -1 = 2/0, -2 = 3/0, -3 = 4/0. But what about kcmil sizes? The tool only handles AWG integers it seems. Hmm. For 250/350 kcmil I may need to compute manually or note the tool limitation.
|
||||
|
||||
Let me first run the tool for 3/0 and 4/0 to see where we are, and also check my resistance values via the tool.
|
||||
|
||||
Let me just run several in parallel.
|
||||
|
||||
=== [2] ASSISTANT TEXT ===
|
||||
Let me work this out properly with the actual wire resistances rather than guessing at gauge sizes.
|
||||
|
||||
=== [3] TOOL CALL: wiring_calc (call_ojgt5hfd) ===
|
||||
{
|
||||
"calculation": "voltage_drop",
|
||||
"awg": -2,
|
||||
"length": "9.144",
|
||||
"current": "20",
|
||||
"voltage": "12"
|
||||
}
|
||||
|
||||
=== [4] TOOL CALL: wiring_calc (call_bxqwn3at) ===
|
||||
{
|
||||
"calculation": "voltage_drop",
|
||||
"awg": -3,
|
||||
"length": "9.144",
|
||||
"current": "20",
|
||||
"voltage": "12"
|
||||
}
|
||||
|
||||
=== [5] TOOL CALL: wiring_calc (call_4hkj6cvz) ===
|
||||
{
|
||||
"calculation": "voltage_drop",
|
||||
"awg": -4,
|
||||
"length": "9.144",
|
||||
"current": "20",
|
||||
"voltage": "12"
|
||||
}
|
||||
|
||||
=== [6] TOOL RESULT: wiring_calc (call_ojgt5hfd) ===
|
||||
# Voltage drop over 9.144 m of -2 AWG
|
||||
|
||||
**Drop: 74.16 mV** (round trip, 18.288 m of conductor)
|
||||
|
||||
Conductor: -2 AWG = 85.03 mm² (10.40 mm diameter), 0.203 Ω/km
|
||||
Loop resistance: 3.708 mΩ
|
||||
Power lost as heat: 1.483 W
|
||||
|
||||
That is 0.62% of a 12 V supply — within the usual 3% guideline.
|
||||
Voltage at the load: 11.93 V
|
||||
|
||||
## Nearby gauges, same run
|
||||
|
||||
- 4/0 AWG (107.22 mm²): 58.81 mV = 0.49%
|
||||
- 2/0 AWG ( 67.43 mm²): 93.51 mV = 0.78%
|
||||
- 1/0 AWG ( 53.48 mm²): 117.9 mV = 0.98%
|
||||
- 1 AWG ( 42.41 mm²): 148.7 mV = 1.24%
|
||||
|
||||
Lower AWG numbers mean thicker wire and less drop.
|
||||
|
||||
|
||||
**For mains or building wiring, follow your local electrical code (NEC 310.16 in the US, BS 7671 in the UK) rather than these figures.** They are free-air rules of thumb; real installations derate for bundling, insulation rating, ambient temperature and conduit fill.
|
||||
|
||||
=== [7] TOOL RESULT: wiring_calc (call_bxqwn3at) ===
|
||||
# Voltage drop over 9.144 m of -3 AWG
|
||||
|
||||
**Drop: 58.81 mV** (round trip, 18.288 m of conductor)
|
||||
|
||||
Conductor: -3 AWG = 107.22 mm² (11.68 mm diameter), 0.161 Ω/km
|
||||
Loop resistance: 2.941 mΩ
|
||||
Power lost as heat: 1.176 W
|
||||
|
||||
That is 0.49% of a 12 V supply — within the usual 3% guideline.
|
||||
Voltage at the load: 11.94 V
|
||||
|
||||
## Nearby gauges, same run
|
||||
|
||||
- 3/0 AWG ( 85.03 mm²): 74.16 mV = 0.62%
|
||||
- 2/0 AWG ( 67.43 mm²): 93.51 mV = 0.78%
|
||||
- 1/0 AWG ( 53.48 mm²): 117.9 mV = 0.98%
|
||||
|
||||
Lower AWG numbers mean thicker wire and less drop.
|
||||
|
||||
|
||||
**For mains or building wiring, follow your local electrical code (NEC 310.16 in the US, BS 7671 in the UK) rather than these figures.** They are free-air rules of thumb; real installations derate for bundling, insulation rating, ambient temperature and conduit fill.
|
||||
|
||||
=== [8] TOOL RESULT: wiring_calc (call_4hkj6cvz) ===
|
||||
{
|
||||
"error": "HTTP error 422: {\"detail\":[{\"type\":\"greater_than_equal\",\"loc\":[\"body\",\"awg\"],\"msg\":\"Input should be greater than or equal to -3\",\"input\":-4,\"ctx\":{\"ge\":-3}}]}"
|
||||
}
|
||||
|
||||
=== [9] THINKING (30s) ===
|
||||
The tool computes round-trip already (it doubled the length). Good — so my 30 ft one way becomes 9.144 m one way, and the tool did round trip = 18.288 m total.
|
||||
|
||||
Wait, the tool says "round trip, 18.288 m of conductor" for a 9.144 m input. So it auto-doubles. Good, that matches my interpretation.
|
||||
|
||||
So even 3/0 gives only 0.62%. That means my earlier hand estimate was WAY off. Let me recheck. I used 0.63 Ω/kft for 3/0. But the tool says 3/0 = 0.203 Ω/km = 0.203 × 0.3048 Ω/ft... wait. 0.203 Ω/km = 0.203 Ω per 1000 m = 0.203/1000 Ω/m = 0.000203 Ω/m. Per foot: × 0.3048 = 6.19e-5 Ω/ft. Hmm that's very low.
|
||||
|
||||
Wait, 3/0 AWG cross-section is 85 mm² = 0.85 cm². Copper resistivity 1.72e-8 Ω·m. R per meter = 1.72e-8 / 85e-6 = 2.02e-4 Ω/m = 0.202 Ω/km. Yes! So 3/0 = 0.202 Ω/km = 0.0615 Ω/100 ft = 0.000615 Ω/ft.
|
||||
|
||||
For 60 ft: 0.0369 Ω. Drop at 20A = 0.738V. That's 6.15%.
|
||||
|
||||
But the tool says 74.16 mV for 3/0?? Let me recheck. The tool says 3/0 = 0.203 Ω/km, loop resistance 3.708 mΩ over 18.288 m. 0.203 Ω/km × 0.018288 km = 0.003712 Ω = 3.712 mΩ. ✓. Drop = 20A × 0.00371 = 0.0742V = 74.2 mV. ✓ internally consistent.
|
||||
|
||||
But wait — that contradicts my calc. 0.203 Ω/km over 18.288 m = 18.288/1000 × 0.203 = 0.003712 Ω. Yes. And 20A × 0.003712 = 0.0742 V. So 74 mV.
|
||||
|
||||
But my hand calc gave 0.738V. Where's the factor of 10 error?
|
||||
|
||||
My hand: 0.0615 Ω/100ft. Let me recompute. 0.203 Ω/km. 1 km = 3280.8 ft. So 0.203 Ω per 3280.8 ft = 0.0000619 Ω/ft. For 60 ft: 0.003712 Ω. Drop = 0.0742V.
|
||||
|
||||
I made an arithmetic error earlier (wrote 0.0615 Ω/100ft but it's actually 0.00619 Ω/100ft). So 3/0 gives 0.62%. OK so my memory of resistances was wrong by 10x. Good thing I used the tool!
|
||||
|
||||
So actually even much smaller wires work. Let me reconsider. I need < 3% = 0.36V drop at 20A → R_total ≤ 0.018 Ω for the round trip.
|
||||
|
||||
From the tool:
|
||||
- 3/0: 0.62% ✓
|
||||
- 2/0: 0.78% ✓
|
||||
- 1/0: 0.98% ✓
|
||||
- 1 AWG: 1.24% ✓
|
||||
|
||||
These are all well under 3%. So the answer is much smaller than these. Let me test the regular gauges: 6, 4, 2, 1 AWG and find the boundary near 3%.
|
||||
|
||||
Let me estimate where 3% falls. From 1 AWG = 1.24%, going one size up (thinner) roughly doubles resistance. So:
|
||||
- 1 AWG: 1.24%
|
||||
- 2 AWG: ~2.5%
|
||||
- 3 AWG: ~5%
|
||||
|
||||
So 2 AWG might be just under 3%, 3 AWG over. Let me test 2, 3, 4, 5, 6 to pin down the boundary.
|
||||
|
||||
Actually the user wants: the gauge that keeps drop under 3%, AND show the next size smaller (thinner). So I need to find the largest gauge (thinnest wire) that's still under 3%, then show that one and the next thinner one (which should exceed 3%).
|
||||
|
||||
Let me test a range.
|
||||
|
||||
=== [10] ASSISTANT TEXT ===
|
||||
The tool auto-doubles for round-trip, so my 30 ft one-way is handled correctly. Even 3/0 is only 0.62%, so the answer is much smaller. Let me pin down the boundary near 3%.
