can you draw/get 3000watts continuously from an power inverter at car idle?

Derrick

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I was told if your alternator on a average car, spinning at 1000 rpm (idle) putting out roughly 20-30amps, so (30amps x 12vdc) = 360 watts, it will not work. I had thought that you can hook up an 2500-3000watt inverter to your cigaret output to power your house light etc. When reading info from a inverter companies they said just hook up and power away. Which is correct?
 
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