ODE-27

First-order τ

RL time constant.

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GoverningFirst-order τ

Governing equation

\\tau=L/R

where

L: L (H)
R: R (Ω)
tau: First-order τ (s)

Lecture brief

Historical brief

Exponential decay, the harmonic oscillator, SIR epidemics, Lotka–Volterra and Bessel are the first solvable ODEs of nature and populations. The lab is rate, period and phase portrait in closed form. This sheet (ODE-27 — First-order τ) is the form associated with First-order τ. Working symbols: $L$ , $R$ $\rightarrow$ $tau$ . RL time constant. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

tau

from

L

R

in Differential equations via

\\tau=L/R

RL time constant. Use it when a real differential equations question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

L = 0.080\,\mathrm{H}

R = 4.000\,\mathrm{Ω}

, the governing relation

\\tau=L/R

yields

tau = 0.020\,\mathrm{s}

. 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

L L0.08 HR R4 Ω

Outputs

First-order τ tau0.020 s

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Narration of this film

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

RL time constant. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube