Uploaded December 2021 | Updated September 2026, 3 weeks ago
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 charge on the the capacitor. There is an alternative method that uses the first order differential equation for the voltage across the capacitor, and you can see that video here: youtu.be/zxnSvf0Utzw
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
00:34 - Develop intuitive idea of what happens in charging RC circuit
03:02 - Derive vc(t), vr(t), and ir(t) equations (this involves calculus, but that's okay, I'll walk you through it)
08:50 - vc(t) = Vs(1-exp(-t/RC))
09:30 - vr(t) = Vs * exp(-t/RC)
09:55 - ir(t) = Vs/R * exp(-t/RC)
10:07 - Challenge question (Video going through the challenge question: youtu.be/4TTZGySaTiw)
Capacitor Playlist: youtube.com/playlist?list=PLQlQ509bAPoHE-TQER88ZnccYWuJ0slUY
Check out my website
electronx.ca
Outro Song Credit:
Music from Uppbeat (free for Creators!):
uppbeat.io/t/mountaineer/voyager
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 charge on the the capacitor. There is an alternative method that uses the first order differential equation for the voltage across the capacitor, and you can see that video here: youtu.be/zxnSvf0Utzw
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
00:34 - Develop intuitive idea of what happens in charging RC circuit
03:02 - Derive vc(t), vr(t), and ir(t) equations (this involves calculus, but that's okay, I'll walk you through it)
08:50 - vc(t) = Vs(1-exp(-t/RC))
09:30 - vr(t) = Vs * exp(-t/RC)
09:55 - ir(t) = Vs/R * exp(-t/RC)
10:07 - Challenge question (Video going through the challenge question: youtu.be/4TTZGySaTiw)
Capacitor Playlist: youtube.com/playlist?list=PLQlQ509bAPoHE-TQER88ZnccYWuJ0slUY
Check out my website
electronx.ca
Outro Song Credit:
Music from Uppbeat (free for Creators!):
uppbeat.io/t/mountaineer/voyager
