With the car running and the A/C on, the clutch will be turning with the belt. You can have someone turn off and on the A/C while you watch the clutch engage/disengage. If it is not, it could be the relay, if not the relay, that would mean that the clutch is slipping and you would typically smell it burning. That is what happened to me, mine began to slip, the air got warm and I could smell the clutch getting really hot from slipping. I have also seen the bearings go bad on them but that usually means grinding noises and some sparks associated with that. I am not sure but the clutch can sometimes be replaced, but in our disposable society, it might not be available for replacement.