We'll focus mainly on ohmic materials for now, those obeying Ohm's Law. A copper wire has a length of 160 m and a diameter of 1.00 mm. The V is the battery voltage, so if R can be determined then the current can be calculated. The resistivity can be found from the table on page 535 in the textbook. The area is the cross-sectional area of the wire.
Power is the rate at which work is done.
It has units of Watts. Batteries and power supplies supply power to a circuit, and this power is used up by motors as well as by anything that has resistance. In many cases, Joule heating is wasted energy. In some cases, however, Joule heating is exploited as a source of heat, such as in a toaster or an electric heater. The electric company bills not for power but for energy, using units of kilowatt-hours.