ELC-42

Joule heating

Ohmic dissipation.

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CircuitsJoule heating

Governing equation

P=I^2 R

$I \in \left[0.1, 40\right]$

where

I: Current (A)
R: R (Ω)
P: Heat (W)

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

P=I^2 R

$I \in \left[0.1, 40\right]$

$I = 0.1$ $P = 0.02$

Along the curve

②

Domain of the variable — blue

I_{\min} = 0.1,\quad I_{\max} = 40

$I \in \left[0.1, 40\right]$

$I = 0.1$ $I = 0.1$

Along the curve

③

Response curve — green

P=I^2 R

$I \in \left[0.1, 40\right]$

$I = 0.1$ $P = 0.02$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}P}{\mathrm{d}I}

$I \in \left[0.1, 40\right]$

$I = 0.351$ $P^{\prime} = 1.404$

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-42 — Joule heating) is the form associated with Joule heating. Working symbols: $I$ , $R$ $\rightarrow$ $P$ . Ohmic dissipation. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

P

from

I

R

in Electrical via

P=I^2 R

Ohmic dissipation. 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 = 8.000\,\mathrm{A}

R = 2.000\,\mathrm{Ω}

, the governing relation

P=I^2 R

yields

P = 128.00\,\mathrm{W}

. One governing identity, SI units, a single sweep on the sheet. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Current I8 AR R2 Ω

Outputs

Heat P128.00 W

Reading speed

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Narration of this film

One governing identity, SI units, a single sweep on the sheet.

Ohmic dissipation. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube