ELC-43

Capacitor energy

Stored electric energy.

Reading speed

CircuitsCapacitor energy

Governing equation

U=\tfrac12 CV^2

$V \in \left[1, 400\right]$

where

C: C (µF)
V: V (V)
U: 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 CV^2

$V \in \left[1, 400\right]$

$V = 1$ $U = 5\times 10^{-5}$

Along the curve

②

Domain of the variable — blue

V_{\min} = 1,\quad V_{\max} = 400

$V \in \left[1, 400\right]$

$V = 1$ $V = 1$

Along the curve

③

Response curve — green

U=\tfrac12 CV^2

$V \in \left[1, 400\right]$

$V = 1$ $U = 5\times 10^{-5}$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}U}{\mathrm{d}V}

$V \in \left[1, 400\right]$

$V = 3.509$ $U^{\prime} = 3.51\times 10^{-4}$

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-43 — Capacitor energy) is the form associated with Capacitor energy. Working symbols: $C$ , $V$ $\rightarrow$ $U$ . Stored electric energy. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

U

from

C

V

in Electrical via

U=\tfrac12 CV^2

Stored electric energy. Use it when a real electrical question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

C = 100.000\,\mathrm{\mu F}

V = 24.000\,\mathrm{V}

, the governing relation

U=\tfrac12 CV^2

yields

U = 0.0288\,\mathrm{J}

. 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

C C100 µFV V24 V

Outputs

Energy U0.0288 J

Reading speed

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Narration of this film

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

Stored electric energy. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube