{
  "schemaVersion": 1,
  "id": "series-rlc-cancellation",
  "title": "Series RLC reactance changes sign through resonance",
  "kind": "series-rlc",
  "inputs": {
    "r": 0.02,
    "l": 1e-09,
    "c": 1e-07
  },
  "inputUnits": {
    "r": "ohm",
    "l": "H",
    "c": "F"
  },
  "checks": [
    {
      "metric": "resonantReal",
      "expected": 0.02,
      "absoluteTolerance": 1e-10,
      "unit": "ohm",
      "derivation": "At ω0=1/sqrt(LC), reactive terms cancel and Z=R."
    },
    {
      "metric": "resonantImag",
      "expected": 0.0,
      "absoluteTolerance": 1e-10,
      "unit": "ohm",
      "derivation": "Inductor and capacitor reactances are equal and opposite."
    },
    {
      "metric": "halfFrequencyImag",
      "expected": -0.15,
      "absoluteTolerance": 1e-10,
      "unit": "ohm",
      "derivation": "sqrt(L/C)=.1 Ω; at half resonance X=.1(.5−2)=−.15 Ω."
    },
    {
      "metric": "doubleFrequencyImag",
      "expected": 0.15,
      "absoluteTolerance": 1e-10,
      "unit": "ohm",
      "derivation": "At twice resonance X=.1(2−.5)=+.15 Ω."
    }
  ],
  "evidence": {
    "type": "analytical",
    "provenance": "First-principles network limits or algebraic reduction of the declared teaching loop, independent of production numerical output."
  },
  "prediction": "Does the capacitor branch remain capacitive above self-resonance?",
  "explanation": "No. The series branch is capacitive below resonance, resistive at resonance, and inductive above it.",
  "limitations": [
    "Lumped series RLC; no bias, temperature, aging or distributed behavior.",
    "This is a branch-level reference rather than a named-part capacitor model."
  ],
  "relatedPage": "/topics/power-integrity/real-capacitors.html",
  "availability": "helper-only"
}