ELC-41

Maximum power transfer

Matched-load power.

Reading speed

CircuitsMaximum power transfer

Governing equation

P_{max}=V_{th}^2/(4R_{th})

$R_{th} \in \left[0.1, 40\right]$

where

V_{th}: Vth (V)
R_{th}: Rth (Ω)
P_{max}: Power (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_{max}=V_{th}^2/(4R_{th})

$R_{th} \in \left[0.1, 40\right]$

$R_{th} = 0.1$ $P_{max} = 360$

Along the curve

②

Domain of the variable — blue

R_{th}_{\min} = 0.1,\quad R_{th}_{\max} = 40

$R_{th} \in \left[0.1, 40\right]$

$R_{th} = 0.1$ $R_{th} = 0.1$

Along the curve

③

Response curve — green

P_{max}=V_{th}^2/(4R_{th})

$R_{th} \in \left[0.1, 40\right]$

$R_{th} = 0.1$ $P_{max} = 360$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}P_{max}}{\mathrm{d}R_{th}}

$R_{th} \in \left[0.1, 40\right]$

$R_{th} = 0.351$ $P_{max}^{\prime} = -598.1$

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-41 — Maximum power transfer) is the form associated with Maximum power transfer. Working symbols: $V_{th}$ , $R_{th}$ $\rightarrow$ $P_{max}$ . Matched-load power. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

P_{max}

from

V_{th}

R_{th}

in Electrical via

P_{max}=V_{th}^2/(4R_{th})

Matched-load power. 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_{th} = 12.000\,\mathrm{V}

R_{th} = 4.000\,\mathrm{Ω}

, the governing relation

P_{max}=V_{th}^2/(4R_{th})

yields

P_{max} = 9.000\,\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

Vth V_{th}12 VRth R_{th}4 Ω

Outputs

Power P_{max}9.000 W

Reading speed

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Narration of this film

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

Matched-load power. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube