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yes it is poss, get a headphone to rca convert and hook it up from there then (dangerous!) us a car battery charger or a a/c-to-d/c converter (easily)but those can be a bit pricey, and last, just use a fan to cool the amp
now this setup would destroy your amplifier and probably electrocute you for wiring it up. you wire up your amp with a power lead straight from the positive on the battery and the negative on the amp connects to the metal chasis of your car. this earth's your amp allowing current to flow directly from your battery to the metal of your car though the amp.
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Home electric runs on a/c, car electric on d/c, and they aren't compatible. In addition, home speakers and car speakers are difference resistance. Car speakers are 4ohm, home speakers are 8ohm, two different things
sorry but my home speakers are 4ohm. this just means that they are harder for my amp to drive. Most car speakers are higher then 8 ohms so that crappy little stereo can run them. then again my sisters speakers are 16 ohm.