Uploaded December 2021 | Updated September 2026, 2 weeks ago

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The equation for a charging capacitor can be derived from first principles of electrical circuits. This video shows how to do that derivation using the first order differential equation for the voltage across the capacitor. There is an alternative method that uses the first order differential equation for the charge on the capacitor, and you can see that video here: youtu.be/Y57y_13O8o8

vc(t) - voltage across capactior
vr(t) - voltage across resistor
ir(t) - current through resistor, which is the same as the current through the capacitor

Video Timeline
00:00 - Intro
00:15 - The RC circuit to analyze
01:15 - Start of vc(t) derivation
05:20 - vc(t) = Vs(1-exp(-t/RC))
05:49 - vr(t) = Vs(exp(-t/RC))
06:10 - Equations for vc(t), vr(t) and ic(t)
06:29 - Qualitative analysis of what happens when capacitor is charging
08:45 - Graphs of vc(t), vr(t) and ic(t) as capacitor charges
09:08 - Challenge question (Video going through the challenge question: youtu.be/4TTZGySaTiw)

Capacitor Playlist: youtube.com/playlist?list=PLQlQ509bAPoHE-TQER88ZnccYWuJ0slUY

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Outro Song Credit:
Music from Uppbeat (free for Creators!):
uppbeat.io/t/mountaineer/voyager