What size of fuse is required for this small 24V system?
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It is not necessarily the battery chemistry that determines the size of your inverter it is the Ah and voltage rating. Also over sizing the inverter (even for short time high wattage loads) can drain your battery faster due to the higher "no load" wattage losses with just the inverter on. A 1500 watt inverter with a even a 5% no load loss will use 75 watts just sitting there. It's a vampire load which reduces the amount your battery can deliver.
1000 w msv draw 200 milliamp on 12 v
Another 1000w 12 v msw draw 1 amp ( the worst)
2300 w. Msw 24 v draw 250 milliamp
It s far from 5%Comment
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Sounds like you have a very efficient inverter. Some of those cheap ones will drain a battery faster than you can blink.Comment
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