Public evidence

electrical.rc_time_constant

Machine-checked verification for calculation version 1.0.0 · tier expert_verified

Open calculator API Capability Download JSON CVP Manifest MCP Review policy

CVP: CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance· First-order RC only · Protocol · Schema · Production report

Declared partition coverage: PASS · 3/3 declared partitions (solve-tau, solve-C, invalid-domain)
Versions: Calculation 1.0.0 · CVP protocol 1.0.0-proposed
CVP identity: 7/7 property · digest c2ad16b2e943

Verification

Legacy regression suite: 16/16 calculation tests · Production surface contract 3/3

Three distinct suites: educational examples on the calculator page, this legacy regression count (16/16 golden + boundary), and the CVP verification suite below. They are not the same number. Property, metamorphic, round-trip, O3, and interface statuses/checks are recorded in the CVP Manifest . SKIP (0/0) means that suite has no published vectors.

This calculator CURRENT · Public schema 1.0.0 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓

CVP verification suite

Protocol checks from the Evidence Manifest. Distinct from the legacy regression suite above. Calculation version 1.0.0. CVP 1.0.0-proposed. 3/3 golden · 6/6 CVP boundary · 4/4 invalid · 7/7 property · 1/1 cross-interface · 1/1 CVP contract. digest c2ad16b2e943.

Golden (oracle-backed) 3 / 3
CVP boundary 6 / 6
Invalid input 4 / 4
Property 7 / 7
Cross-interface 1 / 1
CVP contract 1 / 1
Interfaces PASS · UI (SSR) / REST / MCP
Interface claim ui-ssr is query-result HTML, not a live browser session.
Assurance Engineering

release artifacts aligned PASS
schema valid input executes PASS
engine success output validates schema PASS

Fingerprint sha256:44a23f4cdb8c7ba9c4979efb20f6b570f48cd788929e35ab5268ba587479f0e9

Input schema sha256:8a19eb36a0c3b41066244d15a89316bfa9dfabf56fcf73af20fcf0f65e039d54 · Output schema sha256:30ce3b2538ef51fc1e36f697a136c9298d78e3d0fcca4fd8dc96ceae6705b3c3 · Build-time SHA-256 digests prove published artifacts agree with each other (release_integrity.scope=workspace). Production attestation GETs canonical URLs twice (public/cached view and origin), including Capability HTML, via npm run attest:production --write (published at /.well-known/calculatorx-production-attestation.json) and fails if the public Capability page advertises a different calculation_version. This is artifact consistency, not an independent immutable release log.

Build & scope

Engine identity and declared limitations.

Tool: rc-time-constant
Engine: rc-time-constant
Engine build: 2026-09-10
Evidence core: 2026-09-05T02:35:39.217Z
Rendered: 2026-09-16T22:03:43.712Z
Last reviewed: 2026-08-08

Assumptions

Lumped series first-order RC.
When R and C are both given, tau is taken as R·C.

Limitations

Series first-order RC only — not parallel networks or distributed RC
f_c is the ideal LPF −3 dB corner; not a filter design tool
Fewer than two inputs → NEEDS_TWO_INPUTS; non-positive → VALUE_MUST_BE_POSITIVE
When R and C are both provided, tau is recomputed from R·C

Sources

Standards and references supporting this tool specification. Methods are listed separately — they are algorithms, not bibliographic sources.

IEC 60050 — International Electrotechnical Vocabulary — Time constant of an exponential quantity
Supports: τ definition for exponential RC response
Horowitz & Hill — The Art of Electronics — RC circuits, time constants, and single-pole filters
Supports: τ = RC; ≈2.2τ for 10%–90%; f_c = 1/(2πRC)
NIST Guide to the SI (SP 811) — SI units for resistance, capacitance, and time
Supports: Ω, F, s as coherent units for τ = RC

Legacy published checks

Golden and boundary cases from the legacy Evidence JSON. CVP property, metamorphic, round-trip, O3, and interface statuses/checks are recorded in the Manifest — including SKIP when a suite has no vectors.

ID	Kind	Status	Detail
`rc-10ms`	golden	pass	Expected tau=0.01 · R=10000 · C=0.000001 · f_c=15.915494309189533 · t_10_90=0.022 · t_5tau=0.05 · Actual R=10000 · C=0.000001 · tau=0.01 · f_c=15.915494309189533 · t_10_90=0.022000000000000002 · t_5tau=0.05
`solve-C`	golden	pass	Expected C=2.127659574468085e-7 · tau=0.001 · Actual R=4700 · C=2.1276595744680852e-7 · tau=0.001 · f_c=159.15494309189532 · t_10_90=0.0022 · t_5tau=0.005
`solve-R`	golden	pass	Expected R=470 · tau=0.000047 · Actual R=470 · C=1e-7 · tau=0.000047 · f_c=3386.2753849339438 · t_10_90=0.0001034 · t_5tau=0.000235
`needs-two`	boundary	pass	Expected NEEDS_TWO_INPUTS · Actual NEEDS_TWO_INPUTS
`empty`	boundary	pass	Expected NEEDS_TWO_INPUTS · Actual NEEDS_TWO_INPUTS
`zero-R`	boundary	pass	Expected VALUE_MUST_BE_POSITIVE · Actual VALUE_MUST_BE_POSITIVE
`nan-C`	boundary	pass	Expected INVALID_NUMBER · Actual INVALID_NUMBER
`boundary-rc-10ms`	boundary	pass	Expected tau=0.01 · R=10000 · C=0.000001 · f_c=15.915494309189533 · Actual R=10000 · C=0.000001 · tau=0.01 · f_c=15.915494309189533 · t_10_90=0.022000000000000002 · t_5tau=0.05
`boundary-solve-C`	boundary	pass	Expected C=2.1276595744680852e-7 · tau=0.001 · Actual R=4700 · C=2.1276595744680852e-7 · tau=0.001 · f_c=159.15494309189532 · t_10_90=0.0022 · t_5tau=0.005
`property-tau`	property	pass	10kΩ·1µF → 10 ms
`property-fc`	property	pass	f_c = 1/(2πτ)
`property-rise`	property	pass	2.2τ
`property-5tau`	property	pass	5τ
`property-solve-C`	property	pass	C=τ/R
`property-solve-R`	property	pass	R=τ/C
`property-linear-R`	property	pass	2R → 2τ