quick question about alternator

[jhandy]

I have been having problems keeping my battery charged. I have got a new battery from Autozone and the problem still returns.

If I let the car sit for a day or so, the battery is very low.
I left the lights on tonight when I got pulled over, and I had to get a jump from DPS after only 10 mins of sitting.

I got a warning for no front plate if anyone is wondering.

Anyway, my question is.....

Should my car continue to run if I disconnect the battery. This is a quick way I use to test the alternator in the old days. The thought is that the car only needs the battery to start. The alternator should put out enough juice to run.

With the car started, battery diconnected, it idles rough.......

If I turn on the lights the car dies.

I dont have a multimeter.
What should the alternator be putting out at idle?

Thanks,
James