Anderson Video - Resistance and Resistivity

Professor Anderson
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Hello everybody, welcome back. How's everybody feeling? Good? Hanging in there? I know it's Monday like right around lunchtime and you're just crashing, I understand. We should just you know we could all take a nap here and then the people watching at home would be like: what happened, it went dark. All right, let's continue our discussion. Let's talk about resistance, if I can spell it, resistance and resistivity. Okay. We talked a little bit about resistance, right. Resistance is measured in ohms and it's some reluctance of the current to flow, right? There's rocks in the river and it's preventing them from flowing very easily but let's think about this in terms of this wire that we've been drawing. Okay, here's our wire, it's got cross-sectional area A, it's got some length to it L, and as current is flowing to the right, what that means is there are some sort of charge carriers that are gonna move. Okay, and we know it's electrons moving to the left but don't worry about that, just pretend they're positive charge carriers moving to the right, and when those things move they don't move in a straight line, they bounce around. Okay, why do they bounce around like that? Well, because there's other things in there, right? There's all sorts of atoms and molecules that are in this material and the electron jumping from one to the next wants to move to the left a little bit and then to the right for a few and then maybe straight and then to the left. Okay, and so there is this general drift of the charges in the direction of the current but they bounce around all over the place. So this is our piece of wire, it is resistive. How do we characterize the resistance of this wire? The way we do it is the following: resistance R is Rho times L over A, where Rho is the resistivity, which is kind of like friction. Okay, resistance is Rho times L over R. If you have a wire that is more resistive then it has a bigger overall resistance. If it is longer then there is a bigger overall resistance, but if it is thicker, if it has a bigger cross-sectional area A, then it is less resistive. And this is why when the car battery is attached to the starter motor they use big thick cables because they want to lower the resistance of the cable and so they make the cross sectional area very big. And that should make sense, right? If this really was a river then A would determine, sort of, how wide the river is and the wider it is, the easier it is for current to flow down that river. All right, resistivity is characteristic of the materials. So every material has its own resistivity Rho and the units on resistivity are ohm meters. So for instance, gold and silver have a resistivity of the following: 1.72 times ten to the minus eight or 1.59 times ten to the main -- minus eight. Where as something like silicon has a resistivity of ten to the three and Teflon has a resistivity of 10 to the 16. Okay, and ten to the minus eight up to 10 to the 16, that's a lot, that's 24 orders of magnitude difference between those two and there must be some key here, right? Gold and silver, what types of material are those? Those are metals, right? Those are conductors. Teflon with this huge resistivity is of course an insulator. Silicon is one of these interesting materials that is sort of in between the two and in fact it can act like an insulator or a conductor and that's why we call it a semi conductor. So that's a word that you've heard a lot: a semi conductor. It somewhat conducts or it conducts some of the time. Okay. Semi conductors are of course what powers all of your computer chips. All right, so let's try an example of calculating some resistances of different things. The important thing to remember here is that resistivity depends on the atomic structure, resistance depends on the dimensions. Okay, what it's made out of, but also how long it is and how thick the cable is.
Hello everybody, welcome back. How's everybody feeling? Good? Hanging in there? I know it's Monday like right around lunchtime and you're just crashing, I understand. We should just you know we could all take a nap here and then the people watching at home would be like: what happened, it went dark. All right, let's continue our discussion. Let's talk about resistance, if I can spell it, resistance and resistivity. Okay. We talked a little bit about resistance, right. Resistance is measured in ohms and it's some reluctance of the current to flow, right? There's rocks in the river and it's preventing them from flowing very easily but let's think about this in terms of this wire that we've been drawing. Okay, here's our wire, it's got cross-sectional area A, it's got some length to it L, and as current is flowing to the right, what that means is there are some sort of charge carriers that are gonna move. Okay, and we know it's electrons moving to the left but don't worry about that, just pretend they're positive charge carriers moving to the right, and when those things move they don't move in a straight line, they bounce around. Okay, why do they bounce around like that? Well, because there's other things in there, right? There's all sorts of atoms and molecules that are in this material and the electron jumping from one to the next wants to move to the left a little bit and then to the right for a few and then maybe straight and then to the left. Okay, and so there is this general drift of the charges in the direction of the current but they bounce around all over the place. So this is our piece of wire, it is resistive. How do we characterize the resistance of this wire? The way we do it is the following: resistance R is Rho times L over A, where Rho is the resistivity, which is kind of like friction. Okay, resistance is Rho times L over R. If you have a wire that is more resistive then it has a bigger overall resistance. If it is longer then there is a bigger overall resistance, but if it is thicker, if it has a bigger cross-sectional area A, then it is less resistive. And this is why when the car battery is attached to the starter motor they use big thick cables because they want to lower the resistance of the cable and so they make the cross sectional area very big. And that should make sense, right? If this really was a river then A would determine, sort of, how wide the river is and the wider it is, the easier it is for current to flow down that river. All right, resistivity is characteristic of the materials. So every material has its own resistivity Rho and the units on resistivity are ohm meters. So for instance, gold and silver have a resistivity of the following: 1.72 times ten to the minus eight or 1.59 times ten to the main -- minus eight. Where as something like silicon has a resistivity of ten to the three and Teflon has a resistivity of 10 to the 16. Okay, and ten to the minus eight up to 10 to the 16, that's a lot, that's 24 orders of magnitude difference between those two and there must be some key here, right? Gold and silver, what types of material are those? Those are metals, right? Those are conductors. Teflon with this huge resistivity is of course an insulator. Silicon is one of these interesting materials that is sort of in between the two and in fact it can act like an insulator or a conductor and that's why we call it a semi conductor. So that's a word that you've heard a lot: a semi conductor. It somewhat conducts or it conducts some of the time. Okay. Semi conductors are of course what powers all of your computer chips. All right, so let's try an example of calculating some resistances of different things. The important thing to remember here is that resistivity depends on the atomic structure, resistance depends on the dimensions. Okay, what it's made out of, but also how long it is and how thick the cable is.