Verified calculation capability

RC time constant Calculation Capability

Solve series RC time constant τ = R·C from any two of R, C, tau; also returns −3 dB frequency and common timing multiples. · Electrical

Capability ID electrical.rc_time_constant · version 1.0.0

Open calculator REST API MCP Evidence Evidence JSON CVP Manifest Review policy

Model

Time constant

Time constant: τ = R × C
Solve C: C = τ ÷ R
Solve R: R = τ ÷ C
−3 dB frequency: f_c = 1 ÷ (2π R C)
10%–90% rise (approx.): t₁₀₋₉₀ ≈ 2.2 τ
Settling horizon: t₅τ = 5 τ

Inputs / Outputs

Canonical symbols for this capability. Agent schemas remain the contract.

Symbol	Quantity	Unit	Role
`R`	Resistance (Ω)	—	input / output
`C`	Capacitance (F)	—	input / output
`tau`	Time constant τ (s)	—	input / output
`f_c`	First-order LPF −3 dB frequency 1/(2πRC) (Hz)	—	output
`t_10_90`	Approx. 10%–90% rise time ≈ 2.2τ (s)	—	output
`t_5tau`	Settling horizon 5τ (s)	—	output

Assumptions / Validity

Declared scope for this capability. Do not use it outside this domain.

Assumptions

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

Example

One numerical check. The calculator page holds worked steps and FAQ.

R=10 kΩ, C=1 µF → τ=10 ms, f_c≈15.915 Hz

Open this example in the calculator

Trust

CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance. Computational verification is defined by CVP. Supplemental domain review (internal) and named expert review are defined by the Review policy and do not by themselves determine CVP conformance.

CVP: CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance· View Manifest · CVP overview · Specification
Assurance: Engineering
Declared partition coverage: PASS · 3/3 declared partitions (solve-tau, solve-C, invalid-domain)
Calculation version: 1.0.0
Verification: 16/16 calculation tests · 3/3 legacy golden · 6/6 legacy boundary · 7/7 legacy property
Production surface contract: 3/3
Versions: Calculation 1.0.0 · CVP protocol 1.0.0-proposed
CVP identity: 7/7 property · digest c2ad16b2e943
Reference: O1 model · O2 expected_values · O2 numerical_behavior
Interfaces: PASS · UI (SSR) / REST / MCP
ui-ssr is query-result HTML, not a live browser session.
CVP suite: 3/3 golden · 6/6 CVP boundary · 4/4 invalid · 7/7 property · 1/1 cross-interface · 1/1 CVP contract
Supplemental domain review: Internal · Pass · electrical-engineer
Named expert review: Not performed
Version lock: Supported (409 VERSION_MISMATCH)
Artifact consistency: Build verified · 1.0.0 (workspace artifacts agree)
Review-policy tier: Internal engineering review — catalog token expert_verified; supplemental; not CVP status

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

Call this capability

Human page, REST, and MCP share the same engine and calculation_version. Build verified hashes workspace artifacts only. After deploy, attest:production GETs canonical URLs twice — the public/cached view an Agent actually hits, and origin — including every /capabilities/{id} HTML page. Public Capability HTML version must match catalog before production attestation passes. Live Trust rows above fetch /.well-known/calculatorx-production-attestation.json and the output schema const. Build hashes: release integrity. That proves currently published page / engine / schema / evidence / MCP agree — not that a historical version is independently immutable. Reference Calculation Standard — Production surface contract 3/3.

Tool id: rc-time-constant
Engine: rc-time-constant
REST: POST /api/v1/calc/rc-time-constant
MCP: execute_calculation with capability_id: "electrical.rc_time_constant"
Agent input schema: Canonical (MCP / Agent)
Output schema: JSON Schema (latest)
Versioned input schema: Immutable pin (1.0.0)
Versioned output schema: Immutable pin (1.0.0)

References

Human-readable sources plus CVP reference evidence classes.

Sources

IEC 60050 — International Electrotechnical Vocabulary — Time constant of an exponential quantity
Horowitz & Hill — The Art of Electronics — RC circuits, time constants, and single-pole filters
NIST Guide to the SI (SP 811) — SI units for resistance, capacitance, and time

Reference evidence classes: O1 model · O2 expected_values · O2 numerical_behavior

Try with an agent

Inspect this capability via same-origin MCP, then call execute_calculation.

curl -sS -X POST 'https://www.calculatorx.com/mcp' \
  -H 'Content-Type: application/json' \
  -H 'MCP-Protocol-Version: 2026-07-28' \
  -H 'Mcp-Method: tools/call' \
  -H 'Mcp-Name: inspect_capability' \
  -d '{"jsonrpc":"2.0","id":1,"method":"tools/call","params":{"name":"inspect_capability","arguments":{"capability_id":"electrical.rc_time_constant"}}}'

Inspect the trust tier and required assurance level before execution. Pin calculation_version (1.0.0) when reproducibility matters. Full protocol notes: MCP docs.