To get a good answer you would have to let us know what make and model converter charger or inverter charger you have.
There are basically three stages of charging: Bulk; Acceptance; and Float.
Bulk:
When a low battery bank is connected to a three stage charger it will begin charging rapidly. As it starts to "fill" with amp hours the charger will increase its voltage output to maintain a constant charge rate.... likely in the neighborhood of 25 amps per battery in the bank.
Acceptance:
At a predetermined level of charge, which is designed into the charger, the charge voltage will drop to a constant voltage of around 14.2 volts. During this stage the amps the battery bank charges at will be lower and will taper off as the battery nears a full level of charge.
Float:
Once a full level of charge is reached a multistage charger will again adjust its charge voltage down to around 13.6 volts where it will maintain a healthy voltage for your batteries.
A single stage charger will likely operate only at the Acceptance stage. So, the batteries won't recharge as fast as what is ideal and healthiest and when they reach full charge they will be held at a voltage that is higher than what is ideal for the batteries.
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