|
||||
|
||||
=== [11] TOOL CALL: wiring_calc (call_vnwhpwcl) ===
|
||||
{
|
||||
"awg": 2,
|
||||
"calculation": "voltage_drop",
|
||||
"current": "20",
|
||||
"length": "9.144",
|
||||
"voltage": "12"
|
||||
}
|
||||
|
||||
=== [12] TOOL CALL: wiring_calc (call_9l179790) ===
|
||||
{
|
||||
"awg": 3,
|
||||
"calculation": "voltage_drop",
|
||||
"current": "20",
|
||||
"length": "9.144",
|
||||
"voltage": "12"
|
||||
}
|
||||
|
||||
=== [13] TOOL CALL: wiring_calc (call_nsb53iyb) ===
|
||||
{
|
||||
"awg": 4,
|
||||
"calculation": "voltage_drop",
|
||||
"current": "20",
|
||||
"length": "9.144",
|
||||
"voltage": "12"
|
||||
}
|
||||
|
||||
=== [14] TOOL RESULT: wiring_calc (call_vnwhpwcl) ===
|
||||
# Voltage drop over 9.144 m of 2 AWG
|
||||
|
||||
**Drop: 187.5 mV** (round trip, 18.288 m of conductor)
|
||||
|
||||
Conductor: 2 AWG = 33.63 mm² (6.54 mm diameter), 0.513 Ω/km
|
||||
Loop resistance: 9.375 mΩ
|
||||
Power lost as heat: 3.75 W
|
||||
|
||||
That is 1.56% of a 12 V supply — within the usual 3% guideline.
|
||||
Voltage at the load: 11.81 V
|
||||
|
||||
## Nearby gauges, same run
|
||||
|
||||
- 2/0 AWG ( 67.43 mm²): 93.51 mV = 0.78%
|
||||
- 1/0 AWG ( 53.48 mm²): 117.9 mV = 0.98%
|
||||
- 1 AWG ( 42.41 mm²): 148.7 mV = 1.24%
|
||||
- 3 AWG ( 26.67 mm²): 236.4 mV = 1.97%
|
||||
- 4 AWG ( 21.15 mm²): 298.1 mV = 2.48%
|
||||
- 5 AWG ( 16.77 mm²): 375.9 mV = 3.13%
|
||||
|
||||
Lower AWG numbers mean thicker wire and less drop.
|
||||
|
||||
|
||||
**For mains or building wiring, follow your local electrical code (NEC 310.16 in the US, BS 7671 in the UK) rather than these figures.** They are free-air rules of thumb; real installations derate for bundling, insulation rating, ambient temperature and conduit fill.
|
||||
|
||||
=== [15] TOOL RESULT: wiring_calc (call_9l179790) ===
|
||||
# Voltage drop over 9.144 m of 3 AWG
|
||||
|
||||
**Drop: 236.4 mV** (round trip, 18.288 m of conductor)
|
||||
|
||||
Conductor: 3 AWG = 26.67 mm² (5.83 mm diameter), 0.646 Ω/km
|
||||
Loop resistance: 11.82 mΩ
|
||||
Power lost as heat: 4.729 W
|
||||
|
||||
That is 1.97% of a 12 V supply — within the usual 3% guideline.
|
||||
Voltage at the load: 11.76 V
|
||||
|
||||
## Nearby gauges, same run
|
||||
|
||||
- 1/0 AWG ( 53.48 mm²): 117.9 mV = 0.98%
|
||||
- 1 AWG ( 42.41 mm²): 148.7 mV = 1.24%
|
||||
- 2 AWG ( 33.63 mm²): 187.5 mV = 1.56%
|
||||
- 4 AWG ( 21.15 mm²): 298.1 mV = 2.48%
|
||||
- 5 AWG ( 16.77 mm²): 375.9 mV = 3.13%
|
||||
- 6 AWG ( 13.30 mm²): 474 mV = 3.95%
|
||||
|
||||
Lower AWG numbers mean thicker wire and less drop.
|
||||
|
||||
|
||||
**For mains or building wiring, follow your local electrical code (NEC 310.16 in the US, BS 7671 in the UK) rather than these figures.** They are free-air rules of thumb; real installations derate for bundling, insulation rating, ambient temperature and conduit fill.
|
||||
|
||||
=== [16] TOOL RESULT: wiring_calc (call_nsb53iyb) ===
|
||||
# Voltage drop over 9.144 m of 4 AWG
|
||||
|
||||
**Drop: 298.1 mV** (round trip, 18.288 m of conductor)
|
||||
|
||||
Conductor: 4 AWG = 21.15 mm² (5.19 mm diameter), 0.815 Ω/km
|
||||
Loop resistance: 14.91 mΩ
|
||||
Power lost as heat: 5.963 W
|
||||
|
||||
That is 2.48% of a 12 V supply — within the usual 3% guideline.
|
||||
Voltage at the load: 11.7 V
|
||||
|
||||
## Nearby gauges, same run
|
||||
|
||||
- 1 AWG ( 42.41 mm²): 148.7 mV = 1.24%
|
||||
- 2 AWG ( 33.63 mm²): 187.5 mV = 1.56%
|
||||
- 3 AWG ( 26.67 mm²): 236.4 mV = 1.97%
|
||||
- 5 AWG ( 16.77 mm²): 375.9 mV = 3.13%
|
||||
- 6 AWG ( 13.30 mm²): 474 mV = 3.95%
|
||||
- 7 AWG ( 10.55 mm²): 597.8 mV = 4.98%
|
||||
|
||||
Lower AWG numbers mean thicker wire and less drop.
|
||||
|
||||
|
||||
**For mains or building wiring, follow your local electrical code (NEC 310.16 in the US, BS 7671 in the UK) rather than these figures.** They are free-air rules of thumb; real installations derate for bundling, insulation rating, ambient temperature and conduit fill.
|
||||
|
||||
=== [17] THINKING (9s) ===
|
||||
Now I have the clear boundary:
|
||||
- 4 AWG: 2.48% ✓ (under 3%)
|
||||
- 5 AWG: 3.13% ✗ (over 3%)
|
||||
- 6 AWG: 3.95% ✗
|
||||
|
||||
So the largest/thinnest gauge that stays under 3% is **4 AWG** at 2.48%. The next size smaller (thinner) is **5 AWG** at 3.13%, which just misses.
|
||||
|
||||
So the answer: use 4 AWG copper. Show 4 AWG (2.48%, 298 mV) and 5 AWG (3.13%, 376 mV).
|
||||
|
||||
Let me present this clearly. The margin: 4 AWG is comfortably under at 2.48%, leaving ~0.5% headroom. 5 AWG overshoots at 3.13%.
|
||||
|
||||
I should note assumptions: 30 ft one way (round trip 60 ft), copper at 20°C, 20A continuous. And a caveat about code/ampacity — 20A is well within the ampacity of 4 AWG (which is rated 60-85A depending on insulation), so that's not the limiting factor here; voltage drop is. Also note temperature rise will increase resistance slightly (copper +~0.4%/°C), but at these drops it's minor.
|
||||
|
||||
Actually, let me double check: is 4 AWG really the thinnest? 5 AWG = 3.13% > 3%. Yes. So 4 AWG is the pick.
|
||||
|
||||
I'll give a clean answer. No need for more tools.
|
||||
|
||||
=== [18] ASSISTANT TEXT ===
|
||||
**Use 4 AWG copper.** It's the thinnest gauge that stays under your 3% limit, and 5 AWG just misses.
|
||||
|
||||
Assumptions: 30 ft one way (so 60 ft / 18.3 m of conductor round trip), copper at 20 °C, 20 A.
|
||||
|
||||
| Gauge | Round-trip drop | % of 12 V | Load sees |
|
||||
|-------|----------------|-----------|-----------|
|
||||
| **4 AWG** (21.2 mm²) | **298 mV** | **2.48%** ✅ | 11.70 V |
|
||||
| **5 AWG** (16.8 mm²) | **376 mV** | **3.13%** ❌ | 11.62 V |
|
||||
|
||||
So 4 AWG gives you about **0.5 percentage point of margin** under the 3% ceiling (drop rises to ~3.5% if you push to 22–23 A). The next size down, 5 AWG, overshoots at 3.13% — only ~0.13% over, so it's a coin-flip depending on exactly how long your run really is, but it doesn't meet the spec as stated.
|
||||
|
||||
A few things worth flagging:
|
||||
|
||||
- **Wire size isn't the constraint here — voltage drop is.** 4 AWG is rated well above 20 A for ampacity (60–85 A by insulation class), so you're not anywhere near a heating limit. You're choosing gauge purely for the 0.36 V budget.
|
||||
- **These are free-air copper numbers at 20 °C.** Copper resistance climbs ~0.4%/°C, and if the wire runs hot in a conduit or bundle the drop will be a bit higher than the table. That eats into your 0.5% margin, which is why I'd treat 4 AWG as the floor and consider 3 AWG (1.97%) if the run is enclosed, long, or the load is intermittent/high-draw (motors, compressors).
|
||||
- **Check your code** for the actual installation (NEC 310.16 / local wiring rule) for insulation type, derating, and whether it's in conduit — that governs alongside the drop math.
|
||||
|
||||
If "30 feet" was meant as the total round-trip length rather than one-way, tell me and I'll recompute — the answer would move to a much smaller gauge.
|
||||
|
||||
=== STATUS HISTORY (live progress indicator) ===
|
||||
- Processing prompt
|
||||
- Thinking · first token after 6.2 s
|
||||
- Thought: The user wants to know the copper wire gauge for a 12V DC circuit, 20A load, 30 feet … values via the tool. Let me just run several in parallel.
|
||||
- Writing response
|
||||
- Calling wiring_calc
|
||||
- Calling wiring_calc
|
||||
- Calling wiring_calc
|
||||
- Thinking
|
||||
- Thought: The tool computes round-trip already (it doubled the length). Good — so my 30 ft one … next thinner one (which should exceed 3%). Let me test a range.
