The arc reactor in his body is the one that is powering the suit. He doesn’t need an extra one when that is already doing the job. The one in his body is only essentially an electromagnet and doesn’t use up much power so there is a lot left available to use to power his suits if needed. This is made somewhat explicit it Tony’s initial escape.
Yinsen: That could run your heart for fifty lifetimes.
Tony: Or something very big for fifteen minutes.
Iron Man
He later has arc reactors for his suits independent of the one in his chest because it makes more sense. It means the suit isn’t drawing from the vital power of the one in his body and it can use more power itself. However, that doesn’t mean the one in his chest can’t power his suits just that he chooses for it not to.
