Anderson Video - Capacitor Reactance

Professor Anderson
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Alright welcome back everyone, hopefully you got some more caffeine in your system, it's always a good thing. Let's take a look at the issues with capacitors. So if we have these AC circuits, what we said was things like resistors are just going to behave basically exactly the same as in a DC circuit. But if you put an inductor in there it behaves differently, capacitors also behave differently. So let's think about the capacitor in an AC circuit. When I have a voltage source V and I put a parallel plate capacitor in this circuit, C, What's going to happen? Well, we know charge is going to flow to one side of the capacitor and charge is going to flow back to the other side and it's going to slosh back and forth. There's going to be some associated current with that, and that current, of course, goes sinusoidally just like we had before. I equals I naught cosine of omega t. But when I think about the voltage and the current in relation to the capacitor, we're going to have something similar that we had in the inductor. So if we plot out, as a function of time, the voltage drop across the capacitor, and I want to make sure I get the colors right here, V sub C and I, the current in the system, what does it look like? And I'm looking at the book and figure 2141 just to make sure that we're consistent, we know that I goes like a cosine. But the voltage drop across the capacitor doesn't follow the current, it, in fact, goes like this. It leads by 90 degrees. So the voltage drop across the capacitor is also out of phase by 90 degrees to the current, but it's the other way. Remember the inductor was on the left side, the capacitor now is, in fact, on the right side of the current. So these are complicated circuit elements. When you think about the voltages and the current in AC circuits and they have inductors and capacitors in here, it gets a little more complicated. But the voltage drop still obeys Ohm's law. So let's think about what that reactance looks like for a capacitor compared to what we had before for the inductor. Our equation looks very similar. Alright, we have V equals I times the reactance, but now it is X sub C. It's the voltage drop across the capacitor is I times the reactance. But what is the reactance? Well, let's think about what a capacitor is. A capacitor is a parallel plate. So as the frequency goes down, the reactance would have to go up. Right, if I try to push current across this thing and it's DC current, which is zero frequency, the capacitance will repel that, it won't let it go across that gap. And so this thing has to go like omega, where omega is in the denominator. But it also has to go like the capacitance. Right, if C is big, it's got to lead to a bigger reactance. So let's take a look at what the book has just to make sure we're consistent with their nomenclature for the reactance of a capacitor. And they have it right there, 1 over omega times C. Okay, I think I said that incorrectly about C, C is- if it big, it acts more like a wire. Big capacitor is parallel plates very close to each other, it's easy for the current to affect the other side. If the capacitance is very small, that's like small plates that are very far apart and that looks more like a break in the wire. Alright, so this is the reactance of a capacitor. And, again, it's in units of ohms.
Alright welcome back everyone, hopefully you got some more caffeine in your system, it's always a good thing. Let's take a look at the issues with capacitors. So if we have these AC circuits, what we said was things like resistors are just going to behave basically exactly the same as in a DC circuit. But if you put an inductor in there it behaves differently, capacitors also behave differently. So let's think about the capacitor in an AC circuit. When I have a voltage source V and I put a parallel plate capacitor in this circuit, C, What's going to happen? Well, we know charge is going to flow to one side of the capacitor and charge is going to flow back to the other side and it's going to slosh back and forth. There's going to be some associated current with that, and that current, of course, goes sinusoidally just like we had before. I equals I naught cosine of omega t. But when I think about the voltage and the current in relation to the capacitor, we're going to have something similar that we had in the inductor. So if we plot out, as a function of time, the voltage drop across the capacitor, and I want to make sure I get the colors right here, V sub C and I, the current in the system, what does it look like? And I'm looking at the book and figure 2141 just to make sure that we're consistent, we know that I goes like a cosine. But the voltage drop across the capacitor doesn't follow the current, it, in fact, goes like this. It leads by 90 degrees. So the voltage drop across the capacitor is also out of phase by 90 degrees to the current, but it's the other way. Remember the inductor was on the left side, the capacitor now is, in fact, on the right side of the current. So these are complicated circuit elements. When you think about the voltages and the current in AC circuits and they have inductors and capacitors in here, it gets a little more complicated. But the voltage drop still obeys Ohm's law. So let's think about what that reactance looks like for a capacitor compared to what we had before for the inductor. Our equation looks very similar. Alright, we have V equals I times the reactance, but now it is X sub C. It's the voltage drop across the capacitor is I times the reactance. But what is the reactance? Well, let's think about what a capacitor is. A capacitor is a parallel plate. So as the frequency goes down, the reactance would have to go up. Right, if I try to push current across this thing and it's DC current, which is zero frequency, the capacitance will repel that, it won't let it go across that gap. And so this thing has to go like omega, where omega is in the denominator. But it also has to go like the capacitance. Right, if C is big, it's got to lead to a bigger reactance. So let's take a look at what the book has just to make sure we're consistent with their nomenclature for the reactance of a capacitor. And they have it right there, 1 over omega times C. Okay, I think I said that incorrectly about C, C is- if it big, it acts more like a wire. Big capacitor is parallel plates very close to each other, it's easy for the current to affect the other side. If the capacitance is very small, that's like small plates that are very far apart and that looks more like a break in the wire. Alright, so this is the reactance of a capacitor. And, again, it's in units of ohms.