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*From*: brian whatcott <betwys1@sbcglobal.net>*Date*: Wed, 06 Aug 2014 13:38:43 -0500

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 EnergyMore-or-less everybody assumes that, but it's not necessarily

Dissipation". EG., when a battery charges a capacitor, 1/2 of the

battery-produced energy must be dissipated.

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

**References**:**[Phys-L] LC circuit simulation***From:*Diego Saravia <dsa@unsa.edu.ar>

**Re: [Phys-L] LC circuit simulation***From:*"Bob Sciamanda" <treborsci@verizon.net>

**[Phys-L] charging a capacitor reversibly (or nearly so)***From:*John Denker <jsd@av8n.com>

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