With inverters you also have to take into consideration the efficiency of the inverter itself when calculating power requirement. For example: 12V outlet is rated at about 10A or 120W. Inverter is 87% efficient.
120W * .87 = 104.4 W =Max size of inverter to use is 100W
You can use a battery isolator -check at places that sell equipment for RV's. A battery isolator is a device with 2 diodes inside. The center connection is for the output of the alternator, the one on the left goes to the car's starting battery, the one on the right goes to your inverter
battery. Since diodes conduct in one direction both batteries don't discharge and only function when charging.
Assuming that your inverter is 500W @ 87% = 500/.87 = 574W used at 12V @ 48A
The alternator rating should be listed in owner's manual or written on the back of your alternators casing somewhere.
The bonus feature of a battery isolator is in winter if you a little juice to crank over- just use a single battery cable short the right and left terminal and jump start your vehicle.
Check out these links: https://www.emarineinc.com/categories/Battery-Isolators
http://www.bluewatermarinesvc.com/html/bat_isolator.html
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