2005 Hyundai Elantra - bad alternator?

I replaced an AC belt this morning and about 20 miles down the road my battery light came on and it will sometimes flash but comes right back on. I took the positive battery cable off while running and the car dies does it mean my alternator is bad or could this be another problem.

If something wasn’t blown before disconnecting that cable, there’s a good chance it is now. While that was an acceptable practice 40 years ago, it is no longer the case. Get the car to a pro, tell him the symptoms and what you did, and let him diagnose and fix it.

Don’t do that again. As Mopar says that is outdated theory and can damage electrical expensive things. If the belt also drives your alternator is could just not be tight enough.