Re: There's work, and then there's work

[Bob LaMontagne <rlamont@POSTOFFICE.PROVIDENCE.EDU>]

David Rutherford wrote:

> I noticed this interesting comment at
>
> http://hyperphysics.phy-astr.gsu.edu/hbase/electric/capeng.html
>
> regarding the energy stored on a capacitor:
>
> "From the definition of voltage as the energy per unit charge, one might
> expect that the energy stored on this ideal capacitor would be just QV.
> That is, all the work done on the charge in moving it from one plate to
> the other would appear as energy stored. But in fact, the expression
> above shows that just half of that work appears as energy stored in the
> capacitor. For a finite resistance, one can show that half of the energy
> supplied by the battery for the charging of the capacitor is dissipated
> as heat in the resistor, regardless of the size of the resistor."

Yes - the battery energy is reduced by qV, half going to the resistive
heating and the other 1/2 qV going to  the capacitor. But, since q = CV, the
energy increase in the capacitor is 1/2 CV^2, exactly as argued here many
times.

> If this is true, doesn't it imply that, when the capacitor is
> discharged, only half of the energy stored on the capacitor will be
> dissipated as heat in the resistor, therefore, the calorimeter
> experiment would only give _half_ of the energy stored on the capacitor?

Not at all - it's now a different circuit - the battery is no longer present
- hence no fixed EMF. The energy in the capacitor has no place to go but to
resistive heating. It all appears in the calorimeter.

Bob at PC