1993 Toyota Supra Re: Alternator

Hi,

I suspect my alternator is having issues and need clarification. While my engine is running and I disconnect the battery my engine shuts down. Although the symptom is no longer present, from time to time my car used to stop when idle.

Also, would an issue with my alternator have an impact on other electrical components. My first car stereo stopped functioning one day. The led still lights but it doesn't play or display anything on the screen. I purchased and installed a new stereo and the same problems occurred. Would this problem be cause by under-voltage or over-voltage due to irregular current outputted by the alternator? Is there anything else that could be a likely culprit and what test can I run to rectify this problem?