The question in philosophy is "how does consciousness arise from the physical?" While you can claim it's due to some complex interaction in our brains, and while we have significant evidence that this is the case, I don't think that answers the question. Philosophers want to know the mechanism which produces the experience. Arguing that consciousness (or experience) is physical is a tough thing to do from first principles because of our own intuitive sense of it.

For example, how is it that the electrical signals in our brains produce "us" while electrical signals in other things don't produce conscious things? How are they different? What would it take to make a circuit "conscious"?

I can't give you good definitions for consciousness or experience and I can't even say that the question(s) make(s) sense. I'm just trying to give you give you a picture of what some people think.