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# Re: [Phys-L] charging a capacitor reversibly (or nearly so)

On 8/6/2014 10:38 AM, John Denker wrote:
On 08/06/2014 07:36 AM, Bob Sciamanda wrote:

Perhaps this is a correctly simulated instance of "Mandated Energy
Dissipation". EG., when a battery charges a capacitor, 1/2 of the
battery-produced energy must be dissipated.
More-or-less everybody assumes that, but it's not necessarily
true!

A whole lot of very smart people have gotten that wrong
over the years.

If we are clever, we can dissipate a whole lot less than
half of the energy. Proof by construction:

A battery, by definition, is a collection of /cells/.
Assume all N cells are in series. Assume we have access
to the individual cells. Let the cell voltage be u (small
u) while the battery voltage is V (big V) where V = N u.

Charge the capacitor step by step. Start by hooking it
up to just one cell. This moves a charge (C u) across an
average voltage drop of u/2, so it dissipates energy on
the order of (C u^2/2). This is very small, since u is
small. /snip/

A few other people of indeterminate smartitude suggest that in real world terms where cells all show some internal resistance, the charging voltage waveform is exponential so that the mean voltage across the capacitor would be 0.7 u :-)

Brian Whatcott Altus OK