# m03 — DC voltage drop with a hidden round trip

| | |
|---|---|
| **Difficulty** | medium |
| **Domain** | electrical engineering |
| **Probes** | `wiring_calc`; the round-trip length trap; stating the temperature assumption |
| **Tools expected** | `wiring_calc` |
| **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. |

## Ground truth

3% of 12 V = 0.36 V → max loop resistance 0.018 Ω over 60 ft.

| AWG | Ω/kft @20 °C | drop (60 ft, 20 A) | % | @75 °C |
|---|---|---|---|---|
| 2 | 0.1563 | 0.19 V | 1.6% | 1.9% |
| 3 | 0.1970 | 0.24 V | 2.0% | 2.4% |
| **4** | 0.2485 | **0.30 V** | **2.5%** | 3.0% (borderline) |
| 6 | 0.3951 | 0.47 V | 3.95% | 4.8% |
| 8 | 0.6282 | 0.75 V | 6.3% | 7.6% |

- Expected answer: **AWG 4** (2.5% at 20 °C); the next size smaller, **AWG 6**, fails at ~4%.
- 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.
- 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.

## Scoring (10 points)

### Correctness (5)
- [ ] (2) Uses the round-trip length (60 ft)
- [ ] (2) AWG 4 (or larger with a stated temperature argument)
- [ ] (1) Shows the comparison gauge's drop and that it fails

### Calibration & honesty (2)
- [ ] (1) States the conductor temperature / resistivity assumption
- [ ] (1) Notes ampacity is a separate (easily met) check, or at least does not claim ampacity drove the choice

### Tool use (2)
- [ ] (2) `wiring_calc`. 1 if `matlab_run` with a correct formula and correct resistance values. 0 if mental.

### Communication (1)
- [ ] (1) Gauge first, two drops side by side, one line on assumptions

### Automatic deductions
- −3 picked from the one-way length
- −2 recommends AWG 8 or smaller
- −1 no margin shown
- −1 intent-without-call (set-wide)
- automatic fail (set-wide)

## Grading

One worksheet per round, alongside that round's transcript:

- `v1/grade.md` · `v1/result.txt` — first round (baseline)
- `v2/grade.md` · `v2/result.txt` — second round

Copy the scoring skeleton above into a new round's `grade.md` to add one.