Fan trouble

Hello all, just bought a Dell Inspiron 15 5000 a few weeks ago. Haven't noticed any problems until just now. It has to do with the fan. If my computer is plugged in, the fan starts up and runs on full, regardless of what I am doing. It sounds like it is running fine but should it be running on full when i'm using a word document? Funny thing is the fan stops completely when it is unplugged. Any suggestions? Is this normal? Thanks