 Up to this point, we've talked about how in a purely resistive circuit, the current and the voltage are in sync. They are said to be in phase. We also saw that in a purely inductive circuit that the current lags the voltage by 90 degrees. This video is going to talk about how in a purely capacitive circuit, the voltage lags the current by 90 degrees. It's the exact opposite, as it always seems to be with capacitors and inductors. I know. So let's get into the why of why this is. Here we have a purely capacitive circuit. There's no resistance in this circuit. It's just a source voltage there, a switch there, and we have our capacitor there, which is just two plates separated by some sort of dielectric or insulator. When the switch is open, we have a source voltage here, but we will have no voltage on the plates. And if we have no voltage on the plates with a switch open, we have an open circuit, which means we have no current flowing through the circuit. These will change once we close that switch. Now that the switch is closed, we have our source voltage here. We have a closed pathway for the current to flow. Now with these plates, Kerchoff's law has to be obeyed, which tells us that the sum of the volt drops in the circuit has to equal the source voltage. In order for that to happen, we need to have a difference of potential across the plates here. In order for that to happen, we have to have current, or we have to have electrons on these plates. Now in order to get the electrons on the plates, current has to flow. So we have to get electrons moving. Therefore once that switch is closed, we're going to have current flowing directly across there. Now once these plates reach the full voltage, which is a source voltage, that means that we will have electrons on this side and this side, which means that we will no longer need current to flow, which would mean that current will be at zero. So you're starting to sort of see the pattern here. When the switch is closed and the voltage across the plates is zero, in order to get a volt drop across this, we need to have electrons on these plates, which means current will have to be at its maximum. Once that the plate has full voltage, there's no more need to put electrons on those plates. Therefore current would be at its minimum. So let's take a look and see how that charts out on our sine wave. Okay, here we go. As we said before, when this switch here is closed, that means that the plates here have to get electrons on them, which means that in order for that to happen very quickly, we have to have a high amount of current. So we'll say that current is at our maximum. So let's just draw that in there with a nice purple. When my voltage is zero at this point here, our current is going to be at its maximum. So we're going to throw a little line up there. We'll try this out later. Then when my voltage is at its maximum point across the plates here or in the circuit, that means there's no more need for current to flow. I have all the electrons I need at that plate. Therefore, my current will be at zero. So we'll put that roughly around the middle there. Sorry for the rough drawing here. My fingers aren't as solid as they used to be. Then I, again, am going the opposite way. My voltage gets back down to zero. You see my volt drop here is zero on the wave form. If my volt drop is at zero there, that must mean that my current is going to be at its maximum in the opposite direction. So I'll chart that out here. We'll say that's about our maximum at that point. Again, we've got our voltage here being at its maximum, which means there's no more need for current to flow. So it would be at zero. Now if we take this and we draw this out, if I follow these points, that we're seeing that in our very rough drawing that my voltage is lagging my current or my current at this point. If you see it crosses the x-axis before the voltage does, let me just clean up this wave form a bit. There, that looks a lot better. Now, as I was saying before, we have our current here. Sorry, our current crosses before our voltage crosses. And if you do the math as I did in the inductor, you'll see that in a purely capacitive circuit, my current leads my voltage by 90 degrees. I remember in a purely inductive circuit, it was my voltage leads my current. But in this case, we're going to say that my current needs my voltage by 90 degrees in a purely capacitive circuit.