{"query": "Capacitor — the exponential clock (RC time constant)", "count": 20, "results": [{"id": "card_n_6f5aa0b22245", "title": "Capacitor — the exponential clock (RC time constant)", "shelf": "science", "surface": "secular", "snippet": "A capacitor charging through a resistor follows V(t) = V·(1 − e^(−t/RC)); after one\ntime constant τ = RC it holds exactly 1 − 1/e ≈ 63.2% of the supply — sealed in-domain\n(1000 Ω × 1000 µF = 1 s; 5 V ", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-09", "readable": false, "generated": false}, {"id": "card_c_01a2b706782a", "title": "Radioactive decay — the exponential clock of ↔ Capacitor — the exponential clock (RC time c", "shelf": "connections", "surface": null, "snippet": "The same exponential that discharges a capacitor empties a nucleus's odds — the bench's RC clock and the carbon clock are one curve wearing different constants.  — a concord the card itself states; mi", "authority_tier": "engine_derived", "source": "Concordance miner — 2026-07-11", "readable": false, "generated": false}, {"id": "card_n_cfb57dd6b005", "title": "Radioactive decay — the exponential clock of matter", "shelf": "science", "surface": "secular", "snippet": "Sealed in-domain: after one half-life exactly half remains; after two, exactly one\nquarter (2^(−2) = 1/4, exact); carbon-14's decay constant is ln2/5730 years = 3.833×10⁻¹²\nper second: https://narrowh", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-09", "readable": false, "generated": false}, {"id": "card_c_26c735e9dff1", "title": "Glottochronology — carbon-dating the words ↔ Capacitor — the exponential clock (RC time c", "shelf": "connections", "surface": null, "snippet": "Words decay by RATIO, like atoms, like a capacitor, like everything on the exponential spine.  — a concord the card itself states; mined + verified.", "authority_tier": "engine_derived", "source": "Concordance miner — 2026-07-11", "readable": false, "generated": false}, {"id": "card_c_268b55a98977", "title": "The carbon clock resonates with the capacitor's RC clock", "shelf": "connections", "surface": null, "snippet": "One exponential, two substrates — matter's decay and the bench's discharge. RESONANCE: a map-aid, never a proof of unity.", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-09", "readable": false, "generated": false}, {"id": "card_c_547436596e63", "title": "Diode — the exponential gate ↔ Capacitor — the exponential clock (RC time c", "shelf": "connections", "surface": null, "snippet": "The diode's current grows exponentially with voltage; sealed exactly: e^(x+ln2) = 2e^x — current DOUBLES for every ln2·nVT of forward voltage  — a concord the card itself states; mined + verified.", "authority_tier": "engine_derived", "source": "Concordance miner — 2026-07-11", "readable": false, "generated": false}, {"id": "card_c_49411cccab5a", "title": "Logarithms — multiplication made addition, a ↔ Diode — the exponential gate", "shelf": "connections", "surface": null, "snippet": "the capacitor's RC clock, radioactive decay, compound interest, the diode's curve all rise by multiplying; the logarithm brings them back by adding.  — a concord the card itself states; mined + verifi", "authority_tier": "engine_derived", "source": "Concordance miner — 2026-07-11", "readable": false, "generated": false}, {"id": "card_src_openstax_college_physics_21_6_dc_circuits_containing_resistors_an_bfd0e211", "title": "21.6 DC Circuits Containing Resistors and Capacitors — College Physics", "shelf": "physics", "surface": "secular", "snippet": "21.6\n\nDC Circuits Containing Resistors and Capacitors\n\nWhen you use a flash camera, it takes a few seconds to charge the capacitor that powers the flash. The light flash discharges the capacitor in a ", "authority_tier": "reference", "source": "OpenStax: College Physics (CC-BY 4.0)", "readable": false, "generated": false}, {"id": "card_src_openstax_university_physics_volume_2_10_5_rc_circuits_8769028f", "title": "10.5 RC Circuits — University Physics Volume 2", "shelf": "physics", "surface": "secular", "snippet": "10.5\n\nRC Circuits\n\nLearning Objectives\nBy the end of this section, you will be able to:\n\nDescribe the charging process of a capacitor\n\nDescribe the discharging process of a capacitor\n\nList some applic", "authority_tier": "reference", "source": "OpenStax: University Physics Volume 2 (CC-BY 4.0)", "readable": false, "generated": false}, {"id": "card_src_openstax_college_physics_2e_21_6_dc_circuits_containing_resistors_an_bfd0e211", "title": "21.6 DC Circuits Containing Resistors and Capacitors — College Physics 2e", "shelf": "physics", "surface": "secular", "snippet": "21.6\n\nDC Circuits Containing Resistors and Capacitors\n\nLearning Objectives\n\nBy the end of this section, you will be able to:\n\nExplain the importance of the time constant, τ , and calculate the time co", "authority_tier": "reference", "source": "OpenStax: College Physics 2e (CC-BY 4.0)", "readable": false, "generated": false}, {"id": "card_src_openstax_college_physics_ap_courses_2e_21_6_dc_circuits_containing_resistors_an_bfd0e211", "title": "21.6 DC Circuits Containing Resistors and Capacitors — College Physics for AP® Courses 2e", "shelf": "physics", "surface": "secular", "snippet": "21.6\n\nDC Circuits Containing Resistors and Capacitors\n\nLearning Objectives\n\nBy the end of this section, you will be able to:\n\nExplain the importance of the time constant, τ , and calculate the time co", "authority_tier": "reference", "source": "OpenStax: College Physics for AP® Courses 2e (CC-BY 4.0)", "readable": false, "generated": false}, {"id": "card_src_openstax_university_physics_volume_2_challenge_problems_84c75a9b", "title": "Challenge Problems — University Physics Volume 2", "shelf": "physics", "surface": "secular", "snippet": "Challenge Problems\n\n88.