Electric Power

If a conductor is connected to a voltage source, the charge inside the conductor moves from one to the other pole due to the potential energy that can be written as $$E_\mathrm{pot} = q U$$ Since the electrons drift at a constant speed inside the wire, this energy must be given away to the enviroment. Taking the definition of power $P=\mathrm{d}E/\mathrm{d}t$ into account, the electric power can therefore be written as the product of the applied voltage and the current flowing through the wire. $$\boxed{P = UI}$$ This power is lost in the form of heat due to collisions of the electrons with the atomic cores. Now we can even insert Ohm's law $R = U/I$ and rewrite this formula according to $$\boxed{P = \frac{U^2}{R} = I^2R}$$ We can see from this relation that the power increases with the squared voltage and the squared current. It is important to mention that in this formula $U$ is the potential drop and not the applied voltage. This relation is also the reason why inside a grid, electricity is transported with very high voltages of several 100 kV. Because of $P=UI$, the current in the lines is relatively low and the power dissipation along the wires is therefore small.