Mutual Inductance / Coupled Coil Calculator mechanism

Model scope

The formulas M = k*sqrt(L1*L2), Ltotal(aiding) = L1 + L2 + 2M, and Ltotal(opposing) = L1 + L2 - 2M are standard under the stated unit and polarity assumptions. Review is required because the input-unit policy, k sign/range, physical constraints, and honest user-facing limitations are not specified.

• The algebraic formulas are standard, but the sign convention for k is unspecified. If k is a nonnegative coupling magnitude, M is normally reported as a magnitude and the aiding/opposing choice supplies the sign. If k may be signed, the interaction between the sign of M and the aiding/opposing mode must be defined explicitly.
• The specification does not state that L1 and L2 must be positive finite self-inductances, or that the coupling coefficient must satisfy 0 <= k <= 1 for passive coupled coils.

Units and conventions

• L1 and L2 must use the same inductance unit before multiplication or addition; M and Ltotal use that same unit.
• k is dimensionless.
• sqrt(L1*L2) has the same inductance unit as L1 and L2 because both inductances use the same unit.
• The test vector with mixed H and mH explicitly converts all values to henries before calculation.
• Aiding and opposing refer to the relative winding-polarity/current-reference convention, not merely a numerical label.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "L1": 0.004,
    "L1_unit": "H",
    "L2": 0.009,
    "L2_unit": "H",
    "k": 0.5,
    "connection": "series aiding"
  },
  "expected_outputs": {
    "M": 0.003,
    "M_unit": "H",
    "Ltotal": 0.019,
    "Ltotal_unit": "H"
  },
  "working": "M = k*sqrt(L1*L2) = 0.5*sqrt(0.004*0.009) = 0.5*sqrt(0.000036) = 0.5*0.006 = 0.003 H. Ltotal(aiding) = L1 + L2 + 2M = 0.004 + 0.009 + 2(0.003) = 0.004 + 0.009 + 0.006 = 0.019 H."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The specification leaves the handling of negative inductances, signed coupling coefficients, and invalid square-root arguments unspecified. It can also produce different results if the sign of k and the aiding/opposing switch are both used to encode winding orientation.

Other records

Sources and evidence

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

• VERIFIED_LEDGER.json
• evidence-tranche5/tranche5-results.json
• BOUNDARY_HAZARD_CATALOG.json