ELC-45

Wye–delta R

Balanced wye-delta.

Reading speed

CircuitsWye–delta R

Governing equation

R_\Delta=3R_Y

$R_Y \in \left[0.5, 100\right]$

where

R_Y: Wye (Ω)
R_Delta: Delta (Ω)

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

R_\Delta=3R_Y

$R_Y \in \left[0.5, 100\right]$

$R_Y = 0.5$ $R_Delta = 1.5$

Along the curve

②

Domain of the variable — blue

R_Y_{\min} = 0.5,\quad R_Y_{\max} = 100

$R_Y \in \left[0.5, 100\right]$

$R_Y = 0.5$ $R_Y = 0.5$

Along the curve

③

Response curve — green

R_\Delta=3R_Y

$R_Y \in \left[0.5, 100\right]$

$R_Y = 0.5$ $R_Delta = 1.5$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}R_Delta}{\mathrm{d}R_Y}

$R_Y \in \left[0.5, 100\right]$

$R_Y = 1.126$ $R_Delta^{\prime} = 3$

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-45 — Wye–delta R) is the form associated with Wye–delta R. Working symbols: $R_Y$ $\rightarrow$ $R_Delta$ . Balanced wye-delta. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

R_Delta

from

R_Y

in Electrical via

R_\Delta=3R_Y

Balanced wye-delta. Use it when a real electrical question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

R_Y = 10.000\,\mathrm{Ω}

, the governing relation

R_\Delta=3R_Y

yields

R_Delta = 30.00\,\mathrm{Ω}

. 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

Wye R_Y10 Ω

Outputs

Delta R_Delta30.00 Ω

Reading speed

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Narration of this film

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

Balanced wye-delta. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube