Current and power

In the following figure, we see a metal wire connected between the plates of a capacitor. We will imagine that we have some device (i.e., a battery) that maintains a fixed potential difference ΔV between the plates.

Electrons in the wire are free to move, so they will travel from the low potential to the high potential (electrons are negatively charged!)

We define the electron current, i, as the number of electrons passing by any point on our wire per unit time:

We define the current, I, as the charge passing by any point on our wire per second:

Since the charge on an electron is −e, the current and electron current are related by:

Notice the minus sign.  This says that if the electrons are traveling to the left, then the current  is traveling to the right! We can thank Ben Franklin for this.  The current, I, is always taken as the direction that positive charges would be flowing if they were responsible for the current (which they sometimes are).

We can also calculate the rate at which the charges (electrons, in this case, are losing energy).  Since the change in potential energy of one electron going from the low to high potential is ΔU=eΔV, the rate at which the electrons lose energy is:

Where does the energy go? We will see later that it goes into the internal energy in the wire.  We usually call P the power dissipated.