EEVblog1618 - How To Derive The Equation For Energy In A Capacitor

[EEVblog]

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.

[fzabkar]

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