lights dim when fan turns on?

When my radiator fan kicks on (and it has been on a lot since it is 96 in AZ) the dash lights and headlights dim and the engine sounds like it is going to die. I know it is just the alternator kicking in but does this happen to everyone? I mean, if the A/C is running and the fan kicks in the lights go from halogen to a 10 watt bulb. Is my battery on its way out?

Thanks