Source: https://guthlabs.ai/docs/instruments/pcb-trace-resistance-voltage-drop/mechanism/

instrument mechanism / verified-clean

# PCB Trace Resistance & Voltage Drop mechanism

The inspectable method record for PCB Trace Resistance & Voltage Drop, kept separate from implementation and qualification.

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## Model scope

The core rectangular-trace resistance equation is correct under the stated SI-unit and uniform-copper assumptions. Review is required because input units, temperature treatment, and explicit Vdrop/power formulas are unspecified, while those outputs are claimed.

- The resistance formula R=ρL/(t·w) is standard for a uniform rectangular copper trace, but the specification does not explicitly define the formulas for the other claimed outputs: Vdrop=I·R and power dissipated=P=I²·R=Vdrop·I.

- The specification does not state whether copper resistivity is fixed at a reference temperature or corrected for temperature; copper resistance changes materially with temperature.

- The specification does not define how length and width units are supplied or converted before applying the SI-form resistance formula.

## Units and conventions

- Test vectors use copper resistivity ρ=1.724×10^-8 Ω·m at 20°C.

- Length is in metres, width is in metres, and copper thickness is in metres when evaluating R=ρL/(t·w).

- Copper weight is in oz/ft², with 1 oz copper thickness treated as 1.37 mil=34.798 μm=34.798×10^-6 m; thickness t=(copper weight)×34.798×10^-6 m.

- Current is in amperes, resistance is in ohms, voltage drop is in volts, and power is in watts.

- The trace is assumed to be uniform, solid copper with no vias, connectors, joints, parallel paths, plating contribution, or additional contact resistance.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "length": {
      "value": 0.1,
      "unit": "m"
    },
    "width": {
      "value": 1,
      "unit": "mm"
    },
    "copper_weight": {
      "value": 1,
      "unit": "oz/ft^2"
    },
    "current": {
      "value": 2,
      "unit": "A"
    }
  },
  "expected_outputs": {
    "R": {
      "value": 0.0495431,
      "unit": "ohm"
    },
    "Vdrop": {
      "value": 0.0990862,
      "unit": "V"
    },
    "power_dissipated": {
      "value": 0.198172,
      "unit": "W"
    }
  },
  "working": "t=1×34.798×10^-6=3.4798×10^-5 m; w=1 mm=1.0×10^-3 m; numerator=ρL=(1.724×10^-8)(0.1)=1.724×10^-9; denominator=t·w=(3.4798×10^-5)(1.0×10^-3)=3.4798×10^-8; R=1.724×10^-9/(3.4798×10^-8)=0.0495431 Ω; Vdrop=I·R=2×0.0495431=0.0990862 V; P=I²R=2²×0.0495431=4×0.0495431=0.198172 W."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

The zero-width vector produces an undefined division and must be rejected. The specification also leaves signed-versus-magnitude voltage drop and the mil thickness convention vulnerable to interpretation errors; a permissive implementation could return NaN, Infinity, or a result differing by about 39.37 times.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/pcb-trace-resistance-voltage-drop/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/pcb-trace-resistance-voltage-drop/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/pcb-trace-resistance-voltage-drop/qualification/>)

## Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

- `VERIFIED_LEDGER.json`

- `evidence-tranche4/tranche4-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`