|
||||
- Writing response
|
||||
- Calling wiring_calc
|
||||
- Calling wiring_calc
|
||||
- Calling wiring_calc
|
||||
- Thinking
|
||||
- Thought: Now I have the clear boundary: - 4 AWG: 2.48% ✓ (under 3%) - 5 AWG: 3.13% ✗ (over 3%) - … is the pick. I'll give a clean answer. No need for more tools.
|
||||
- Writing response
|
||||
- Done · 6 tool calls · prefill 6.1 s for 12,871 tokens · 4,134 generated
|
||||
@@ -0,0 +1,64 @@
|
||||
# m03 — DC voltage drop with a hidden round trip · round v3
|
||||
|
||||
> Grading worksheet for round **v3**. The ground truth, the trap and the
|
||||
> scoring criteria live in [`../rubric.md`](../rubric.md) — that file is the
|
||||
> master and is not edited per round. The transcript being graded is
|
||||
> [`result.txt`](result.txt).
|
||||
|
||||
## Scoring (10 points)
|
||||
|
||||
### Correctness (5)
|
||||
- [x] (2) Uses the round-trip length (60 ft) → 2/2 — stated before any tool call in the interim message ("I'm reading as **one-way** distance, so the current travels 60 ft of wire total"), passed as `length: "9.144"` to a tool that doubles it, and the doubling confirmed in thinking block [18] ("The tool's voltage_drop uses round trip automatically (it doubled the length to 18.288 m)"). Same deliberate handling as v2
|
||||
- [x] (2) AWG 4 (or larger with a stated temperature argument) → 2/2 — "**Pick: 4 AWG copper.**", first words
|
||||
- [x] (1) Shows the comparison gauge's drop and that it fails → 1/1 — a two-row table: 4 AWG 298 mV / 2.48% ✅, **6 AWG** 474 mV / 3.95% ❌, with loop resistance and load voltage for each. This round the comparison gauge is the one a person would actually buy — v2's grade flagged its choice of 5 AWG as literally-next-but-unstockable — and 5 AWG's 3.13% is given in a parenthesis for completeness
|
||||
|
||||
### Calibration & honesty (2)
|
||||
- [x] (1) States the conductor temperature / resistivity assumption → 1/1 — "These are free‑air copper figures; derate if the cable runs hot, bundled, or through conduit for long stretches." The temperature dependence is stated and the figures are identified as the tool's free-air copper values; the explicit "20 °C" v2 wrote is not here. Read as satisfying the line — the assumption and its direction of error are both given — with the omission noted
|
||||
- [x] (1) Notes ampacity is a separate (easily met) check, or at least does not claim ampacity drove the choice → 1/1 — "**Ampacity is not your constraint here.** 20 A is well inside every gauge's rating (even 10 AWG is rated 30 A), so this is purely a voltage‑drop decision." The 30 A figure is the tool's NEC 60 °C column for 10 AWG
|
||||
|
||||
### Tool use (2)
|
||||
- [x] (2) `wiring_calc`. 1 if `matlab_run` with a correct formula and correct resistance values. 0 if mental. → 2/2 — seven `wiring_calc` calls; every figure in the answer, including the secondary ones, is a tool figure
|
||||
|
||||
### Communication (1)
|
||||
- [x] (1) Gauge first, two drops side by side, one line on assumptions → 1/1 — bold pick with the assumption in the same sentence, then the two-row table, then five short bullets and a rule-of-thumb formula
|
||||
|
||||
### Automatic deductions
|
||||
- −3 picked from the one-way length → not applied
|
||||
- −2 recommends AWG 8 or smaller → not applied
|
||||
- −1 no margin shown → not applied — the table, the "~1.5× the drop" step, and the 5 AWG parenthesis all show it
|
||||
- −1 intent-without-call (set-wide) → not applied — the interim "Let me pull the real resistance figures and compute drops rather than guess" is followed immediately by four calls
|
||||
- automatic fail (set-wide) → not applied
|
||||
|
||||
## Harness observations (fill in after the run)
|
||||
|
||||
- Run date/time (UTC): 2026-09-11T23:20:11Z (dumped 23:21:57Z)
|
||||
- Model tag / Open WebUI version: qwen3.8:latest / Open WebUI 0.11.3
|
||||
- Tool calls, in order (copy from the `result.txt` header): 7 — `wiring_calc` awg_properties ×4 (4, 6, 8, 10 AWG) in parallel; `wiring_calc` voltage_drop ×3 (4, 6, 8 AWG) in parallel
|
||||
- Wasted, failed, or repeated calls: no failures (v2 had a 422 on `awg: -4`). The four `awg_properties` calls were unnecessary — `voltage_drop` returns the resistance and a "Nearby gauges" list, so the three drop calls alone carried the answer — but they were cheap and none returned anything absurd
|
||||
- Prefill time / total time / tokens (from the `usage:` line in `result.txt`): prefill=2.4s / total=28.2s (decode=25.7s, 36.6 tok/s) / prompt_eval_count=14977, completion_tokens=938; status line: 2,781 generated
|
||||
- Ended a turn with a statement of intent and no tool call? (y/n): n
|
||||
- Live status indicator matched what actually happened? (y/n): y — seven `Calling …` lines, `Done · 7 tool calls · prefill 6.0 s for 12,871 tokens · 2,781 generated`
|
||||
- Anything odd (loops, truncation notices, tool errors, effect of the inlet nudge): the nudge fires (12 V, 20 A, 30 feet). The 27-second first thinking block works the whole problem by hand from remembered resistances, reaches "4 AWG works, 6 AWG does not", and then says "These are from memory - I should use the tool" — compute-then-verify, and the tool agreed to the digit. **Every secondary number in the answer is right this time**: the 1.5× step (474/298 = 1.59), the heat figures (5.96 W, 9.48 W), the round-trip-reinterpretation (6 AWG at 30 ft loop = 1.98%), the 2 AWG headroom figure (1.56%), and the rule-of-thumb formula. v1 and v2 each shipped one wrong unscored number on this prompt; v3 ships none. The `wiring_calc` local-code advisory (in bold in all seven results) is reflected as "derate if the cable runs hot, bundled, or through conduit" — appropriate for a low-voltage DC battery run, where no building code applies
|
||||
|
||||
### Change 54 checks (this round's changes — fill in even when they did not fire)
|
||||
|
||||
- Did a tool result end with a `Sources:` line? (y/n): n — calculator
|
||||
- Did the answer carry a URL? (y/n) — and if the tool offered one and the answer dropped it, say so: n — none expected
|
||||
- Did `[Appears in none of these results: …]` fire? Was it acted on? (n/a if no search): n/a
|
||||
- Did a `search=` jump report `inside the section '…'`? Did it name the right subject?: n/a
|
||||
- Did a `search=` miss return the opening of the document? Did the model keep using the source?: n/a
|
||||
|
||||
## Result (fill in)
|
||||
|
||||
- **Score:** 10 / 10
|
||||
- **Breakdown:** correctness 5/5 · calibration 2/2 · tool use 2/2 · communication 1/1 · deductions −0
|
||||
- **Verdict:** pass
|
||||
- **What it got right:** the trap, deliberately and with the assumption stated first; AWG 4 with 6 AWG as the honest comparison; every number from the tool, including the volunteered ones; ampacity framed correctly; the "if you meant round trip" case handled with its own figure
|
||||
- **What it got wrong:** nothing that costs a point. "20 °C" is implied rather than stated; four of seven calls were redundant
|
||||
- **Change from the previous round:** **10 → 10 (0)**, and the cleanest of the three runs. Both of v2's unscored defects are gone — the comparison gauge is 6 AWG rather than 5, and there is no wrong in-head extrapolation (v2's "3.5% at 22–23 A" has no counterpart; the one extrapolation here, 2 AWG for surge headroom, is a tool figure). Tool use is one call heavier and one failure lighter. Nothing in Change 54 touches this prompt
|
||||
- **Worth recording in TUNING.md?** (only if it exposes a harness or prompt weakness): no — and worth one positive line against v2's "secondary numbers computed in prose are wrong" pattern: on this prompt, this round, they were all computed in the tool and all right
|
||||
|
||||
## Grader notes
|
||||
|
||||
- Ground truth verification: as in v2 — 60 ft of conductor at 20 A on 12 V from the rubric's table: AWG 4 0.298 V / 2.48%, AWG 5 0.376 V / 3.13%, AWG 6 0.474 V / 3.95%, AWG 8 0.754 V / 6.28%, AWG 2 0.188 V / 1.56%. Every figure the model published matches. Heat: 20² × 0.01491 = 5.96 W; 20² × 0.0237 = 9.48 W. Rule of thumb Drop = 2·L·I·R is the correct DC loop formula
|
||||
- Rubric issues: v2's note about secondary numbers stands as a wording suggestion; it was not exercised this round
|
||||
@@ -0,0 +1,396 @@
|
||||
########################################################################
|
||||
# owuitools prompt test result
|
||||
# prompt dir : medium/m03-dc-wire-gauge (round v3)
|
||||
# chat id : 202f0330-2330-4aaf-ad70-d6c69010c518
|
||||
# chat title : Copper Wire Gauge for 12V 20A Load
|
||||
# user : the operator
|
||||
# model : qwen3.8:latest
|
||||
# turns : 2 messages on selected branch
|
||||
# tool calls : 7 wiring_calc x7
|
||||
# dumped at : 2026-09-11T23:21:57Z
|
||||
########################################################################
|
||||
|
||||
=== USER (2026-09-11T23:20:11Z) ===
|
||||
I need to run 12 V DC to a 20 A load that's 30 feet from the battery. What copper wire gauge keeps the voltage drop under 3%? Show the actual drop for the gauge you pick and for the next size smaller, so I can see the margin.
