27 Circuit Elements
Ideal Batteries
This section is about the power coming out of the wall or a battery, which is probably the first thing you think of when you start thinking about electricity and electric circuits.
One of the important things is what is the electron volt as a unit, to go through the math, we’re starting with the definition of potential, if we put a charge in a potential we get a potential energy, , charge, is which gives me or one electron volt (1 eV). And in fact, this is what an electron volt is, the potential energy gained by a single electron going over a volt. We’ve mentioned this number before, the energy you need to ionize hydrogen gas is electron volts, meaning that you have to give that electron electron volts to rip it away from its nucleus. Based upon this you can say that the potential difference, not the potential energy, between the ground state of the electron and very far away is volts.
Instructor’s Note
Keeping this distinction between electron volts as energy and volts as potential is going to be really important for this section.
Our question for this section is: what is a battery?
Essentially, it’s two pieces of metal in contact. If you think back to Unit 1 we talked about this photoelectric effect, and we explained how much energy you need to remove electrons from a metal. That was described by the work function, which we used to find how much energy we need to remove an electron from the surface of a metal.
Instructor’s Note
We connected this with photons and other things but the key thing you need right now is that there is this material dependent number that essentially tells you how much energy you need to rip an electron off the surface and it’s called that work function.
If we take gold and platinum and touch them together, we can make a simple battery. Gold has a work function of about and platinum have a work function of about . This means that an electron in the surface of the gold has a potential energy of because the charge of an electron is negative, so the potential energy might take this positive and we get a negative potential.
What’s going to happen when we touch these two things together?
Well the electron in the gold is going to slide down because now that’s a lower energy state in gold it has a potential energy of in platinum it has a potential energy of , it can lower its potential energy by by sliding down from the gold to the platinum.
The energy sliding the electrons sliding over it is losing , if the potential energy difference is then the potential difference is , so we have a potential difference and electrons spontaneously moving from two metals in contact.
So, what is a battery?
A potential difference that, if I connect the two metals across the terminals the electrons spontaneously move. This is essentially the simplest battery I can think of. And eventually this repulsion is going to stop the flow, you’re going to build up a negatively charged thing and electrons aren’t going