Maximum power/current for a battery?
[is] the 'total cell energy' varying?


Here's the third-roughest behavioral model of an electrochemical cell (rougher models omit one or both resistors).  For a typical cell of any chemistry, R1 varies with the state of charge -- it gets bigger as the battery discharges.  There are more complicated models, but I think this one is good enough.

So a 9V battery is just 6 1.5V dry cells in series, and they're both small and they've been made of a size to jam into a 9V battery package.  Because of these constraints, 9V batteries are notoriously wimpy.

If you just short the battery, then all of the voltage drops across the cells internal resistances.  The battery gets warm -- possibly discernibly so -- but no useful work is done outside of it.

If you draw current very slowly from the battery, then up to a point you'll get the maximum energy out of the battery -- but above that point, the battery's self-discharge current (which I've modeled with R2) dominates.  If you just leave the battery sitting on a shelf, it loses charge (over years, if it's a well-made dry-cell battery), and delivers no useful energy.

So -- does the total electrical energy that you can get out of the battery vary by the load you put on it?  Yes -- every battery has an optimal load.  When you're designing a product, if you dig you'll find that every product has an optimal battery, too.  Even for dry cells, some brands and models will do better with long slow loads, and some will do better for high loads.  Get into the wider world of rechargeable cells, and you'll find that particularly with NiMH, NiCd and LiPo cells, different cells are available in (roughly) the same size that are suited for different tasks.

But -- does the total energy in the battery vary by the load you put on it?  I don't think so, but I don't know for sure.  It would be an interesting science fair project to put some dry cell batteries into a calorimeter and compare the amount of energy released as heat by the cell and wiring when you short (or nearly short) a cell to the energy released as heat + electrical energy when you discharge a cell more slowly.

If the total energy released does vary, it would be because discharging a battery fast may "lock in" some charge*, but the total chemical energy in the cell would have to be the same, by conservation of energy.







simulate this circuit &ndash; Schematic created using CircuitLab

* Dry cells don't like getting discharged quickly, and at least older cells would develop a region in the electrolyte that wouldn't conduct electricity -- for those older cells, you could revive them by baking them in an oven to break up the non-conducting layer.