### Author Topic: EEVblog1618 - How To Derive The Equation For Energy In A Capacitor  (Read 2918 times)

0 Members and 1 Guest are viewing this topic.

#### EEVblog

• Posts: 38179
• Country:
##### EEVblog1618 - How To Derive The Equation For Energy In A Capacitor
« on: May 22, 2024, 02:37:53 am »
How To Derive The Equation For Energy In A Capacitor, E = 1/2 C.V²

NOTE: Re-edited from an old impromptu video to remove all unrelated stuff about the dumpster whiteboard I found.

« Last Edit: May 23, 2024, 01:40:11 am by EEVblog »

The following users thanked this post: boB

#### fzabkar

• Super Contributor
• Posts: 2512
• Country:
##### Re: EEVblog1618 - How To Derive The Equation For Energy In A Capacitor
« Reply #1 on: May 28, 2024, 04:39:46 am »
Code: [Select]
I = C . dV/dt

P = V . I = V . (C . dV/dt) = C . V. dV/dt

Energy acquired by capacitor during time interval dt is ...

dE = P . dt = (C . V. dV/dt) . dt = C .  V . dV

Energy E acquired by capacitor as it charges from V = 0 to V = Vf is ...

_   V = Vf
| |
|
|  C .  V . dV
|_|
V = 0

V = Vf
=  [ 1/2 . C . V^2 ]
V = 0

=  1/2 . C . Vf^2

« Last Edit: May 28, 2024, 04:42:21 am by fzabkar »

Smf