**Concept:** Capacitors & Capacitance (Intro)

Hey guys. In this video we're going to be talking about these things called capacitors and a quantity that's related to them called capacitance. Now, you've probably seen capacitors before but these next two videos are going to be a lot more in depth. Alright, let's get to it. What a capacitor is, is it's two surfaces of equal and opposite charge brought into the general vicinity of one another, right? If I take two equal opposite charges, q and minus q, and bring them near each other, we know that they share an electric interaction and so they share a stored energy u, just an electric potential energy, likewise, if I have some positive plates with a bunch of positive charges and I'll say a total charge of positive q, and a negative plate, right? With all these negative charges and it's total charge negative q, all those positive and negative charges are going to interact, there's going to be all these interactions here and there's going to be a larger stored energy u, but still a stored energy, this is because anytime there's a separation of charge there's always some potential energy stored. Now, the most common type of capacitor you guys are going to see are called parallel plate capacitors. So, imagine some plate with some area a, and a charge q, and another plate with the same area a and the same shape and it charge negative q, any time you have two plates of the same area in the same shape brought close together you form a parallel plate capacitor, alright?

Now, in this figure here, we have a battery which is the symbol on the left in a capacitor the symbol on the right connected by conducting wires, these are the conducting wires, okay? What this forms is known as a circuit, if you connect a capacitor to a battery you form a simple circuit all the circuit is, is it's a loop of conducting wire with some things in it so that charges can move, okay? Electrons are going to be what moved side of conducting wires because proton can't move inside of materials, the question is, why would charges even move? what is the motivation for charges to move in a circuit? This motivation comes from a potential difference, okay? These electrons want to increase their potential, they want to go through some potential difference. So that when they're done, if they're at a higher potential, okay? A battery is a good provider of that potential difference, that motivation. Now, let's look at this battery, okay? The upper plate, the longer plate is going to be positively charged, by convention the lower plate, the smaller one is going to be negatively charged by convention, okay? And we're going to consider the capacitor as being initially uncharged. So, it's just two parallel plates with no charge, let's say this capacitor, the upper plate is at a potential 4 volts and the lower plate is at a potential negative 4 volts. Notice that this means that the potential difference Delta V is going to be 8 volts, okay? And just remember guys, we call potential difference voltage, okay? So, the potential difference is 8 volts, the voltage is 8 volts, okay? Because this capacitor is initially uncharged, has no charge both of its plates are at 0 volts, it has no potential because it has no charge, okay? Both of these are at 0 volts. Now, what we want to do, is consider an electron sitting on the negative plate of the batteries, right? Now, it's at a voltage of negative 4 volts but it could increase its potential up to 0 volts, if it travels through this wire, so it will, there's motivation for those electrons to move through the wire and accumulate on this bottom face of the capacitor, likewise, an electron on the top plate of the capacitor is currently at 0 volts but it could increase its potential to 4 volts, if it traveled through the wire, so it will, there's motivation, that means that the top plate is losing electrons. So, it's becoming positively charged. Now, as those electrons are moving, as they're accumulating on the bottom plate of the capacitor and leaving the top plate the potential of those plates are changing, since the bottom plate is negative it's gaining negative potential, since the top plate is positive it's gaining positive potential, eventually the bottom plate is going to be negative 4 volts and the top plate is going to be 4 volts. Now, consider an electron on the negative plate of the battery, does it have any motivation to move? No, because the battery is at negative 4 volts of potential and the capacitor plate is at negative 4 volts of potential, it has no reason to move because the potential difference is 0 okay. Notice, what is the potential difference on the capacitor, what is the potential difference or the voltage between those two plates, Delta V is also 8 volts, these two are equal, this is always going to be true, whenever you connect a single capacitor to a single battery. the voltage of the battery equals the voltage of the capacitor, okay? And that's always true. Now, the question is, how much charge was transferred, right? How much charge did that capacitor gain? Well, according to our equation it gained some amount C times V, where C is the capacitance and V is the voltage, the question is, what is the capacitance C? Well, the capacitance measures the strength of the capacitor, the larger the capacitance the stronger the capacitor so the more charge stored, right? The larger the capacitor the larger the charge stored because that is a stronger capacitor. Now, if we want to actually measure capacitance, we're going to take our equation to equal C, V and divide V over, mathematically, capacitance can be defined as the charge per unit voltage, okay? And the units are going to be capital F which are farads q over V. Now, something I said about this equation here, the above equation and our equation here is that V is voltage, not potential. Remember, that we always said V was potential and voltage or potential difference was always Delta V, we've made a really big stink about it when covering electric potential, potential V, voltage is Delta V. Well, the thing is that from now on we're pretty much only going to be talking about the voltages, about potential differences. So, your book and your professor are just going to drop that Delta, okay? This is not a very good notation and sorry, it's going to make your lives more complicated but you need to get used to it because everyone pretty much uses this, objectively stupid notation. Alright, let's put this all together and do a quick example, what is the charge on the capacitor in the following figure? Well, our above equation at the top tells us that the charge on a capacitor is C times V, we know that capacitance, right? It's 3 volts but we don't know the voltage of the capacitor, this V is the voltage of the capacitor, not the voltage of the battery, which we do know, however it's important to remember that when a single capacitor is connected to a single battery their voltages are the same. So, this voltage is the voltage of the capacitor. So, we do in fact know the capacitance, 3 volts, and the voltage of the capacitor, so this is going to be 3 farads, 9 volts and that's 27 coulombs, okay? That wraps up our discussion on capacitance and capacitors, thanks for watching guys.