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Dielectrics in capacitors
In most capacitors, a non-conducting material is placed between the two metal pieces that make up that capacitor. There's two reasons for this. For one, the non-conducting material prevents the pieces of metal from touching each other, which is important because if the pieces of metal were touching, no charge would ever get stored since you've completed the circuit. But there's another bonus to inserting a non-conducting material between the plates of a capacitor. It will always increase the capacitance of that capacitor. As long as the material is non-conducting, it doesn't even matter what it is. As long as you don't change the area or separation between the plates, inserting a non-conducting material will always increase the capacitance. The name we give to non-conducting materials place between capacitor plates is a dielectric. But why does a dielectric increase the capacitance? To find out, let's look at this example. When you hook up a battery of voltage V to a capacitor, charge will get separated. Now let's say you remove the battery. The charge is stuck on the plate since the negatives don't have a path in which to get back to the positives. So even after removing the battery, the charge on the plates is going to remain the same. And the voltage will also remain the same as the voltage of the battery that charged it up. Now imagine placing a dielectric in between the plates of the capacitor. The dielectric material is made out of atoms and molecules, and when placed in between the plates of this charged up capacitor, the negative charges in the dielectric are going to get attracted to the positive plate of the capacitor. But those negatives can't travel to the positive plate since this dielectric is a non-conducting material. However, the negatives can shift or lean towards the positive plate. This causes the charge in the atoms and molecules within the dielectric to become polarized. To put it another way, the atom kind of stretches and one end becomes overall negative and the other end becomes overall positive. It's also possible that the dielectric material started off polarized because some molecules are just naturally polarized like water. In this case, when the dielectric is placed between the charged up capacitor plates, the attraction between the negative side of the polarized molecule and the positive plate of the capacitor would cause the polarized molecules to rotate, allowing the negatives to be a little bit closer to the positively charged capacitor plate. Either way, the end result is that the negatives in the atoms and molecules are going to face the positive capacitor plate and the positives in the atoms and molecules are going to face the negative capacitor plate. So how does this increase the capacitance? The reason this increases the capacitance is because it reduces the voltage between the capacitor plates. It reduces the voltage because even though there's still just as many charges on the capacitor plates, their contribution to the voltage across the plates is being partially cancelled. In other words, some of the positive charges on the capacitor plate are having their contribution to the voltage negated by the fact that there's a negative charge right next to them now. Similarly, on the negative side there's just as much negative charge as there ever was, but some of the negative charges are having their contribution to the voltage canceled by the fact that there's a positive charge right next to them. So the total charge on this capacitor has remained the same, but the voltage across the plates has been decreased because of the polarization of the dielectric. If we look at the definition of capacitance, we see that if the charge stays the same and the voltage decreases, the capacitance is going to increase, because dividing by a smaller number for the voltage is going to result in a larger value for the capacitance. So inserting a dielectric in this case, increase the capacitance by lowering the voltage. Let's look at another case of inserting a dielectric. Imagine we, again, let a battery of voltage V fully charge this capacitor. And let's insert a dielectric between the plates. But this time, let's leave the battery connected. Now what's going to happen? Well, just like before, the atoms and molecules in the dielectric are going to stretch and orient themselves so that the negatives are facing the positive plate and the positives are facing the negative plate, which again reduces the voltage between the two capacitor plates. But remember, we left the battery connected and this battery is going to try to do whatever it has to do in order to make sure the voltage across the capacitor is the same as the voltage of the battery V. Because that's just what batteries do. They try to maintain a constant voltage. So since the dielectric reduced the voltage by canceling the contributions from some of the charges, the battery's just going to cause even more charges to get separated until the voltage across the capacitor is again the same as the voltage of the battery. So the charge stored on the capacitor is going to increase, but the voltage is going to stay the same. Looking at the definition of capacitance, the charge on the capacitor increased after we inserted the dielectric. But the voltage across the capacitor plates stayed the same, since it's still hooked up to the same battery. So the effect of inserting a dielectric again is to increase the capacitance, this time by storing more charge for the same amount of voltage. To figure out how much you've increased the capacitance, you just need to know what's called the dielectric constant of the material that you've inserted between the capacitor plates. The dielectric constant is often represented with a Greek letter kappa or simply a K. The formula for finding out how the dielectric will change the capacitance is simple. If the capacitance of a capacitor before inserting a dielectric was C, then the capacitance after inserting a dielectric is just going to be k times C. We should note that since a dielectric always increases the capacitance, the dielectric constant k for a non-conducting material is always greater than 1. So for example, if a capacitor as a capacitance of 4 farads, when you insert a dialect with dielectric constant 3, the capacitance will become 12 farads.