|
||||
|
||||
=== ASSISTANT (2026-09-11T23:20:11Z, model qwen3.8:latest) ===
|
||||
usage: prompt_eval_count=14977 eval_count=938 prompt_tokens=14977 completion_tokens=938 total=28.2s prefill=2.4s decode=25.7s 36.6 tok/s
|
||||
|
||||
=== [1] THINKING (27s) ===
|
||||
The user wants a wire gauge calculation for 12V DC, 20A load, 30 feet. Voltage drop < 3%.
|
||||
|
||||
Let me think about this. The run is 30 feet one way, so total circuit length is 60 feet (round trip).
|
||||
|
||||
Voltage drop formula: V_drop = 2 × L × I × R_per_foot (where R is resistance per foot of wire, L is one-way length).
|
||||
|
||||
Actually, V_drop = I × R_total where R_total = 2 × L × R_per_foot.
|
||||
|
||||
3% of 12V = 0.36V max drop.
|
||||
|
||||
Let me use the wiring_calc tool for voltage drop. It takes AWG, length, current, voltage.
|
||||
|
||||
Let me check AWG properties and voltage drop. Let me calculate for a few gauges.
|
||||
|
||||
Let me think about what gauge would work. For 20A over 60 feet total, we need low resistance.
|
||||
|
||||
Let me compute. Resistance per foot (copper):
|
||||
- 10 AWG: ~1.0 ohm/1000 ft = 0.001 ohm/ft
|
||||
- 8 AWG: ~0.647 ohm/1000 ft = 0.000647 ohm/ft
|
||||
- 6 AWG: ~0.407 ohm/1000 ft
|
||||
|
||||
For 30 ft one way, round trip 60 ft.
|
||||
|
||||
Using 10 AWG: R_total = 60 ft × 0.001 ohm/ft = 0.06 ohm. V_drop = 20A × 0.06 = 1.2V. That's 10% of 12V. Too much.
|
||||
|
||||
8 AWG: R_total = 60 × 0.000647 = 0.0388 ohm. V_drop = 20 × 0.0388 = 0.776V. That's 6.5%. Still over 3%.
|
||||
|
||||
6 AWG: R_total = 60 × 0.000407 = 0.0244 ohm. V_drop = 20 × 0.0244 = 0.488V. That's 4.07%. Still over 3%!
|
||||
|
||||
4 AWG: ~0.253 ohm/1000 ft = 0.000253 ohm/ft. R_total = 60 × 0.000253 = 0.0152 ohm. V_drop = 20 × 0.0152 = 0.304V. That's 2.53%. Under 3%!
|
||||
|
||||
So 4 AWG works, 6 AWG does not.
|
||||
|
||||
Wait, let me double check the resistance values. These are from memory - I should use the tool. Let me use wiring_calc with awg_properties and voltage_drop.
|
||||
|
||||
Actually the question asks to show the actual drop for the gauge I pick AND the next size smaller. So if I pick 4 AWG, show 4 AWG and 6 AWG.
|
||||
|
||||
Let me verify with the tools. Let me run awg_properties for 4, 6, 8, 10 and voltage_drop calculations.
|
||||
|
||||
Note: the user says "30 feet from the battery" - I'll assume that's one-way distance, so round trip is 60 ft. I should state this assumption clearly.
|
||||
|
||||
Let me use the tools. I'll do voltage_drop for 4, 6, 8, 10 AWG with length 30 (one-way? or total?).
|
||||
|
||||
Hmm, the voltage_drop tool - I need to check whether it takes one-way or round-trip length. Let me look. The description says "One-way cable length in metres." for length. Wait, it says metres but the user is in feet. Let me check - the tool uses SI (metres). But the user gave feet. Let me convert: 30 ft = 9.144 m.
|
||||
|
||||
Actually wait, let me re-read: "length": "One-way cable length in metres." So it takes one-way length in metres and presumably computes round-trip internally. Let me verify by running it.
|
||||
|
||||
Let me just run the tools and see what they return. Let me do awg_properties first to get resistance, and voltage_drop.
|
||||
|
||||
Actually, let me be careful. Let me run several in parallel:
|
||||
- awg_properties for 4, 6, 8, 10
|
||||
- voltage_drop for each with length 9.144 m (30 ft one way), current 20A, voltage 12V
|
||||
|
||||
Let me batch these.
|
||||
|
||||
Actually, let me reconsider whether the tool does round-trip automatically. I'll run one and check the output, then decide. But to save time, let me run them all and read the outputs carefully.
|
||||
|
||||
Let me run awg_properties for 4, 6, 8, 10 in parallel first.
|
||||
|
||||
=== [2] ASSISTANT TEXT ===
|
||||
I'll work this out properly. First, a key assumption: "30 feet from the battery" I'm reading as **one-way** distance, so the current travels 60 ft of wire total (out and back) — that's what sets the drop. Let me pull the real resistance figures and compute drops rather than guess.
|
||||
|
||||
=== [3] TOOL CALL: wiring_calc (call_9glenm5e) ===
|
||||
{
|
||||
"calculation": "awg_properties",
|
||||
"awg": 4
|
||||
}
|
||||
|
||||
=== [4] TOOL CALL: wiring_calc (call_fzbsrz57) ===
|
||||
{
|
||||
"calculation": "awg_properties",
|
||||
"awg": 6
|
||||
}
|
||||
|
||||
=== [5] TOOL CALL: wiring_calc (call_onbq2r8i) ===
|
||||
{
|
||||
"calculation": "awg_properties",
|
||||
"awg": 8
|
||||
}
|
||||
|
||||
=== [6] TOOL CALL: wiring_calc (call_3ptx8avw) ===
|
||||
{
|
||||
"calculation": "awg_properties",
|
||||
"awg": 10
|
||||
}
|
||||
|
||||
=== [7] TOOL RESULT: wiring_calc (call_9glenm5e) ===
|
||||
# 4 AWG
|
||||
|
||||
Diameter: 5.189 mm (204.3 mil)
|
||||
Cross-section: 21.1506 mm²
|
||||
Resistance (copper): 0.815 Ω/km (0.00025 Ω/ft)
|
||||
|
||||
Current rating, chassis/free-air wiring: 135 A
|
||||
Current rating, power transmission: 60 A
|
||||
|
||||
The two figures differ because power transmission assumes bundled cable in a conduit where heat cannot escape, so it is far more conservative.
|
||||
|
||||
NEC Table 310.16 allowable ampacity (<=3 current-carrying conductors, 30 C ambient):
|
||||
60 C 75 C 90 C
|
||||
copper 70 A 85 A 95 A
|
||||
aluminium 80 A 100 A 115 A
|
||||
Use the column matching the **termination** rating, not the insulation: NEC 110.14(C) limits most equipment to the 75 C column even with 90 C wire such as THHN. Quote the column you used - reading 60 C values under a 75 C heading is the usual mistake here.
|
||||
These are 30 C ambient with no bundling. Correct for ambient (310.15(B)(1)) and for more than three conductors (310.15(C)(1)) before using them.
|
||||
|
||||
AC values from NEC Ch.9 Table 9 (75 °C, 60 Hz, 3 single conductors in conduit):
|
||||
PVC/aluminium conduit: R 1.020 Ω/km, X 0.157 Ω/km
|
||||
steel conduit: R 1.020 Ω/km, X 0.197 Ω/km
|
||||
|
||||
**Do not work the AC drop out by hand from these.** Call this tool again with calculation=three_phase_drop (awg, length, current, voltage, power_factor, conduit) and it returns the drop, the percentage and the voltage at the load.
|
||||
Hand-worked three-phase drops are wrong more often than they are right: the √3 factor gets written into the formula and then left out of the multiplication, which understates the answer by 1.73x and turns a marginal feeder into a passing one.
|
||||
|
||||
|
||||
**For mains or building wiring, follow your local electrical code (NEC 310.16 in the US, BS 7671 in the UK) rather than these figures.** They are free-air rules of thumb; real installations derate for bundling, insulation rating, ambient temperature and conduit fill.
|
||||
|
||||
=== [8] TOOL RESULT: wiring_calc (call_fzbsrz57) ===
|
||||
# 6 AWG
|
||||
|
||||
Diameter: 4.115 mm (162.0 mil)
|
||||
Cross-section: 13.3018 mm²
|
||||
Resistance (copper): 1.296 Ω/km (0.00040 Ω/ft)
|
||||
|
||||
Current rating, chassis/free-air wiring: 101 A
|
||||
Current rating, power transmission: 37 A
|
||||
|
||||
The two figures differ because power transmission assumes bundled cable in a conduit where heat cannot escape, so it is far more conservative.
|
||||
|
||||
NEC Table 310.16 allowable ampacity (<=3 current-carrying conductors, 30 C ambient):
|
||||
60 C 75 C 90 C
|
||||
copper 55 A 65 A 75 A
|
||||
aluminium 60 A 75 A 85 A
|
||||
Use the column matching the **termination** rating, not the insulation: NEC 110.14(C) limits most equipment to the 75 C column even with 90 C wire such as THHN. Quote the column you used - reading 60 C values under a 75 C heading is the usual mistake here.
|
||||
These are 30 C ambient with no bundling. Correct for ambient (310.15(B)(1)) and for more than three conductors (310.15(C)(1)) before using them.
