Rough idle only when stopped in gear with lights on

A couple of days ago i noticed while i was stopped at a light in gear at nighttime with my headlights on my elantra would start to idle rough.. just slightly at first then the longer i sit it just gets worse ;-( its sorta like a sputter every second or two.. the only thing i can think maybe it has something to do with my battery.. when i turn my loights off it almost immediatly gets better. about a week ago i installed a power inverter. maybe it slowly drains power even when its off? any ideas? TIA!

It sounds like your alternator is working overtime...is the inverter fused? if so try pulling the fuse to the inverter when you have the car started and lights on, to disable it, if the problems solved, it would be the inverter draining your battery and the alternator working harder to make up the current drain..

like fractured said your alt is doing double duty especially at an idle your alt is hardly producing any amp check your battery too if its the stock so-lite its probaly so-dead