What does the auto belt tensioner have to do with my air conditioning?

I was told that my tensioner burnt up because of the compressor problems with my air conditioner?

Is this right? I am trying to make the connection!

The tensioner, by reference of it's name, keeps tension on the serpentine belt. If a pulley (a/c in this case) locks up or goes out of alignment, it puts strain on the tensioners pulley. A bad tensioner will lead to belt failure and charging problems.

To the same effect, I have seen where alternators go bad on a serpentine setup and shortly after it's been corrected, and if the A/C compressor is horizontal from it, the A/C clutch goes bad.

Tensioners are fairly easy to replace based on their location and obstructions.