{
  "schemaVersion": 1,
  "id": "pdn-shared-rl-dc-limit",
  "title": "Two loads on a shared R-L path: the DC limit is resistance only",
  "kind": "pdn-shared-rl",
  "availability": "helper-only",
  "inputs": {
    "node2Current": 2,
    "node1Current": 1,
    "sharedResistance": 0.3,
    "finalLinkResistance": 0.3
  },
  "inputUnits": {
    "node2Current": "A",
    "node1Current": "A",
    "sharedResistance": "ohm",
    "finalLinkResistance": "ohm"
  },
  "prediction": "Two loads draw 2 A and 1 A from different nodes of one R-L chain. Predict each node’s steady rail deviation before the inductances are considered.",
  "explanation": "At DC the inductances carry no voltage, so each observation is minus the sum of R*I along the paths the two currents actually share. Both currents pass through the source-to-node-1 link; only the node-2 current traverses the final one. That gives -1.5 V at node 2 and -0.9 V at node 1 — numbers that depend on which path is shared, which is the whole point of a two-load model and is invisible in a single-load one.",
  "limitations": [
    "Helper only: there is no exact Lab C scenario that reproduces this network, and inventing one would imply a replay the page cannot perform.",
    "The DC limit says nothing about the transient, which is checked separately against a causal reference in tests/check-pdn-multi.js."
  ],
  "evidence": {
    "type": "analytical",
    "provenance": "KCL and KVL on the shared paths recorded in tests/fixtures/pdn/shared-rl-tone.json, whose derivation field states them. Evaluated here through the public K.pdnMultiTransient path with the currents held constant, so the inductive terms vanish."
  },
  "relatedPage": "/topics/labs/pdn-chain.html",
  "checks": [
    {
      "metric": "dcNode2",
      "expected": -1.5,
      "absoluteTolerance": 1e-09,
      "unit": "V",
      "derivation": "-(0.6*2 + 0.3*1) = -1.5 V: both currents through 0.3 ohm, node-2 current also through the 0.3 ohm final link, counted as the fixture records it."
    },
    {
      "metric": "dcNode1",
      "expected": -0.9,
      "absoluteTolerance": 1e-09,
      "unit": "V",
      "derivation": "-(0.3*2 + 0.3*1) = -0.9 V: only the shared 0.3 ohm link carries both."
    }
  ],
  "sourceFile": "tests/fixtures/pdn/shared-rl-tone.json"
}