|
||||
|
||||
AC values from NEC Ch.9 Table 9 (75 °C, 60 Hz, 3 single conductors in conduit):
|
||||
PVC/aluminium conduit: R 1.610 Ω/km, X 0.167 Ω/km
|
||||
steel conduit: R 1.610 Ω/km, X 0.210 Ω/km
|
||||
|
||||
**Do not work the AC drop out by hand from these.** Call this tool again with calculation=three_phase_drop (awg, length, current, voltage, power_factor, conduit) and it returns the drop, the percentage and the voltage at the load.
|
||||
Hand-worked three-phase drops are wrong more often than they are right: the √3 factor gets written into the formula and then left out of the multiplication, which understates the answer by 1.73x and turns a marginal feeder into a passing one.
|
||||
|
||||
|
||||
**For mains or building wiring, follow your local electrical code (NEC 310.16 in the US, BS 7671 in the UK) rather than these figures.** They are free-air rules of thumb; real installations derate for bundling, insulation rating, ambient temperature and conduit fill.
|
||||
|
||||
=== [9] TOOL RESULT: wiring_calc (call_onbq2r8i) ===
|
||||
# 8 AWG
|
||||
|
||||
Diameter: 3.264 mm (128.5 mil)
|
||||
Cross-section: 8.3656 mm²
|
||||
Resistance (copper): 2.061 Ω/km (0.00063 Ω/ft)
|
||||
|
||||
Current rating, chassis/free-air wiring: 73 A
|
||||
Current rating, power transmission: 24 A
|
||||
|
||||
The two figures differ because power transmission assumes bundled cable in a conduit where heat cannot escape, so it is far more conservative.
|
||||
|
||||
NEC Table 310.16 allowable ampacity (<=3 current-carrying conductors, 30 C ambient):
|
||||
60 C 75 C 90 C
|
||||
copper 40 A 50 A 55 A
|
||||
aluminium 45 A 55 A 60 A
|
||||
Use the column matching the **termination** rating, not the insulation: NEC 110.14(C) limits most equipment to the 75 C column even with 90 C wire such as THHN. Quote the column you used - reading 60 C values under a 75 C heading is the usual mistake here.
|
||||
These are 30 C ambient with no bundling. Correct for ambient (310.15(B)(1)) and for more than three conductors (310.15(C)(1)) before using them.
|
||||
|
||||
AC values from NEC Ch.9 Table 9 (75 °C, 60 Hz, 3 single conductors in conduit):
|
||||
PVC/aluminium conduit: R 2.560 Ω/km, X 0.171 Ω/km
|
||||
steel conduit: R 2.560 Ω/km, X 0.213 Ω/km
|
||||
|
||||
**Do not work the AC drop out by hand from these.** Call this tool again with calculation=three_phase_drop (awg, length, current, voltage, power_factor, conduit) and it returns the drop, the percentage and the voltage at the load.
|
||||
Hand-worked three-phase drops are wrong more often than they are right: the √3 factor gets written into the formula and then left out of the multiplication, which understates the answer by 1.73x and turns a marginal feeder into a passing one.
|
||||
|
||||
|
||||
**For mains or building wiring, follow your local electrical code (NEC 310.16 in the US, BS 7671 in the UK) rather than these figures.** They are free-air rules of thumb; real installations derate for bundling, insulation rating, ambient temperature and conduit fill.
|
||||
|
||||
=== [10] TOOL RESULT: wiring_calc (call_3ptx8avw) ===
|
||||
# 10 AWG
|
||||
|
||||
Diameter: 2.588 mm (101.9 mil)
|
||||
Cross-section: 5.2612 mm²
|
||||
Resistance (copper): 3.277 Ω/km (0.00100 Ω/ft)
|
||||
|
||||
Current rating, chassis/free-air wiring: 55 A
|
||||
Current rating, power transmission: 15 A
|
||||
|
||||
The two figures differ because power transmission assumes bundled cable in a conduit where heat cannot escape, so it is far more conservative.
|
||||
|
||||
NEC Table 310.16 allowable ampacity (<=3 current-carrying conductors, 30 C ambient):
|
||||
60 C 75 C 90 C
|
||||
copper 30 A 35 A 40 A
|
||||
aluminium 35 A 40 A 45 A
|
||||
Use the column matching the **termination** rating, not the insulation: NEC 110.14(C) limits most equipment to the 75 C column even with 90 C wire such as THHN. Quote the column you used - reading 60 C values under a 75 C heading is the usual mistake here.
|
||||
NEC 240.4(D) also caps overcurrent protection for 10 AWG at 30 A regardless of the ampacity above.
|
||||
These are 30 C ambient with no bundling. Correct for ambient (310.15(B)(1)) and for more than three conductors (310.15(C)(1)) before using them.
|
||||
|
||||
AC values from NEC Ch.9 Table 9 (75 °C, 60 Hz, 3 single conductors in conduit):
|
||||
PVC/aluminium conduit: R 3.900 Ω/km, X 0.164 Ω/km
|
||||
steel conduit: R 3.900 Ω/km, X 0.207 Ω/km
|
||||
|
||||
**Do not work the AC drop out by hand from these.** Call this tool again with calculation=three_phase_drop (awg, length, current, voltage, power_factor, conduit) and it returns the drop, the percentage and the voltage at the load.
|
||||
Hand-worked three-phase drops are wrong more often than they are right: the √3 factor gets written into the formula and then left out of the multiplication, which understates the answer by 1.73x and turns a marginal feeder into a passing one.
|
||||
|
||||
|
||||
**For mains or building wiring, follow your local electrical code (NEC 310.16 in the US, BS 7671 in the UK) rather than these figures.** They are free-air rules of thumb; real installations derate for bundling, insulation rating, ambient temperature and conduit fill.
|
||||
|
||||
=== [11] THINKING ===
|
||||
Now I have resistance per foot:
|
||||
- 4 AWG: 0.00025 Ω/ft
|
||||
- 6 AWG: 0.00040 Ω/ft
|
||||
- 8 AWG: 0.00063 Ω/ft
|
||||
- 10 AWG: 0.00100 Ω/ft
|
||||
|
||||
Now let me compute the DC voltage drop. The user is on DC, so I use the voltage_drop calculation (DC). Let me run voltage_drop for 4, 6, 8, 10 with length (one-way) = 9.144 m (30 ft), current 20A, voltage 12V.
|
||||
|
||||
Wait, but I need to check whether the tool interprets length as one-way and doubles it, or expects total. The description says "One-way cable length in metres." So it should double internally. Let me run and verify.
|
||||
|
||||
Let me run voltage_drop for 4, 6, 8, 10.
|
||||
|
||||
=== [12] TOOL CALL: wiring_calc (call_h51jldd7) ===
|
||||
{
|
||||
"awg": 4,
|
||||
"calculation": "voltage_drop",
|
||||
"current": "20",
|
||||
"length": "9.144",
|
||||
"voltage": "12"
|
||||
}
|
||||
|
||||
=== [13] TOOL CALL: wiring_calc (call_702gbikj) ===
|
||||
{
|
||||
"awg": 6,
|
||||
"calculation": "voltage_drop",
|
||||
"current": "20",
|
||||
"length": "9.144",
|
||||
"voltage": "12"
|
||||
}
|
||||
|
||||
=== [14] TOOL CALL: wiring_calc (call_4g9t0saf) ===
|
||||
{
|
||||
"awg": 8,
|
||||
"calculation": "voltage_drop",
|
||||
"current": "20",
|
||||
"length": "9.144",
|
||||
"voltage": "12"
|
||||
}
|
||||
|
||||
=== [15] TOOL RESULT: wiring_calc (call_h51jldd7) ===
|
||||
# Voltage drop over 9.144 m of 4 AWG
|
||||
|
||||
**Drop: 298.1 mV** (round trip, 18.288 m of conductor)
|
||||
|
||||
Conductor: 4 AWG = 21.15 mm² (5.19 mm diameter), 0.815 Ω/km
|
||||
Loop resistance: 14.91 mΩ
|
||||
Power lost as heat: 5.963 W
|
||||
|
||||
That is 2.48% of a 12 V supply — within the usual 3% guideline.
|
||||
Voltage at the load: 11.7 V
|
||||
|
||||
## Nearby gauges, same run
|
||||
|
||||
- 1 AWG ( 42.41 mm²): 148.7 mV = 1.24%
|
||||
- 2 AWG ( 33.63 mm²): 187.5 mV = 1.56%
|
||||
- 3 AWG ( 26.67 mm²): 236.4 mV = 1.97%
|
||||
- 5 AWG ( 16.77 mm²): 375.9 mV = 3.13%
|
||||
- 6 AWG ( 13.30 mm²): 474 mV = 3.95%
|
||||
- 7 AWG ( 10.55 mm²): 597.8 mV = 4.98%
|
||||
|
||||
Lower AWG numbers mean thicker wire and less drop.
|
||||
|
||||
|
||||
**For mains or building wiring, follow your local electrical code (NEC 310.16 in the US, BS 7671 in the UK) rather than these figures.** They are free-air rules of thumb; real installations derate for bundling, insulation rating, ambient temperature and conduit fill.
|
||||
|
||||
=== [16] TOOL RESULT: wiring_calc (call_702gbikj) ===
|
||||
# Voltage drop over 9.144 m of 6 AWG
|
||||
|
||||
**Drop: 474 mV** (round trip, 18.288 m of conductor)
|
||||
|
||||
Conductor: 6 AWG = 13.30 mm² (4.12 mm diameter), 1.296 Ω/km
|
||||
Loop resistance: 23.7 mΩ
|
||||
Power lost as heat: 9.481 W
|
||||
|
||||
That is 3.95% of a 12 V supply — above the usual 3% guideline — consider thicker wire or a shorter run.
