Dometic fridges have a setting where you can Set a safety cut off at a certain voltage to avoid killing the battery. (Three settings low medium and high)
If your single LB is original I would think it wouldn't cope with more than a day powering a fridge, most definitely if you try and charge phones pads etc. unless you run the engine or use Electric hook up.
when new, the single LB will run the fridge for 3-4 days, this does deplete over time.
Driving will recharge thd LB quite quickly. (Avoid idling the engine whilst stationary on site )
Factors affecting run time from the battery: dependant on ambient outside temp (how hard the compressor has to work, and what temperature you set the fridge / freezer too). It's basically the same fridge freezer as at home, the lower harder it has to work to maintain temp, the more current it requires.
You can mitigate some of the battery usage by initially cooling the fridge and contents fully at home b4 loading the fridge into the van (you can also add ice packs to ensure the fridge is using minimal power). We quite after taken frozen food with us for the first few days meals. Allowing it to defrost naturally and slowly in the fridge before using over a couple of days, this helps keep battery depletion to a minimum.
Similarly depends on how many times you open the fridge to retrieve drinks, food etc.
As far as reading the voltage, there are two easily accessible 12v sockets i. The living area and one in the boot area, in the living area: one on the passenger B pillar , the other at the rear of the sliding door on the trim panel, by the useless cup holder.
Buy yourself a cheap 12v plug in charger that shows the voltage. These can be used periodically to keep an Eye on the LB voltage.
The 12v plug in voltage display (see image below) is useful for the front 12v socket , when plugged in you can keep an eye on when the van goes into Regen (voltage increases to 14+ volts constantly, the engine revs at idle increase to 1000 instead of the normal 800 revs, also start stop is disabled during Regen , the use of all three can assist in understanding when the can is In Regen (look up post regarding Regen and allowing the van to complete a Regen regularly)
Solar will fully top up the LB even on cloudy days (not very cloudy or heavy rain)
Hope that helps a bit - plenty of reading to do!
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