ELC-09

Ohm's law

V = I R. The linear constitutive law of a resistor.

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CircuitsOhm

Governing equation

V=IR

$I \in \left[0.01, 20\right]$

where

I: Current (A)
R: Resistance (Ω)
V: 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=IR

$I \in \left[0.01, 20\right]$

$I = 0.01$ $V = 0.1$

Along the curve

②

Domain of the variable — blue

I_{\min} = 0.01,\quad I_{\max} = 20

$I \in \left[0.01, 20\right]$

$I = 0.01$ $I = 0.01$

Along the curve

③

Response curve — green

V=IR

$I \in \left[0.01, 20\right]$

$I = 0.01$ $V = 0.1$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}V}{\mathrm{d}I}

$I \in \left[0.01, 20\right]$

$I = 0.136$ $V^{\prime} = 10$

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-09 — Ohm's law) is the form associated with Ohm. Working symbols: $I$ , $R$ $\rightarrow$ $V$ . R = ρ L / A for a homogeneous prism. Temperature shifts ρ.

Purpose

Purpose: compute

V

from

I

R

in Electrical via

V=IR

V = I R. The linear constitutive law of a resistor. Use it when a real electrical question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

I = 2.000\,\mathrm{A}

R = 10.000\,\mathrm{Ω}

, the governing relation

V=IR

yields

V = 20.000\,\mathrm{V}

. A resistor, a current, a voltage drop. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Current I2 AResistance R10 Ω

Outputs

Voltage V20.000 V

Reading speed

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Narration of this film

A resistor, a current, a voltage drop.

R = ρ L / A for a homogeneous prism. Temperature shifts ρ.

Reading speed

Watch on YouTube