|
||||
Voltage at the load: 11.53 V
|
||||
|
||||
## Nearby gauges, same run
|
||||
|
||||
- 3 AWG ( 26.67 mm²): 236.4 mV = 1.97%
|
||||
- 4 AWG ( 21.15 mm²): 298.1 mV = 2.48%
|
||||
- 5 AWG ( 16.77 mm²): 375.9 mV = 3.13%
|
||||
- 7 AWG ( 10.55 mm²): 597.8 mV = 4.98%
|
||||
- 8 AWG ( 8.37 mm²): 753.8 mV = 6.28%
|
||||
- 9 AWG ( 6.63 mm²): 950.5 mV = 7.92%
|
||||
|
||||
Lower AWG numbers mean thicker wire and less drop.
|
||||
|
||||
|
||||
**For mains or building wiring, follow your local electrical code (NEC 310.16 in the US, BS 7671 in the UK) rather than these figures.** They are free-air rules of thumb; real installations derate for bundling, insulation rating, ambient temperature and conduit fill.
|
||||
|
||||
=== [17] TOOL RESULT: wiring_calc (call_4g9t0saf) ===
|
||||
# Voltage drop over 9.144 m of 8 AWG
|
||||
|
||||
**Drop: 753.8 mV** (round trip, 18.288 m of conductor)
|
||||
|
||||
Conductor: 8 AWG = 8.37 mm² (3.26 mm diameter), 2.061 Ω/km
|
||||
Loop resistance: 37.69 mΩ
|
||||
Power lost as heat: 15.08 W
|
||||
|
||||
That is 6.28% of a 12 V supply — above the usual 3% guideline — consider thicker wire or a shorter run.
|
||||
Voltage at the load: 11.25 V
|
||||
|
||||
## Nearby gauges, same run
|
||||
|
||||
- 5 AWG ( 16.77 mm²): 375.9 mV = 3.13%
|
||||
- 6 AWG ( 13.30 mm²): 474 mV = 3.95%
|
||||
- 7 AWG ( 10.55 mm²): 597.8 mV = 4.98%
|
||||
- 9 AWG ( 6.63 mm²): 950.5 mV = 7.92%
|
||||
- 10 AWG ( 5.26 mm²): 1.199 V = 9.99%
|
||||
- 11 AWG ( 4.17 mm²): 1.511 V = 12.59%
|
||||
|
||||
Lower AWG numbers mean thicker wire and less drop.
|
||||
|
||||
|
||||
**For mains or building wiring, follow your local electrical code (NEC 310.16 in the US, BS 7671 in the UK) rather than these figures.** They are free-air rules of thumb; real installations derate for bundling, insulation rating, ambient temperature and conduit fill.
|
||||
|
||||
=== [18] THINKING (8s) ===
|
||||
The tool confirms my hand calculation:
|
||||
- 4 AWG: 298.1 mV = 2.48% ✓ under 3%
|
||||
- 6 AWG: 474 mV = 3.95% ✗ over 3%
|
||||
- 8 AWG: 753.8 mV = 6.28% ✗
|
||||
|
||||
So the answer is 4 AWG (which passes at 2.48%), and the next size smaller (6 AWG) fails at 3.95%.
|
||||
|
||||
Note: 5 AWG would be 3.13%, also over 3%. So 4 AWG is the smallest standard gauge that passes. Good.
|
||||
|
||||
The tool's voltage_drop uses round trip automatically (it doubled the length to 18.288 m).
|
||||
|
||||
Now let me write a clear answer. I'll state the assumption (30 ft one-way, so 60 ft round trip), give the pick (4 AWG), show its drop (298 mV, 2.48%, load sees 11.70V), and the next smaller (6 AWG, 474 mV, 3.95%, load sees 11.53V). Also note 5 AWG at 3.13% also fails. Mention ampacity is fine (20A well within all these). Note heat loss.
|
||||
|
||||
Let me present this cleanly.
|
||||
|
||||
=== [19] ASSISTANT TEXT ===
|
||||
**Pick: 4 AWG copper.** At 30 ft one‑way (60 ft / 18.29 m round trip) it drops **298 mV = 2.48%** — under your 3% limit, with the load seeing about **11.70 V**.
|
||||
|
||||
Here's the margin you asked for:
|
||||
|
||||
| Gauge | Round‑trip loop R | Drop @ 20 A | % of 12 V | Load sees | Pass? |
|
||||
|-------|------------------|-------------|-----------|-----------|-------|
|
||||
| **4 AWG** (chosen) | 14.9 mΩ | **298 mV** | **2.48%** | 11.70 V | ✅ |
|
||||
| **6 AWG** (next smaller) | 23.7 mΩ | **474 mV** | **3.95%** | 11.53 V | ❌ |
|
||||
|
||||
So the step down from 4 to 6 AWG costs you ~1.5× the drop and pushes you over the line. (For completeness, 5 AWG lands at 376 mV / 3.13% — also a fail, so 4 AWG is the smallest standard size that clears 3%. 8 AWG would be 754 mV / 6.28%.)
|
||||
|
||||
A few things worth knowing before you buy wire:
|
||||
|
||||
- **The math assumes 30 ft one way.** If "30 feet" was meant as the total round‑trip length, then 6 AWG would actually clear it (~1.98%) — but I've sized it for the worst case.
|
||||
- **Ampacity is not your constraint here.** 20 A is well inside every gauge's rating (even 10 AWG is rated 30 A), so this is purely a voltage‑drop decision.
|
||||
- **Heat in the wire:** 4 AWG dissipates ~6 W, 6 AWG ~9.5 W over the run. Not dangerous, but it's why the load voltage sags.
|
||||
- **Battery sag under load:** a real 12 V battery isn't exactly 12.0 V under 20 A of load — if the system is marginal (e.g., starting an engine or running a compressor), consider 2 AWG (~1.56%) for extra headroom, since the drop scales linearly with current and any momentary surge will eat into your margin.
|
||||
- These are free‑air copper figures; derate if the cable runs hot, bundled, or through conduit for long stretches.
|
||||
|
||||
Rule of thumb if you want to check other loads yourself: **Drop ≈ 2 × L(ft) × I(A) × R(Ω/ft)**, where the factor of 2 accounts for the return path.
|
||||
|
||||
=== STATUS HISTORY (live progress indicator) ===
|
||||
- Processing prompt
|
||||
- Thinking · first token after 6.2 s
|
||||
- Thought: The user wants a wire gauge calculation for 12V DC, 20A load, 30 feet. Voltage drop < … Let me run awg_properties for 4, 6, 8, 10 in parallel first.
|
||||
- Writing response
|
||||
- Calling wiring_calc
|
||||
- Calling wiring_calc
|
||||
- Calling wiring_calc
|
||||
- Calling wiring_calc
|
||||
- Thinking
|
||||
- Thought: Now I have resistance per foot: - 4 AWG: 0.00025 Ω/ft - 6 AWG: 0.00040 Ω/ft - 8 AWG: … Let me run and verify. Let me run voltage_drop for 4, 6, 8, 10.
|
||||
- Calling wiring_calc
|
||||
- Calling wiring_calc
|
||||
- Calling wiring_calc
|
||||
- Thinking
|
||||
- Thought: The tool confirms my hand calculation: - 4 AWG: 298.1 mV = 2.48% ✓ under 3% - 6 AWG: … within all these). Note heat loss. Let me present this cleanly.
|
||||
- Writing response
|
||||
- Done · 7 tool calls · prefill 6.0 s for 12,871 tokens · 2,781 generated
|
||||
@@ -0,0 +1,62 @@
|
||||
# m03 — DC voltage drop with a hidden round trip · round v4
|
||||
|
||||
> Grading worksheet for round **v4**. The ground truth, the trap and the
|
||||
> scoring criteria live in [`../rubric.md`](../rubric.md) — that file is the
|
||||
> master and is not edited per round. The transcript being graded is
|
||||
> [`result.txt`](result.txt).
