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In a dual-battery system2) some of the alternator output is used to charge the house batteries. Since the house battery is electrically isolated from the starter battery when the ignition is off3), these are sometimes called battery isolators.
Alternator charging is generally only practical for the bulk charge stage due to relatively low voltage output and the long time periods required for absorption. It is unlikely to get the house battery completely charged unless one is driving significant distances. This can have an impact on battery longevity. If one drives often a combination of the alternator doing bulk charging and a small solar doing the rest is good match.
Charging the house batteries from the alternator increases the load on the alternator and can be expected to contribute to earlier failure. SternWake reports idling while charging causes a sharp increase in alternator temperature.4) So don't idle it!
Also see Is Solar Mandatory? for ideas on how to charge primarly by alternator.
Power from the alternator is shared with the house battery using an isolator of some sort. This allows the house battery to charge but does not allow the house battery to pull power from the starter battery.
If an isolator is oversized it will cost more for no benefit and will self-consume somewhat more energy to hold the combining circuit closed.7)
If an isolator is undersized (less common) it will not be able to carry enough current, resulting in overheating and/or sudden shutdown.
Consumer-grade AGM batteries typically will accept C/5 - C/3.
Example: a 200Ah AGM bank will pull up to 67A in Bulk. A 75A isolator11) would be sufficient.
Note: high-end AGM like Lifeline, Odyssey, Rolls, etc, can pull massive current when charging. 200A+ would be possible for the example bank and could shorten the life of a stock alternator.
Lithium also has the ability to accept massive amounts of charging. It will do so across the entire charging range, as lithium does not have an Absorption phase the way lead-acid does.
Example: 200Ah of lithium could easily accept 200Ah+. There are mitigating factors, however.
Sudden disconnection of a large load12) when the alternator is running can damage the alternator and any operating chassis electronics. Sudden disconnection can occur when:
Idling the engine to run the alternator can seriously overheat the alternator. It is usually cooled by wind from the vehicle's forward motion; a fan may help cool the alternator.
2 gauge copper wire connecting the coach and house is recommended for most alternator charging installs. SternWake recommends attaching at the alternator rather than the battery.13)
Note that you will only have to run the POS+ leg of wire to the house battery as the chassis ground is the other leg.
There are ways to get the alternator to pump out more power:
A simple possible approach would be to replace the starter battery with a marine or AGM battery.15)