ELC-36

Inductor voltage v=L di/dt

v = L di/dt. Dual of the capacitor law i = C dv/dt.

Reading speed

CircuitsFaraday

Governing equation

v=L\dfrac{\mathrm{d}i}{\mathrm{d}t}

$\mathrm{d}i/\mathrm{d}t \in \left[-400, 400\right]$

where

L: Inductance (mH)
\mathrm{d}i/\mathrm{d}t: Current slope (A/s)
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.

00:0 / 00:08

①

Governing law — red

v=L\dfrac{\mathrm{d}i}{\mathrm{d}t}

$\mathrm{d}i/\mathrm{d}t \in \left[-400, 400\right]$

$\mathrm{d}i/\mathrm{d}t = -400$ $v = -4.8$

Along the curve

②

Domain of the variable — blue

\mathrm{d}i/\mathrm{d}t_{\min} = -400,\quad \mathrm{d}i/\mathrm{d}t_{\max} = 400

$\mathrm{d}i/\mathrm{d}t \in \left[-400, 400\right]$

$\mathrm{d}i/\mathrm{d}t = -400$ $\mathrm{d}i/\mathrm{d}t = -400$

Along the curve

③

Response curve — green

v=L\dfrac{\mathrm{d}i}{\mathrm{d}t}

$\mathrm{d}i/\mathrm{d}t \in \left[-400, 400\right]$

$\mathrm{d}i/\mathrm{d}t = -400$ $v = -4.8$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}v}{\mathrm{d}\mathrm{d}i/\mathrm{d}t}

$\mathrm{d}i/\mathrm{d}t \in \left[-400, 400\right]$

$\mathrm{d}i/\mathrm{d}t = -395$ $v^{\prime} = 0.012$

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-36 — Inductor voltage v=L di/dt) is the form associated with Faraday. Working symbols: $L$ , $\mathrm{d}i/\mathrm{d}t$ $\rightarrow$ $v$ . Flux linkage λ = L i, and v = dλ/dt. A linear inductor opposes a change of current.

Purpose

Purpose: compute

v

from

L

\mathrm{d}i/\mathrm{d}t

in Electrical via

v=L\dfrac{\mathrm{d}i}{\mathrm{d}t}

v = L di/dt. Dual of the capacitor law i = C dv/dt. Use it when a real electrical question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

L = 12.000\,\mathrm{mH}

\mathrm{d}i/\mathrm{d}t = 40.000\,\mathrm{A/s}

, the governing relation

v=L\dfrac{\mathrm{d}i}{\mathrm{d}t}

yields

v = 0.480\,\mathrm{V}

. A coil, a current ramp, a constant voltage. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Inductance L12 mHCurrent slope \mathrm{d}i/\mathrm{d}t40 A/s

Outputs

Voltage v0.480 V

Reading speed

Watch on YouTube

Free library

Full library

Free PDF / open book

YouTube channels

00:0 / 00:08

Narration of this film

A coil, a current ramp, a constant voltage.

Flux linkage λ = L i, and v = dλ/dt. A linear inductor opposes a change of current.

Reading speed

Watch on YouTube