Inverter

I have read quite a few posts here and have a few questions:  I just bought a 800 watt power invertor for $60 and I started to think about a few things I read on here.  I do not remember the reasons for doing so: but a few people had new alternators put in so there car could handle the load of their amp or something.  will I have any trouble running this 800 watt invertor or will it really drag down my car.  I may be just admitting my ignorance here, but I was just concerned.  I have seen something close to a 3000 watt invertor and I was curious even if my 800 watt would work fine, at what point would an invertor grag down the car enough to where a new alternator was necessary.  Like i said I may just have no idea what I am talking about.

Thanks