CVP verified calculation capability

RLC resonance Calculation Capability

Compute ideal series or parallel RLC resonant frequency, Q, bandwidth, and reactance at resonance from L, C, and R.

Electrical Capability ID electrical.rlc_resonance version 1.0.0 CVP VERIFIED CURRENT Engineering

Model

Resonant frequency

Resonant frequency: f₀ = 1 ÷ (2π √(L C))
Angular frequency: ω₀ = 1 ÷ √(L C) = 2π f₀
Q (series): Qₛ = (1/R) √(L/C) = ω₀ L / R
Q (parallel): Qₚ = R √(C/L) = R / (ω₀ L)
Bandwidth: BW = f₀ ÷ Q
Reactance at resonance: X₀ = ω₀ L = 1 ÷ (ω₀ C)

Modes: series · parallel

Inputs / Outputs

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

Symbol	Quantity	Unit	Role
`L`	Inductance	—	input / output
`C`	Capacitance	—	input / output
`R`	Resistance	—	input / output
`f0`	Resonant frequency	—	output
`omega0`	Angular resonant frequency	—	output
`Q`	Quality factor	—	output
`BW`	−3 dB bandwidth f0/Q	—	output
`X0`	ω0·L = 1/	—	output
`Z_res`	Ideal \|Z\| at resonance	—	output

Assumptions / Validity

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

Assumptions

Lumped ideal R, L, C.
Parallel mode is ideal R across LC (no coil ESR).

Example

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

series, L=1 mH, C=1 µF, R=10 Ω → f0≈5032.92 Hz, Q≈3.162

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 (series, parallel, invalid-domain)
Calculation version: 1.0.0
Verification: 14/14 calculation tests · 2/2 legacy golden · 5/5 legacy boundary · 7/7 legacy property
Production surface contract: 6/6
Versions: Calculation 1.0.0 · CVP protocol 1.0.0-proposed
CVP identity: 7/7 property · digest 64605e550910
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: 2/2 golden · 4/4 CVP boundary · 4/4 invalid · 7/7 property · 1/1 cross-interface · 4/4 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 6/6.

curl -sS -X POST 'https://www.calculatorx.com/api/v1/calc/rlc-resonance' \
  -H 'Content-Type: application/json' \
  -d '{"inputs":{"mode":"series","L":0.001,"C":0.000001,"R":10},"calculation_version":"1.0.0"}'

{
  "inputs": {
    "mode": "series",
    "L": 0.001,
    "C": 0.000001,
    "R": 10
  },
  "calculation_version": "1.0.0"
}

POST /api/v1/calc/rlc-resonance. This is a POST calculate endpoint — do not GET it.

Full REST contract: REST API docs.

Tool id: rlc-resonance
Engine: rlc-resonance
REST: POST /api/v1/calc/rlc-resonance
MCP: execute_calculation with capability_id: "electrical.rlc_resonance"
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)

Operations

Declared calculation modes for this capability.

series
parallel

References

Human-readable sources plus CVP reference evidence classes.

Sources

IEC 60050 — International Electrotechnical Vocabulary — Resonance, quality factor, and bandwidth
Horowitz & Hill — The Art of Electronics — RLC resonance, Q, and bandwidth
NIST Guide to the SI (SP 811) — SI units for inductance, capacitance, and frequency

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

Try with an agent

Inspect, then execute. Same engine as REST and the human calculator.

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.rlc_resonance"},"_meta":{"io.modelcontextprotocol/protocolVersion":"2026-07-28","io.modelcontextprotocol/clientInfo":{"name":"calculatorx-docs-example","version":"1.0.0"},"io.modelcontextprotocol/clientCapabilities":{}}}}'

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: execute_calculation' \
  -d '{"jsonrpc":"2.0","id":2,"method":"tools/call","params":{"name":"execute_calculation","arguments":{"capability_id":"electrical.rlc_resonance","inputs":{"mode":"series","L":0.001,"C":0.000001,"R":10},"calculation_version":"1.0.0"},"_meta":{"io.modelcontextprotocol/protocolVersion":"2026-07-28","io.modelcontextprotocol/clientInfo":{"name":"calculatorx-docs-example","version":"1.0.0"},"io.modelcontextprotocol/clientCapabilities":{}}}}'

Pin calculation_version (1.0.0) when the result must stay reproducible.

Inspect the trust tier and required assurance level before execution. Full protocol notes: MCP docs.