ELC-33

Line voltage drop

ΔV ≈ I (R cosφ + X sinφ) per phase. Approximate phasor drop.

Reading speed

PowerIEC 60364

Governing equation

\Delta V=I(R\cos\varphi+X\sin\varphi)

$I \in \left[0.5, 800\right]$

where

I: Current (A)
R: Resistance (Ω)
X: Reactance (Ω)
\varphi: Load angle (°)
\Delta V: Voltage drop (V)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

\Delta V=I(R\cos\varphi+X\sin\varphi)

$I \in \left[0.5, 800\right]$

$I = 0.5$ $\Delta V = 0.151$

Along the curve

②

Domain of the variable — blue

I_{\min} = 0.5,\quad I_{\max} = 800

$I \in \left[0.5, 800\right]$

$I = 0.5$ $I = 0.5$

Along the curve

③

Response curve — green

\Delta V=I(R\cos\varphi+X\sin\varphi)

$I \in \left[0.5, 800\right]$

$I = 0.5$ $\Delta V = 0.151$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}\Delta V}{\mathrm{d}I}

$I \in \left[0.5, 800\right]$

$I = 5.528$ $\Delta V^{\prime} = 0.303$

Along the curve

Lecture brief

Historical brief

Ohm (1827), Kirchhoff (1845) and Maxwell’s circuit reduction still run every board: RLC transients, transformers, skin effect and three-phase power. The sheets are those network laws, not a SPICE deck. This sheet (ELC-33 — Line voltage drop) is the form associated with IEC 60364. Working symbols: $I$ , $R$ , $X$ , $\varphi$ $\rightarrow$ $\Delta V$ . The in-phase component of the IZ drop is I R cosφ + I X sinφ for a lagging load.

Purpose

Purpose: compute

\Delta V

from

I

R

X

\varphi

in Electrical via

\Delta V=I(R\cos\varphi+X\sin\varphi)

ΔV ≈ I (R cosφ + X sinφ) per phase. Approximate phasor drop. Use it when a real electrical question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

I = 40.000\,\mathrm{A}

R = 0.250\,\mathrm{Ω}

X = 0.180\,\mathrm{Ω}

\varphi = 25.000\,\mathrm{^{\circ}}

, the governing relation

\Delta V=I(R\cos\varphi+X\sin\varphi)

yields

\Delta V = 12.11\,\mathrm{V}

. A feeder, an I arrow, a voltage sag. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Current I40 AResistance R0.25 ΩReactance X0.18 ΩLoad angle \varphi25 °

Outputs

Voltage drop \Delta V12.11 V

Reading speed

Watch on YouTube

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Narration of this film

A feeder, an I arrow, a voltage sag.

The in-phase component of the IZ drop is I R cosφ + I X sinφ for a lagging load.

Reading speed

Watch on YouTube