A couple of useful tools to work with electricity are a digital voltmeter (multimeter) and a Kill A Watt meter. Harbor Freight sells an inexpensive digital multimeter for $6.39. Don't bother with a pointer style (analog) meter. You need a meter that shows tenths of a volt.
If you can easily get to the plug for the fridge you can use the Kill A Watt meter to show you amps, watts and volt-amps when the fridge is running.
A second alternator in the truck is of little help because of the thin wiring from truck to trailer. That's where the loss occurs. I added #4 gauge wiring from alternator to 7 pin receptacle and from 7 conductor cable on the trailer to the positive connection at the batteries and inverter. I also bonded the negative wiring to the chassis of both truck and trailer at the wiring ends. It made a BIG difference.
As stated earlier, measure voltage at running truck and trailer batteries WITH A KNOWN LOAD in the trailer like incandescent lights or the furnace blower. You want to see more than 13.2 volts in the trailer. Compare that with the running truck battery. It should be over 14 volts. If you're not running anything in the trailer you can't get any meaningful information. More load, more voltage drop. Anything less that 12.7 volts in the trailer means the trailer batteries are not charging.
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