All right, guys. So, for this video, we're going to take a look at these objects called dielectrics and how they play a role in capacitors and capacitor circuits. Let's check it out. Basically, what it does is it always increases the capacitance of that capacitor. Now the equation we're going to use to relate those is c=kcc0, where c is going to be effectively the new capacitance, and k is going to be a constant. The c0 is going to be what the capacitance is in a vacuum, or otherwise the old capacitance, if you will. Now this k constant, or kappa, but the Greek letter kappa, is called the dielectric constant. That dielectric constant is a number with no units and it's always greater than 1. It basically serves to weaken the electric field inside a capacitor. So that means if you stick a dielectric, it'll always weaken what the electric field is, and that's given by this equation right here, where the new electric field is going to be the old electric field or the electric field in a vacuum divided by this k constant. And if it's always greater than 1, then that means the electric field is always going to be less. Now, a lot of the time in these problems, you won't know which equations to use. There are 2 basic ways that we can connect dielectrics to capacitors. Let's go ahead and check them out.

The first is where you'll have a battery that's initially hooked up to a capacitor and you'll have these charges that build up on these plates right here. So, you have positive charges and negative charges. Now what happens is the battery is disconnected and then what happens is the dielectric material is inserted between the capacitor. So that's given by this green little material right here. Now we know that this dielectric material is going to increase the capacitance of this capacitor. But what happens is if the battery is not connected, then these charges have to remain the same. These charges have to remain conserved. So, in this situation, we have constant charge. And what happens in these examples, we can relate the charge, the capacitance, and the voltage to see how these variables will change. And we know that the capacitance is going to increase. We know that the charge is going to remain the same. The only way that happens is if the capacitance increases and the voltage decreases. So that means that the voltage has to decrease between the plates to maintain that constant charge. Now we also know that the charge is going to remain the same. So what does that mean for the potential energy? Well, we know that the capacitance is going to increase. And if this is in the denominator, then it means the potential energy also decreases. Now what ends up happening is that the potential energy ends up doing some work in compressing the capacitor together, so that that energy actually goes somewhere. Now what about the energy density? Well, we see that the energy density, the electric field is always going to be weakened by the presence of a dielectric material. So that means that this is always going to go down, and that means that the energy density is going to decrease over here. And, by the way, this equation also holds for our other scenario where we have a constant voltage. Let's go ahead and check out how that works.

So, in this case, we have the battery that is still connected when the capacitor when the dielectric material is inserted. So now you have a battery, and then you still have these positive charges that build up on the plates, the negative charges build up on these plates over here. And now what happens is, rather than the battery being disconnected, you have the dielectric material that's inserted while the battery is still connected. Now what happens is we know that the voltage wants to decrease, but if this thing is still connected to the battery, then what happens is that these positive charges sort of get released from the batteries, and they basically build up on the plates to effectively increase the charge. Let's see how that works just by using the equation.