Shuttind down the sub will save alot of drain. Even with your system fully crancked, your front stage will only pull about 100 watts continuously. Your main problem will be the toyota alternator and battery. Even my camry only has a 90 amp alternator. I haven't checked the corolla, but some small import cars are as small as 45 amps. I do know that the corolla battery will only hold a 500 amp charge. I would go with a deep cell battery first thing. That should at least give you more time to run the system with the ignition off. Do your lights dim when the car is running and the bass hits? If so, then keep your sub lowered down untill you can replace the alternator with a high current one. I will take a look at my corolla and see what it is rated at. If it is anything around the 45 amp range, it will be a must to replace it. A 90 amp alternator will be plenty for most users. At that range, it all deepends on the style of music and listening level achieved. Just be aware that if your current alternator and battery fail, the warranty will not cover it. Aftermarket installs void the electrical warranty.
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2003 Maroon Alero GLS Sedan. (Purchased new in 2003 with 18 miles, and sold in 2006)
2004 Toyota Corolla LE (Purchased new in 2003 with 87 original miles)
2007 Toyota Camry LE (12 original miles)
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