ELC-44

Voltage divider

Resistive divider.

Reading speed

CircuitsVoltage divider

Governing equation

V_o=V_i R_2/(R_1+R_2)

$R_2 \in \left[10, 10000\right]$

where

V_i: Input (V)
R_1: R1 (Ω)
R_2: R2 (Ω)
V_o: Output (V)

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

V_o=V_i R_2/(R_1+R_2)

$R_2 \in \left[10, 10000\right]$

$R_2 = 10$ $V_o = 0.119$

Along the curve

②

Domain of the variable — blue

R_2_{\min} = 10,\quad R_2_{\max} = 10000

$R_2 \in \left[10, 10000\right]$

$R_2 = 10$ $R_2 = 10$

Along the curve

③

Response curve — green

V_o=V_i R_2/(R_1+R_2)

$R_2 \in \left[10, 10000\right]$

$R_2 = 10$ $V_o = 0.119$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}V_o}{\mathrm{d}R_2}

$R_2 \in \left[10, 10000\right]$

$R_2 = 72.83$ $V_o^{\prime} = 0.01$

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-44 — Voltage divider) is the form associated with Voltage divider. Working symbols: $V_i$ , $R_1$ , $R_2$ $\rightarrow$ $V_o$ . Resistive divider. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

V_o

from

V_i

R_1

R_2

in Electrical via

V_o=V_i R_2/(R_1+R_2)

Resistive divider. 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_i = 12.000\,\mathrm{V}

R_1 = 1000.000\,\mathrm{Ω}

R_2 = 1000.000\,\mathrm{Ω}

, the governing relation

V_o=V_i R_2/(R_1+R_2)

yields

V_o = 6.000\,\mathrm{V}

. 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

Input V_i12 VR1 R_11000 ΩR2 R_21000 Ω

Outputs

Output V_o6.000 V

Reading speed

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Narration of this film

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

Resistive divider. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube