Cooler fans

Hello together, I have a V70 with 144 hp and the problem when I switch on the air conditioning of the fan motor after a short time, but does not switch off anymore, it always runs, only when I switch off the engine and start again is the first time off. Is this normal that the fan always runs, would not have to go out in between or if I switch off the air conditioning. If the climate is not on, the fan only starts when I stand a little longer in idle mode, then it goes out again when I drive. Could the relay at the front of the cooler have a defect? Greeting F90