Capacitors and capacitance

What's a capacitor? Well this is a capacitor. OK, but what's inside of this? Inside of this capacitor is the same thing that's inside basically all capacitors. Two pieces of conducting material like metal, that are separated from each other. These pieces of paper are put in here to make sure that the two metal pieces don't touch. But what would this be useful for? Well, if you connect two pieces of metal to a battery, those pieces of metal can store charge. And that's what capacitors are useful for. Capacitors store charge. Once the battery is connected, negative charges on the right side get attracted towards the positive terminal of the battery. And on the left side, negative charges get repelled away from the negative terminal of the battery. As negative charges leave the piece of metal on the right, it causes that piece of metal to become positively charged, because now that piece of metal has less negatives than it does positives. And the piece of metal on the left becomes negatively charged, because now it has more negatives than it does positives. It's important to note that both pieces of metal are going to have the same magnitude of charge. In other words, if the charge on the right piece of metal is 6 coulombs, then the charge on the left piece of metal has to be negative 6 coulombs. Because for every 1 negative that was removed from the right side, exactly 1 negative was deposited on the left side. Even if the two pieces of metal were different sizes and shapes, they'd still have to store equal and opposite amounts of charge. Now I've only show negative charges moving, because in reality it's the negatively charged electrons that get to move freely throughout a metal, or a piece of wire. The positively charged protons are pretty much stuck in place, and have to stay where they are. This process of charge switching sides won't continue to happen forever, though. Negative charges on the right side that are attracted toward the positive terminal of the battery will start to also get attracted toward the positively charged piece of metal. Eventually the negative charges will get attracted to the positive piece of metal, just as much as they're attracted toward the positive terminal of the battery. Once this happens, the process stops, and the accumulated charge just sits there on the pieces of metal. You can even remove the battery, and the charges will still just continue to sit there. The negatives want to go back to the positives, because opposites attract. But there's no path for them to take to get there. This also explains why the pieces of metal have to be separated. If the pieces of metal were touching during the charging process, then no charges would ever get separated. The negatives would just flow around in a loop because you've completed the circuit. That's why you want the paper in there, to keep the two pieces of metal from touching. So capacitors are devices used to store charge. But not all capacitors will store the same amount of charge. One capacitor hooked up to a battery might store a lot of charge. But another capacitor hooked up to the same battery might only store a little bit of charge. The capacitance of a capacitor is the number that tells you how good that capacitor is at storing charge. A capacitor with a large capacitance will store a lot of charge, and a capacitor with a small capacitance will only store a little charge. The actual definition of capacitance is summarized by this formula. Capacitance equals the charge stored on a capacitor, divided by the voltage across that capacitor. Even though technically the net charge on a capacitor is 0, because it stores just as much positive charge as it does negative charge. The Q in this formula is referring to the magnitude of charge on one side of the capacitor. What the voltage is referring to in this formula is the fact that when a capacitor stores charge, it will create a voltage, or a difference in electric potential, between the two pieces of metal. Electric potential is high near positive charges, and electric potential is low near negative charges. So if you ever have positive charges sitting next to, but not on top of, negative charges, there's going to be a difference in electric potential in that region, which we call a voltage. It's useful to know if you let a battery fully charge up a capacitor, then the voltage across that capacitor will be the same as the voltage of the battery. Looking at the formula for capacitance, we can see that the units are going to be coulombs per volt. A coulomb per volt is called a farad, in honor of the English physicist Michael Faraday. So if you allow a 9 volt battery to fully charge up a 3 farad capacitor, the charge stored is going to be 27 coulombs. For another example, say that a 2 farad capacitor stores a charge of 6 coulombs. We could use this formula to solve for the voltage across this capacitor, which in this case is 3 volts. You might think that as more charge gets stored on a capacitor, the capacitance must go up. But the value of the capacitance stays the same. Because as the charge increases, the voltage across that capacitor increases, which causes the ratio to stay the same. The only way to change the capacitance of a capacitor is to alter the physical characteristics of that capacitor. Like making the pieces of metal bigger, or placing the pieces of metal further apart. Just changing the charge or the voltage is not going to change the ratio that represents the capacitance. [MUSIC PLAYING]