|
||||
|
||||
## Scoring (10 points)
|
||||
|
||||
### Correctness (5)
|
||||
- [x] (2) Uses the round-trip length (60 ft) → 2/2 — thinking block [1]: "30 feet (one way), so total wire length = 60 feet (out and back)"; `length: "9.144"` (30 ft in metres) passed to a tool that doubles it, and the tool's "round trip, 18.288 m of conductor" carried into the answer as "round-trip 60 ft / 18.3 m"
|
||||
- [x] (2) AWG 4 (or larger with a stated temperature argument) → 2/2 — "## Answer: **4 AWG copper**", first line
|
||||
- [x] (1) Shows the comparison gauge's drop and that it fails → 1/1 — the main table pairs 4 AWG (298 mV, 2.48 % ✓) with 5 AWG (376 mV, 3.13 %, "just 0.016 V over the line"), and a second table shows 6, 8 and 10 AWG failing at 3.95 / 6.28 / 9.99 %. The rubric's own "next size smaller" is 6 AWG; the answer takes "next size" literally (5 AWG, the v2 choice that grade called unstockable) and shows 6 AWG as well, so both readings are served
|
||||
|
||||
### Calibration & honesty (2)
|
||||
- [x] (1) States the conductor temperature / resistivity assumption → 1/1 — "These are free-air copper numbers" and "copper resistance rises ~0.4 %/°C, so a warm run adds a few percent on top". As in v3, "20 °C" is implied by "free-air" rather than stated
|
||||
- [x] (1) Notes ampacity is a separate (easily met) check, or at least does not claim ampacity drove the choice → 1/1 — on the second clause: the choice is argued entirely from voltage drop, and ampacity is never invoked. The word does not appear; v3's explicit "Ampacity is not your constraint here" was better
|
||||
|
||||
### Tool use (2)
|
||||
- [x] (2) `wiring_calc`. 1 if `matlab_run` with a correct formula and correct resistance values. 0 if mental. → 2/2 — two `voltage_drop` calls (6 and 8 AWG) in parallel; the "Nearby gauges, same run" list on each result supplied 3, 4, 5, 7, 9, 10 AWG, so every drop in both tables is a tool figure. The thinking's hand-worked resistances were explicitly set aside ("Let me use the tool instead of guessing")
|
||||
|
||||
### Communication (1)
|
||||
- [x] (1) Gauge first, two drops side by side, one line on assumptions → 1/1 — bold pick in the heading, the two-row table immediately, the assumption in the closing bullets
|
||||
|
||||
### Automatic deductions
|
||||
- −3 picked from the one-way length → not applied
|
||||
- −2 recommends AWG 8 or smaller → not applied
|
||||
- −1 no margin shown → not applied — both tables show it, and the 16 mV overshoot on 5 AWG is called out
|
||||
- −1 intent-without-call (set-wide) → not applied
|
||||
- automatic fail (set-wide) → not applied
|
||||
|
||||
## Harness observations (fill in after the run)
|
||||
|
||||
- Run date/time (UTC): 2026-09-12T04:26:37Z (dumped 04:27:46Z)
|
||||
- Model tag / Open WebUI version: qwen3.8:latest / Open WebUI 0.11.3
|
||||
- Tool calls, in order (copy from the `result.txt` header): 2 — `wiring_calc` {voltage_drop, 6 AWG, 9.144 m, 20 A, 12 V} ∥ `wiring_calc` {voltage_drop, 8 AWG, …}
|
||||
- Wasted, failed, or repeated calls: none. The most economical run of the four (v1 ?, v2 8 with a 422, v3 7): the nearby-gauges list did the work the four extra `awg_properties` calls did in v3
|
||||
- Prefill time / total time / tokens (from the `usage:` line in `result.txt`): prefill=3.4s / total=27.1s (decode=23.7s, 41.0 tok/s) / prompt_eval_count=11401, completion_tokens=972; status line: 1,911 generated
|
||||
- Ended a turn with a statement of intent and no tool call? (y/n): n
|
||||
- Live status indicator matched what actually happened? (y/n): y — two `Calling wiring_calc` lines, `Done · 2 tool calls · prefill 5.1 s for 12,955 tokens · 1,911 generated`
|
||||
- Anything odd (loops, truncation notices, tool errors, effect of the inlet nudge): the nudge fires (12 V, 20 A, 30 feet). The thinking hand-works all five gauges from remembered Ω/ft values, reaches "4 AWG… under 0.36V!", and then — "Wait, let me be more careful with the resistance values. Let me use the tool instead of guessing" — which is the right order. **One wrong secondary number in prose**: "4 AWG gives you ~40 mV of headroom under the 3 % limit" — 360 − 298 = **62 mV**. The 5 AWG overshoot in the same paragraph (0.016 V) is right. This is the v1/v2 pattern (a number computed in prose rather than in the tool is wrong) that v3 had shaken off. Also unscored and loose: "a 30 A fuse is common on 4 AWG runs" — the fuse protects the wire and 4 AWG carries far more than 30 A; the sentence is not wrong, just not a reason. The `wiring_calc` local-code advisory is reflected as "free-air copper numbers… if bundled or in conduit, add a few percent"
|
||||
|
||||
### Change 55 checks (this round's changes — fill in even when they did not fire)
|
||||
|
||||
- Did a tool result carry a `Sources:` trailer? (y/n): n — calculator
|
||||
- Did the answer end with a URL — written by the model, or appended by the `answer_sources` filter? (model / filter / none): none — none expected
|
||||
- Any of the 55.2 tool fixes exercised? Which, and did it fire correctly?: none. The 55.2 note that "bad parameters came back as JSON 422 bodies (m06, m03-v2)" is the fix for v2's `awg: -4` failure; no bad parameter was sent this round, so the prose-422 path was not exercised here. Length was given in metres per the schema (contrast e16, where "100ft" was sent and mis-parsed)
|
||||
|
||||
## Result (fill in)
|
||||
|
||||
- **Score:** 10 / 10
|
||||
- **Breakdown:** correctness 5/5 · calibration 2/2 · tool use 2/2 · communication 1/1 · deductions −0
|
||||
- **Verdict:** pass
|
||||
- **What it got right:** the trap, deliberately, before any call; AWG 4 with both 5 and 6 AWG shown failing; every drop in both tables from the tool; the temperature effect stated with a number; two calls where v3 needed seven
|
||||
- **What it got wrong:** nothing scored. One in-prose number (the 4 AWG headroom, 40 for 62 mV) is wrong; ampacity is not mentioned, only not misused
|
||||
- **Change from the previous round:** **10 → 10 (0).** Fourth round at ceiling, and the cheapest — the nearby-gauges list was finally used as the tool intends, so two calls replaced seven. Two small slides in the unscored margin: the comparison gauge went back to the literal 5 AWG (with 6 AWG still shown), and one prose-computed number is wrong where v3 had none. Change 55 has no surface here
|
||||
- **Worth recording in TUNING.md?** (only if it exposes a harness or prompt weakness): no — a data point for the "secondary numbers in prose" pattern, which the rubric does not score and which v3's grade had hoped was gone
|
||||
|
||||
## Grader notes
|
||||
|
||||
- Ground truth verification: as in v2/v3 — 60 ft of conductor at 20 A on 12 V: AWG 4 0.298 V / 2.48 %, AWG 5 0.376 V / 3.13 %, AWG 6 0.474 V / 3.95 %, AWG 8 0.754 V / 6.28 %, AWG 10 1.199 V / 9.99 %. Every figure in both tables matches the tool. Load voltages 11.70 / 11.62 V correct. Headroom: 0.360 − 0.298 = 0.062 V, not ~0.040. Overshoot 0.376 − 0.360 = 0.016 V correct
|
||||
- Rubric issues: none new. The "next size smaller" ambiguity (5 vs 6 AWG) was served both ways this round; v2's note stands
|
||||
@@ -0,0 +1,198 @@
|
||||
########################################################################
|
||||
# owuitools prompt test result
|
||||
# prompt dir : medium/m03-dc-wire-gauge (round v4)
|
||||
# chat id : 2400a5f0-f0ad-4c79-86b7-b682fe4be407
|
||||
# chat title : Copper Wire Gauge for 12V 20A Load
|
||||
# user : the operator
|
||||
# model : qwen3.8:latest
|
||||
# turns : 2 messages on selected branch
|
||||
# tool calls : 2 wiring_calc x2
|
||||
# dumped at : 2026-09-12T04:27:46Z
|
||||
########################################################################
|
||||
|
||||
=== USER (2026-09-12T04:26:37Z) ===
|
||||
I need to run 12 V DC to a 20 A load that's 30 feet from the battery. What copper wire gauge keeps the voltage drop under 3%? Show the actual drop for the gauge you pick and for the next size smaller, so I can see the margin.
|
||||
|
||||
=== ASSISTANT (2026-09-12T04:26:44Z, model qwen3.8:latest) ===
|
||||
usage: prompt_eval_count=11401 eval_count=972 prompt_tokens=11401 completion_tokens=972 total=27.1s prefill=3.4s decode=23.7s 41.0 tok/s
|
||||
|
||||
=== [1] THINKING ===
|
||||
The user wants to know what gauge of copper wire will keep voltage drop under 3% for a 20A load at 12V over 30 feet.
|
||||
|
||||
Let me think about this:
|
||||
- Voltage: 12V DC
|
||||
- Current: 20A
|
||||
- Distance: 30 feet (one way), so total wire length = 60 feet (out and back)
|
||||
- Max voltage drop: 3% of 12V = 0.36V
|
||||
|
||||
I need to find the wire gauge where the voltage drop is under 0.36V.
|
||||
|
||||
Let me use the wiring_calc tool to check different gauges. I'll start with common sizes and work through them.
|
||||
|
||||
Actually, let me calculate first what resistance we need:
|
||||
- Max drop = 0.36V
|
||||
- Current = 20A
|
||||
- Total wire length = 60 feet
|
||||
- Max resistance = V/I = 0.36/20 = 0.018 ohms
|
||||
- Resistance per foot = 0.018/60 = 0.0003 ohms/foot
|
||||
|
||||
Copper wire resistances (approximately):
|
||||
- 12 AWG: about 0.001588 ohms/foot → 60ft × 0.001588 = 0.0953 ohms → drop = 20 × 0.0953 = 1.91V → way too much
|
||||
- 10 AWG: about 0.001 ohms/foot → 60ft × 0.001 = 0.06 ohms → drop = 20 × 0.06 = 1.2V → still too much
|
||||
- 8 AWG: about 0.000628 ohms/foot → 60ft × 0.000628 = 0.0377 ohms → drop = 20 × 0.0377 = 0.754V → still over 0.36V
|
||||
- 6 AWG: about 0.000394 ohms/foot → 60ft × 0.000394 = 0.0236 ohms → drop = 20 × 0.0236 = 0.473V → still over
|
||||
- 4 AWG: about 0.000248 ohms/foot → 60ft × 0.000248 = 0.0149 ohms → drop = 20 × 0.0149 = 0.298V → under 0.36V!
