Electronic – How does a lead acid battery accept more current when it is discharged than when it is charged if the resistance is higher when it is discharged

You will probably need an intelligent charger (micro controller based with a custom program to handle inputs from V&A meters, solar charge controller, & a power regulator).

Common methods of determining the SOC of a 12V(nominal) battery aren't very accurate. Most often people use a generic table that shows V & SOC %. The problem with that data set is that it applies to a new/good battery and as a battery ages & deteriorates the internal battery resistance increases, charge capacity decreases, & charge rate decreases (i.e. the charge rate of an aged battery is slower at a specific voltage than a new battery)--so you can't rely on it as a reliable method to charge a battery with solar energy while the engine is off & power is being drawn from the battery.

If you use a micro controller based smart charger with a good program, you should be able to do the following to determine the maximum safe voltage to apply to the battery while the engine is off: 1. measure the battery V 2. measure the A draw of the system 3. To maintain the battery's current SOC, your power system must produce as much power as the system is consuming. Your program would calculate the optimal charge A & V to provide sufficient charge current to offset the power consumption rate. 4. To add a net charge increase in the battery, your computer program will have to provide a higher charge rate than the charge consumption rate (you can decide that rate or make it a user configurable parameter).

Note: The regulated charging system of a running vehicle provides sufficient power to charge the battery & maintain other electrical loads. Your smart charger will have to emulate the same power availability while the engine is off (which might mean you'll need quite a bit of PV surface area (depending on loads).

Okay, lots of stuff to talk about.

The thing about battery charging is that the battery has its own voltage, so resistance is only half of the story. If the charger is at 12 volts, and the battery is at 11.6, then the .4 volts difference is all that is pushing the current into the battery. This small voltage divided by whatever resistance it finds in the cables and battery determines that current. You might see a 100 amp peak, say when starting an actual car. That causes a rather large voltage transient.

And then, that isn't exactly right either. The voltages that you see while charging will be really very close to each other, and what's actually happening is you are replacing electrons in the battery chemistry to make its reaction go backwards. Its just a lot easier to model this mathematically as an ideal voltage source behind some internal resistance.

But the resistance is a real thing. Professional tools actually place a small value of AC current through the cell and take an AC voltage reading across the cell. This and Ohm's law gets you the value of the internal resistance for the pack or cell, wherever you can get terminals to check it. But, generally, this won't matter to you.

Hooking it all up together will work, with the caveat that diode Vladimir mentions needs to be in the line so the battery doesn't discharge through it. It may be built into the alternator already, maybe not. Do check that. What will happen is that when the battery voltage and the alternator voltage are the same, with no other loads connected, no current will flow.