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}

where

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

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