\n\nSome camera flashes use flash tubes that require a high voltage. They obtain a high voltage by charging capacitors in parallel and then internally changing the connections of ", "authority_tier": "reference", "source": "OpenStax: University Physics Volume 2 (CC-BY 4.0)", "readable": false, "generated": false}, {"id": "card_domchk_electrical_claimed_capacitor_voltage_V", "title": "Electrical: capacitor voltage V", "shelf": "electrical", "surface": "secular", "snippet": "A worked check in electrical: capacitor voltage V.\n\nGIVEN\n  current_A = 0.5\n  elapsed_s = 0.001\n  power_W_claim = 6\n  resistance_ohm = 24\n  supply_V = 5\n  voltage_V = 12\n\nCLAIMED\n  claimed_capacitor_v", "authority_tier": "reference", "source": "The verifier's own documented relation, and a run this engine performed against it (deterministic; re-runnable with tools/domain_goldens.py)", "readable": false, "generated": false}, {"id": "card_calc_v_electrical_rc_time_constant", "title": "Rc time constant", "shelf": "calculations", "surface": "secular", "snippet": "Rc time constant — electrical. Formula: v = V(1 - e^-t/RC). Canonical FORM: decay (y = y0 e^(-kt)) — engine verifier electrical.rc_time_constant — the deterministic check the concordance runs. Same fo", "authority_tier": "reference", "source": "The Calculation Map — every calculation, mapped by form", "readable": false, "generated": false}, {"id": "card_src_openstax_university_physics_volume_2_additional_problems_a55603fc", "title": "Additional Problems — University Physics Volume 2", "shelf": "physics", "surface": "secular", "snippet": "Additional Problems\n\n67.\n\nA circuit contains a D cell battery, a switch, a resistor, and four 20-mF capacitors connected in series. (a) What is the equivalent capacitance of the circuit? (b) What is t", "authority_tier": "reference", "source": "OpenStax: University Physics Volume 2 (CC-BY 4.0)", "readable": false, "generated": false}, {"id": "card_c_5592b5e8c1e7", "title": "Logarithms — multiplication made addition, a ↔ Capacitor — the exponential clock (RC time c", "shelf": "connections", "surface": null, "snippet": "it is the exact INVERSE of the exponential that is the spine of this whole map: the capacitor's RC clock, radioactive decay, compound interest, the diode's curve all rise by multiplying; the logarithm", "authority_tier": "engine_derived", "source": "Concordance miner — 2026-07-11", "readable": false, "generated": false}, {"id": "card_c_b71d6ddb4a46", "title": "Logarithms — multiplication made addition, a ↔ Radioactive decay — the exponential clock of", "shelf": "connections", "surface": null, "snippet": "it is the exact INVERSE of the exponential that is the spine of this whole map: the capacitor's RC clock, radioactive decay, compound interest, the diode's curve all rise by multiplying; the logarithm", "authority_tier": "engine_derived", "source": "Concordance miner — 2026-07-11", "readable": false, "generated": false}, {"id": "card_calc_rc_discharge", "title": "RC circuit discharge", "shelf": "calculations", "surface": "secular", "snippet": "RC circuit discharge — electrical. Formula: V = V0 e^(-t/RC). Canonical FORM: decay (y = y0 e^(-kt)) — charge drains in proportion to the voltage left. Same form, different domain: this is the decay c", "authority_tier": "reference", "source": "The Calculation Map — every calculation, mapped by form", "readable": false, "generated": false}, {"id": "card_calc_capacitor_charge", "title": "RC charging curve", "shelf": "calculations", "surface": "secular", "snippet": "RC charging curve — electrical. Formula: V = V0 (1 - e^(-t/RC)). Canonical FORM: decay (y = y0 e^(-kt)) — the mirror of discharge — approach in proportion to the gap remaining. Same form, different do", "authority_tier": "reference", "source": "The Calculation Map — every calculation, mapped by form", "readable": false, "generated": false}, {"id": "card_n_5d1c28bd4ea5", "title": "Logarithms — multiplication made addition, and the grammar of the senses", "shelf": "science", "surface": "secular", "snippet": "The logarithm turns multiplication into addition: log(15) = log(3)+log(5), sealed. That\none property made calculation possible before computers (Napier 1614 -> slide rules -> every\nengineer until 1970", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-09", "readable": false, "generated": false}], "house": {"door": "FIND", "kind": "cards", "trail": "results", "seal": null, "next_step": {"do": "open the top card", "door": "FIND", "tool": "card_get", "params": {"id": "card_n_6f5aa0b22245"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}