{"id": "card_n_cdb747a427d2", "kind": "note", "title": "Electronics — the resonant chain, from Ohm's law to the radio wave", "body": "One sealed chain runs the whole bench: Ohm's law (V = I·R), the capacitor's\nexponential clock (one time constant → 63.2% charged), the diode's exponential gate (current\ndoubles every ln2·nVT ≈ 17.9 mV at room temperature), the LC oscillator (100 µH + 100 pF →\n1.591 MHz — the middle of the AM band), the varactor's tuning law (halve C and the frequency\nrises by exactly √2), and the wave that oscillator launches (λ = c/f ≈ 188 m). Seven steps,\neach CONFIRMED, one receipt: https://narrowhighway.com/s/1ee0d3ed486453eee0967146a531984888709198b39fb16a7b2c2a5f58ef1b73 — and the null test (\"halving C halves the frequency\")\nsealed BROKEN with the exact residual √2 − 1/2: https://narrowhighway.com/s/9ad4a43e7d3c0dd5cea7d1e8756669e79996fc98b70bf02bf35bc143d42108ac .\n\nRead the chain backwards and it is a crystal radio: a ~hundred-meter wave arrives, an LC\ncircuit selects it, a diode rectifies it — no battery, powered by the wave itself. Read it\nupwards in scale and it is the Schumann cavity: the same resonance physics, planet-sized.\nThe honest boundary holds throughout: the RELATIONS seal; the material constants (diode drops,\nvaractor profiles, oscillator Q) are empirical properties measured, not derived.", "source": {"label": "Concordance assay — 2026-07-09", "url": "https://narrowhighway.com/s/1ee0d3ed486453eee0967146a531984888709198b39fb16a7b2c2a5f58ef1b73", "ref": "electronics_dig", "authority_tier": "engine_derived"}, "shelf": "science", "box": "electronics", "bands": ["electronics", "resonant chain", "ohms law", "capacitor", "diode", "oscillator", "varactor", "radio", "crystal radio", "capstone"], "connections": [], "author": "engine", "created_at": "2026-07-10T00:59:49.508624+00:00", "updated_at": "2026-07-10T00:59:49.508624+00:00", "visibility": "public", "lifecycle_stage": "public", "volatility": "permanent", "surface": "secular", "metrics": {"paperclips_count": 0, "helpful_count": 0, "not_helpful_count": 0, "cite_count": 0, "walks_through_count": 0, "flagged_count": 0}, "source_hash": "48e0cbebf2b7f59b690cd274e2f8fdb2433e6ea7805603e997b4bab0a1435415"}