Controlled circuit evidence and engineering approximation

Controlled Steady-State Voltage-Drop Record

Calculate a documented two-wire DC, single-phase AC or balanced three-phase AC voltage-drop result from the actual conductor resistance and reactance supplied for the declared operating conditions. This worksheet does not size cable, embed a universal IEC limit or issue a compliance decision.

User-supplied R and XDisplacement cos φExplicit AC scopeNo cable recommendation

सुरक्षा सीमा: voltage drop is only one cable-design check. Ampacity, installation method, insulation temperature, grouping, harmonics, fault protection, short-circuit withstand, neutral loading, protective-device coordination and equipment limits require a competent electrical design.

Circuit, impedance and operating record

Case / calculation ID *

Circuit / cable identifier *

Declared circuit model *

Sending voltage U *Across the two-wire/single-phase circuit, or line-to-line for three-phase.

Steady-state RMS/design current I *

One-way conductor length L *

Per-conductor resistance R *

Per-conductor reactance X *

Conductor operating temperature *

आवृत्ति *

Displacement power factor cos φ *

Reactive state *

Voltage/current method, source and uncertainty *

R/X source and applicability *

Steady-state scope and excluded conditions *

Reviewer and date *

Optional controlled permitted-limit comparison

Leave all four fields blank for arithmetic only. If any field is used, complete the whole controlled record. No percentage is supplied by the worksheet.

User-entered permitted value

Comparison rule

Controlled document, edition and exact clause/table

Jurisdiction, supply type, load category and applicability

IEC boundary: the official IEC 60364-5-52:2009+AMD1:2024 CSV record identifies Clause 525 and a relevant annex. The complete controlled limits and categories are not reproduced here and remain NEEDS_LICENSED_SOURCE.

Eight evidence and applicability gates

Circuit topology, current path and equal go/return impedance or three-phase balance are verified.

Voltage definition, RMS current, one-way length, source record and uncertainty are verified.

R and X match the actual conductor, construction, layout, operating temperature and frequency.

For AC, displacement cos φ and leading/lagging state are verified; true PF was not substituted.

The steady-state approximation is applicable; starting, switching, fault and transient cases are excluded or separately assessed.

Balance, neutral current, harmonics, skin/proximity effects and parallel paths are absent or already included in the impedance/current evidence.

No compliance limit is needed, or the entered limit, edition, clause, jurisdiction and category are controlled and applicable.

A competent reviewer will retain every input, source and applicability record with the result.

No current result

Complete the controlled record and submit explicitly.

Steady-state approximation and evidence state

Signed voltage change ΔU—

Signed percentage—

Estimated receiving voltage—

Per-conductor R over L—

Per-conductor X over L—

Resistive conductor loss—

Controlled limit stateNot compared

Evidence state0 / 8 complete

No calculation record

No current numerical result is available.

Engineering formula, units and applicability

DC two-wire: ΔU = 2 I L R

Single-phase AC: ΔU ≈ 2 I L (R cos φ ± X sin φ)

Balanced three-phase AC: ΔU_LL ≈ √3 I L (R cos φ ± X sin φ)

L is in km and R/X are per-conductor Ω/km at the declared operating conditions. Use + for lagging/inductive and − for leading/capacitive current. U is the two-wire/single-phase voltage or three-phase line-to-line voltage. The percent result is 100ΔU/U. Negative ΔU means the approximation predicts voltage rise.

P_loss = n I² R L; n = 2 for the declared two-wire/single-phase path and n = 3 for the declared balanced three-phase path

वर्गीकरण: these are documented steady-state engineering relations, not formulas prescribed by IEC 60364. They do not model unbalance, neutral/harmonic current, motor starting, faults, switching transients, shunt capacitance or protection.

Source register and permitted use

आईडी	Official source and lifecycle	Used for	Not used for
S1	IEC 60364-5-52:2009+AMD1:2024 CSV, Edition 3.1 — published 2024-11-22, stability 2028; includes COR1:2011	Wiring-system scope and the public record that Clause 525 points to a relevant voltage-drop annex.	Protected limits/categories: NEEDS_LICENSED_SOURCE; none embedded.
S2	IEC 60228:2023, Edition 4.0 — published, stability 2030	Finished cable-conductor resistance scope and existence of Annex B temperature correction guidance.	Protected resistance tables/factors: NEEDS_LICENSED_SOURCE; none embedded.
S3	Schneider Electric Electrical Installation Guide — steady-load voltage drop	Common R/X/cos φ single-phase and balanced three-phase engineering relations and units.	Not treated as an IEC-prescribed formula or a cable-selection rule.
S4	Schneider Electric Electrical Installation Guide — maximum voltage-drop limit	Limits vary by country, supply/load category and operating state.	No universal 3%/5% threshold is embedded.
S5	Schneider Electric PowerLogic PM8000 Help — PF, updated 2026-04-27	True PF includes harmonics; displacement PF concerns the fundamental frequency.	No harmonic-rich case is reduced to cos φ arithmetic.

Corrections made during review

Power factor and reactance were restored to the AC model

The former unity-PF resistive shortcut was removed. AC now requires controlled R, X, displacement cos φ and leading/lagging state.

Physical resistance was separated from the √3 circuit factor

The output reports per-conductor R·L and X·L. It never labels √3R as cable resistance.

Generic material resistivity and hot-cable shortcut were removed

No 0.0175/0.0283 table or add-about-20-percent rule remains. R/X must come from the actual conductor record at declared conditions.

Universal 3%/5% decisions were removed

An optional comparison exists only for a user-entered controlled limit with edition, clause, jurisdiction, category and comparison rule.

Cable sizing and presets were removed

No house, motor, panel or cable-area recommendation is produced; voltage drop alone cannot prove cable suitability.

Scope, traceability and strict input were added

Circuit path, voltage definition, temperature, frequency, impedance source, operating state and reviewer are retained; point/comma decimals are strict.

Detached automatic state was removed

No default, auto-calculation, URL state, localStorage, clipboard or dynamic result HTML remains; edits make a result stale.

FAQ schema and external dependencies were removed

Detached simplified claims, external fonts and KaTeX no longer create separate or failing content paths.