ELC-34

Short-circuit current

Isc = V / Z with Z = √(R²+X²). The bolted-fault current.

Reading speed

PowerIEC 60909

Governing equation

I_{\mathrm{sc}}=V/Z,\quad Z=\sqrt{R^2+X^2}

$X \in \left[0.1, 800\right]$

where

V: Source voltage (V)
R: Resistance (mΩ)
X: Reactance (mΩ)
Z: Impedance (mΩ)
I_{\mathrm{sc}}: Fault current (kA)

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

I_{\mathrm{sc}}=V/Z,\quad Z=\sqrt{R^2+X^2}

$X \in \left[0.1, 800\right]$

$X = 0.1$ $Z = 16$

Along the curve

②

Domain of the variable — blue

X_{\min} = 0.1,\quad X_{\max} = 800

$X \in \left[0.1, 800\right]$

$X = 0.1$ $X = 0.1$

Along the curve

③

Response curve — green

I_{\mathrm{sc}}=V/Z,\quad Z=\sqrt{R^2+X^2}

$X \in \left[0.1, 800\right]$

$X = 0.1$ $Z = 16$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}Z}{\mathrm{d}X}

$X \in \left[0.1, 800\right]$

$X = 5.131$ $Z^{\prime} = -0.117$

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-34 — Short-circuit current) is the form associated with IEC 60909. Working symbols: $V$ , $R$ , $X$ $\rightarrow$ $Z$ , $I_{\mathrm{sc}}$ . A metallic short reduces the load to the Thevenin impedance of the source. IEC 60909 factors refine it.

Purpose

Purpose: compute

Z

I_{\mathrm{sc}}

from

V

R

X

in Electrical via

I_{\mathrm{sc}}=V/Z,\quad Z=\sqrt{R^2+X^2}

Isc = V / Z with Z = √(R²+X²). The bolted-fault current. Use it when a real electrical question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

V = 400.000\,\mathrm{V}

R = 25.000\,\mathrm{mΩ}

X = 80.000\,\mathrm{mΩ}

, the governing relation

I_{\mathrm{sc}}=V/Z,\quad Z=\sqrt{R^2+X^2}

yields

Z = 83.82\,\mathrm{mΩ}

I_{\mathrm{sc}} = 4.772\,\mathrm{kA}

. A source, a fault bolt, a large I arrow. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Source voltage V400 VResistance R25 mΩReactance X80 mΩ

Outputs

Impedance Z83.82 mΩ
Fault current I_{\mathrm{sc}}4.772 kA

Reading speed

Watch on YouTube

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Narration of this film

A source, a fault bolt, a large I arrow.

A metallic short reduces the load to the Thevenin impedance of the source. IEC 60909 factors refine it.

Reading speed

Watch on YouTube