EMG-30

RC charging

Series RC voltage.

Reading speed

GoverningRC charging

Governing equation

V=V_0(1-e^{-t/RC})

$t \in \left[1, 4000\right]$

where

V0: V0 (V)
R: R (kΩ)
C: C (uF)
t: t (ms)
V: RC charging (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=V_0(1-e^{-t/RC})

$t \in \left[1, 4000\right]$

$t = 1$ $V = 0.012$

Along the curve

②

Domain of the variable — blue

t_{\min} = 1,\quad t_{\max} = 4000

$t \in \left[1, 4000\right]$

$t = 1$ $t = 1$

Along the curve

③

Response curve — green

V=V_0(1-e^{-t/RC})

$t \in \left[1, 4000\right]$

$t = 1$ $V = 0.012$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}V}{\mathrm{d}t}

$t \in \left[1, 4000\right]$

$t = 26.15$ $V^{\prime} = 0.012$

Along the curve

Lecture brief

Historical brief

Coulomb, Gauss, Ampère, Faraday and Maxwell (1861–65) unified charge, current and light. The lab computes fields, induction, Poynting flux and the electromagnetic wave in SI. This sheet (EMG-30 — RC charging) is the form associated with RC charging. Working symbols: $V0$ , $R$ , $C$ , $t$ $\rightarrow$ $V$ . Series RC voltage. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

V

from

V0

R

C

t

in Electromagnetism via

V=V_0(1-e^{-t/RC})

Series RC voltage. Use it when a real electromagnetism question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

V0 = 12.000\,\mathrm{V}

R = 10.000\,\mathrm{kΩ}

C = 100.000\,\mathrm{uF}

t = 400.000\,\mathrm{ms}

, the governing relation

V=V_0(1-e^{-t/RC})

yields

V = 3.956\,\mathrm{V}

. 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

V0 V012 VR R10 kΩC C100 uFt t400 ms

Outputs

RC charging V3.956 V

Reading speed

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Narration of this film

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

Series RC voltage. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube