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I've received a bunch of emails regarding XBOX 360 Power, so here is what I have:
When I ran my setup, I borrowed a 750W True Sine inverter from work.
My 360 AC Power Brick has the following written on its label
Input 100 - 127V - 5A
Output DC 203W
12V @ 16.5A
5V @ 1A
So, the maximum AC input power is 127V x 5A = 635W
The total DC output power is (12V x 16.5A) + (5V x 1A) = 203W, which adds up to what they say.
My guess is the AC input power is max at 5A, but not nominal, I wouldn't expect the brick to be 203W/635W = 32% efficient. In other words, at 635W input, it would be giving off 432 W of heat.
Anyway, the question is how much inverter power do you really need? Well, anything over 635W would be the max. I'd say that 500W should work for sure. My best guess is that a 300W would be the absolute minimum that would work, but you are going to have to try it. Each inverter manufacturer is different, so a cheapo 300W may not work, but a good 300W inverter might.
with a min of 8 guage wire to the battery
Make sure you hard-wire it as well, cigarette lighters will have max amps which can go through them and a 360 will be way over that.
but with the wiring to the battery i would use a relay or fuse inline, no more than 30cm away from the positive terminal.
Use 8ga cable to wire up the invertor. I also have my doubts that it will run properly, but you never know you might get away with it. I hope for your sake you didnt go on the advice of someone from dick smith's or something... they really have no clue.