ELC-02

Resistive voltage divider

Vout = Vin R2 /(R1+R2) from KVL and Ohm.

Reading speed

CircuitsKirchhoff 1845

Governing equation

V_{\mathrm{out}}=V_{\mathrm{in}}\dfrac{R_2}{R_1+R_2}

$R_2 \in \left[1, 1\times 10^{6}\right]$

where

V_{\mathrm{in}}: Input voltage (V)
R_1: Upper resistor (Ω)
R_2: Lower resistor (Ω)
V_{\mathrm{out}}: Output voltage (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_{\mathrm{out}}=V_{\mathrm{in}}\dfrac{R_2}{R_1+R_2}

$R_2 \in \left[1, 1\times 10^{6}\right]$

$R_2 = 1$ $V_{\mathrm{out}} = 0.003$

Along the curve

②

Domain of the variable — blue

R_2_{\min} = 1,\quad R_2_{\max} = 1\times 10^{6}

$R_2 \in \left[1, 1\times 10^{6}\right]$

$R_2 = 1$ $R_2 = 1$

Along the curve

③

Response curve — green

V_{\mathrm{out}}=V_{\mathrm{in}}\dfrac{R_2}{R_1+R_2}

$R_2 \in \left[1, 1\times 10^{6}\right]$

$R_2 = 1$ $V_{\mathrm{out}} = 0.003$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}V_{\mathrm{out}}}{\mathrm{d}R_2}

$R_2 \in \left[1, 1\times 10^{6}\right]$

$R_2 = 6290.3$ $V_{\mathrm{out}}^{\prime} = 6.94\times 10^{-4}$

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-02 — Resistive voltage divider) is the form associated with Kirchhoff 1845. Working symbols: $V_{\mathrm{in}}$ , $R_1$ , $R_2$ $\rightarrow$ $V_{\mathrm{out}}$ . Kirchhoff's loop rule plus two Ohm drops yields the divider; it is the elementary application of KVL.

Purpose

Purpose: compute

V_{\mathrm{out}}

from

V_{\mathrm{in}}

R_1

R_2

in Electrical via

V_{\mathrm{out}}=V_{\mathrm{in}}\dfrac{R_2}{R_1+R_2}

Vout = Vin R2 /(R1+R2) from KVL and Ohm. 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_{\mathrm{in}} = 12.000\,\mathrm{V}

R_1 = 4700.000\,\mathrm{Ω}

R_2 = 4700.000\,\mathrm{Ω}

, the governing relation

V_{\mathrm{out}}=V_{\mathrm{in}}\dfrac{R_2}{R_1+R_2}

yields

V_{\mathrm{out}} = 6.000\,\mathrm{V}

. No load current at the tap. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Input voltage V_{\mathrm{in}}12 VUpper resistor R_14700 ΩLower resistor R_24700 Ω

Outputs

Output voltage V_{\mathrm{out}}6.000 V

Reading speed

Watch on YouTube

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Narration of this film

No load current at the tap.

Kirchhoff's loop rule plus two Ohm drops yields the divider; it is the elementary application of KVL.

Reading speed

Watch on YouTube