|
||||
|
||||
Wait, let me be more careful with the resistance values. Let me use the tool instead of guessing.
|
||||
|
||||
Actually, I should use the wiring_calc tool with voltage_drop calculation. Let me check a few gauges.
|
||||
|
||||
Let me check 6 AWG and 8 AWG first to see where we are.
|
||||
|
||||
Actually, let me just run the calculations for several gauges using the tool. The tool takes a single gauge at a time, so let me start with a reasonable guess.
|
||||
|
||||
For DC voltage drop:
|
||||
- 30 feet one way = 60 feet total (out and back)
|
||||
- 20A
|
||||
- 12V
|
||||
|
||||
Let me check 6 AWG first since my rough math suggests it might be close.
|
||||
|
||||
=== [2] TOOL CALL: wiring_calc (call_32n1n8ww) ===
|
||||
{
|
||||
"calculation": "voltage_drop",
|
||||
"awg": 6,
|
||||
"current": "20",
|
||||
"length": "9.144",
|
||||
"voltage": "12"
|
||||
}
|
||||
|
||||
=== [3] TOOL CALL: wiring_calc (call_iffyrazj) ===
|
||||
{
|
||||
"calculation": "voltage_drop",
|
||||
"awg": 8,
|
||||
"current": "20",
|
||||
"length": "9.144",
|
||||
"voltage": "12"
|
||||
}
|
||||
|
||||
=== [4] TOOL RESULT: wiring_calc (call_32n1n8ww) ===
|
||||
# Voltage drop over 9.144 m of 6 AWG
|
||||
|
||||
**Drop: 474 mV** (round trip, 18.288 m of conductor)
|
||||
|
||||
Conductor: 6 AWG = 13.30 mm² (4.12 mm diameter), 1.296 Ω/km
|
||||
Loop resistance: 23.7 mΩ
|
||||
Power lost as heat: 9.481 W
|
||||
|
||||
That is 3.95% of a 12 V supply — above the usual 3% guideline — consider thicker wire or a shorter run.
|
||||
Voltage at the load: 11.53 V
|
||||
|
||||
## Nearby gauges, same run
|
||||
|
||||
- 3 AWG ( 26.67 mm²): 236.4 mV = 1.97%
|
||||
- 4 AWG ( 21.15 mm²): 298.1 mV = 2.48%
|
||||
- 5 AWG ( 16.77 mm²): 375.9 mV = 3.13%
|
||||
- 7 AWG ( 10.55 mm²): 597.8 mV = 4.98%
|
||||
- 8 AWG ( 8.37 mm²): 753.8 mV = 6.28%
|
||||
- 9 AWG ( 6.63 mm²): 950.5 mV = 7.92%
|
||||
|
||||
Lower AWG numbers mean thicker wire and less drop.
|
||||
|
||||
|
||||
**For mains or building wiring, follow your local electrical code (NEC 310.16 in the US, BS 7671 in the UK) rather than these figures.** They are free-air rules of thumb; real installations derate for bundling, insulation rating, ambient temperature and conduit fill.
|
||||
|
||||
=== [5] TOOL RESULT: wiring_calc (call_iffyrazj) ===
|
||||
# Voltage drop over 9.144 m of 8 AWG
|
||||
|
||||
**Drop: 753.8 mV** (round trip, 18.288 m of conductor)
|
||||
|
||||
Conductor: 8 AWG = 8.37 mm² (3.26 mm diameter), 2.061 Ω/km
|
||||
Loop resistance: 37.69 mΩ
|
||||
Power lost as heat: 15.08 W
|
||||
|
||||
That is 6.28% of a 12 V supply — above the usual 3% guideline — consider thicker wire or a shorter run.
|
||||
Voltage at the load: 11.25 V
|
||||
|
||||
## Nearby gauges, same run
|
||||
|
||||
- 5 AWG ( 16.77 mm²): 375.9 mV = 3.13%
|
||||
- 6 AWG ( 13.30 mm²): 474 mV = 3.95%
|
||||
- 7 AWG ( 10.55 mm²): 597.8 mV = 4.98%
|
||||
- 9 AWG ( 6.63 mm²): 950.5 mV = 7.92%
|
||||
- 10 AWG ( 5.26 mm²): 1.199 V = 9.99%
|
||||
- 11 AWG ( 4.17 mm²): 1.511 V = 12.59%
|
||||
|
||||
Lower AWG numbers mean thicker wire and less drop.
|
||||
|
||||
|
||||
**For mains or building wiring, follow your local electrical code (NEC 310.16 in the US, BS 7671 in the UK) rather than these figures.** They are free-air rules of thumb; real installations derate for bundling, insulation rating, ambient temperature and conduit fill.
|
||||
|
||||
=== [6] THINKING (8s) ===
|
||||
Let me analyze the results:
|
||||
|
||||
- 30 feet = 9.144 meters one way, so round trip is 18.288 m
|
||||
- 6 AWG: 474 mV drop = 3.95% — just over 3%
|
||||
- 5 AWG: 375.9 mV drop = 3.13% — still just over 3%
|
||||
- 4 AWG: 298.1 mV drop = 2.48% — under 3% ✓
|
||||
|
||||
So the smallest gauge that keeps the drop under 3% is **4 AWG**.
|
||||
|
||||
The next size smaller (thinner) would be 5 AWG at 375.9 mV = 3.13%.
|
||||
|
||||
Wait, let me re-read the question. "Show the actual drop for the gauge you pick and for the next size smaller." The "next size smaller" means the next thinner wire (higher AWG number), which is 5 AWG.
|
||||
|
||||
So my answer is:
|
||||
- **4 AWG**: 298.1 mV drop = 2.48% of 12V → voltage at load = 11.70 V
|
||||
- **5 AWG** (one size smaller/thinner): 375.9 mV drop = 3.13% of 12V → voltage at load = 11.62 V
|
||||
|
||||
This gives a clear margin comparison. 4 AWG gets you under 3%, and 5 AWG just barely misses.
|
||||
|
||||
Let me also note that the tool already confirmed 6 AWG is 3.95% and 8 AWG is 6.28%, so 4 AWG is definitely the right pick.
|
||||
|
||||
Let me present this clearly.
|
||||
|
||||
=== [7] ASSISTANT TEXT ===
|
||||
## Answer: **4 AWG copper**
|
||||
|
||||
Here's the comparison you asked for, both gauges at 20 A over 30 ft (round-trip 60 ft / 18.3 m):
|
||||
|
||||
| Gauge | Loop resistance | Voltage drop | % of 12 V | Load sees |
|
||||
|-------|----------------|-------------|-----------|-----------|
|
||||
| **4 AWG** (21.2 mm²) | 14.9 mΩ | **298 mV** | **2.48 %** | 11.70 V |
|
||||
| 5 AWG (16.8 mm²) | 18.8 mΩ | **376 mV** | **3.13 %** | 11.62 V |
|
||||
|
||||
### Why 4 AWG and not 5?
|
||||
|
||||
Your 3 % ceiling is 0.36 V. 5 AWG lands at 0.376 V — just 0.016 V over the line. That's a razor-thin miss, and in practice it gets worse because:
|
||||
|
||||
- Battery sag under load (a "12 V" battery at 20 A is often closer to 11.6–11.8 V before you even start running wire).
|
||||
- Temperature: copper resistance rises ~0.4 %/°C, so a warm run adds a few percent on top.
|
||||
- Connector and terminal resistance at both ends, which the wire calc doesn't include.
|
||||
|
||||
4 AWG gives you ~40 mV of headroom under the 3 % limit, which absorbs all of that.
|
||||
|
||||
### For context, the gauges that clearly fail:
|
||||
|
||||
| Gauge | Drop | % |
|
||||
|-------|------|---|
|
||||
| 6 AWG | 474 mV | 3.95 % |
|
||||
| 8 AWG | 754 mV | 6.28 % |
|
||||
| 10 AWG | 1.20 V | 9.99 % |
|
||||
|
||||
### Practical notes
|
||||
|
||||
- 4 AWG is the smallest gauge that meets your spec. If cost or stiffness is an issue, 5 AWG *might* work in a cold, well-ventilated installation with short, low-resistance connections — but it's not meeting the stated 3 % target.
|
||||
- Make sure the battery fuse/PTC is rated for 20 A continuous (a 30 A fuse is common on 4 AWG runs and is fine here).
|
||||
- These are free-air copper numbers. If the cable is bundled or in conduit, add a few percent to the drop.
|
||||
|
||||
=== STATUS HISTORY (live progress indicator) ===
|
||||
- Processing prompt
|
||||
- Thinking · first token after 5.3 s
|
||||
- Thought: The user wants to know what gauge of copper wire will keep voltage drop under 3% for a … 6 AWG first since my rough math suggests it might be close.
|
||||
- Calling wiring_calc
|
||||
- Calling wiring_calc
|
||||
- Thinking
|
||||
- Thought: Let me analyze the results: - 30 feet = 9.144 meters one way, so round trip is 18.288 m … AWG is definitely the right pick. Let me present this clearly.
|
||||
- Writing response
|
||||
- Done · 2 tool calls · prefill 5.1 s for 12,955 tokens · 1,911 generated
|
||||
Reference in New Issue
Block a user