ELC-26

Inductor energy ½LI²

U = ½ L I² stored in the magnetic field of an inductor.

Reading speed

EnergyMaxwell

Governing equation

U=\tfrac12 L I^2

$I \in \left[0.01, 80\right]$

where

L: Inductance (mH)
I: Current (A)
U: Stored energy (J)

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

U=\tfrac12 L I^2

$I \in \left[0.01, 80\right]$

$I = 0.01$ $U = 1\times 10^{-6}$

Along the curve

②

Domain of the variable — blue

I_{\min} = 0.01,\quad I_{\max} = 80

$I \in \left[0.01, 80\right]$

$I = 0.01$ $I = 0.01$

Along the curve

③

Response curve — green

U=\tfrac12 L I^2

$I \in \left[0.01, 80\right]$

$I = 0.01$ $U = 1\times 10^{-6}$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}U}{\mathrm{d}I}

$I \in \left[0.01, 80\right]$

$I = 0.513$ $U^{\prime} = 0.01$

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-26 — Inductor energy ½LI²) is the form associated with Maxwell. Working symbols: $L$ , $I$ $\rightarrow$ $U$ . The work to establish current is ∫ L i di = ½ L I². Dual of the capacitor ½ C V².

Purpose

Purpose: compute

U

from

L

I

in Electrical via

U=\tfrac12 L I^2

U = ½ L I² stored in the magnetic field of an inductor. Use it when a real electrical question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

L = 20.000\,\mathrm{mH}

I = 5.000\,\mathrm{A}

, the governing relation

U=\tfrac12 L I^2

yields

U = 0.2500\,\mathrm{J}

. A coil, a current, an energy bar. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Inductance L20 mHCurrent I5 A

Outputs

Stored energy U0.2500 J

Reading speed

Watch on YouTube

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Narration of this film

A coil, a current, an energy bar.

The work to establish current is ∫ L i di = ½ L I². Dual of the capacitor ½ C V².

Reading speed

Watch on YouTube