How do charges move through an insulated wire connected across a battery? Use the terms potential difference, current, conductor, and insulator in answer.

The battery has both a positive side and a negative side. The potential difference will be the potential of the positive end of the battery minus the potential of the negative end, which will result in positive potential, or power. This potential is what gives the electrons the ability to flow from the positive end to the negative end, or to make a current. While the outside of the insulated wire is the insulator, the inside of the wire has copper, which is the conductor of the current. So, this current will go through the copper of the wire (and not the insulator) from the positive side to the negative.