All right, guys. So we talked about resistances in conductors. We want to talk about two related concepts in this video, which are the resistivity of a material and also how we deal with resistors in circuits. Alright? Let's go ahead and check it out. So any material has a property called the resistivity. So this resistivity is just a measure of how effective this particular material is at resisting charges and currents that flow through it. So it's given by this Greek letter rho and the units for that are in ohm meters. So if I have this conductor right here and I have some length and some cross-sectional area, then in order to figure out the resistance of this conductor or this material, I need to know the resistivity, which is basically just a constant and it just depends on what it's made of. And the resistance of this whole entire conductor is gonna be ρ·ℓ/A, where I just want to reiterate that this resistivity depends only on the material that it's made of. So basically, it's just a constant that's gonna be given to you. For instance, rho lead has a resistivity of this number right here. But if we're dealing with copper or gold or silver, those are gonna have all different numbers. You're not gonna be expected to memorize any of them. They're gonna be given to you on tests or homeworks. But this is basically the relationship between resistances and resistivity, which is a property of that material. Okay? So it just depends on how effective it is at resisting charges and also how long it is too, divided by how wide it is. Okay? So similar to how we talked about circuits with capacitors, first we talked about capacitance and then we talked about what a capacitor is in a circuit. It's the same thing here. We've talked about resistances and a resistor is just a circuit element that has some resistance. And we're gonna hook it up to a battery to form a simple circuit just like we did with capacitors. But in circuits, we're always gonna consider or assume that wires have zero resistance. And really, they have some, you know, nonzero. It's like very very small. What that means is that when we have a circuit connected to this resistor, but which by the way is given by this symbol right here, these little squiggly lines, we're gonna say that this resistor here R has some resistance, but that the wires that hook up this resistor to the battery have little to no resistance. We're just gonna go ahead and assume that these things have zero resistance. Let me go ahead and write that out a second. So we've got these wires here have zero resistance. Okay? So let's go ahead and check out an example problem right here. You've got a wire that's 25.1 meters long and 6 millimeters in diameter. It's got a resistance of 15 milliohms. Ohms. This number is actually pretty small already and we can see that a wire that's 25 meters is required for a very very small amount of resistance. This is why in circuit problems, we assume wires to have almost zero resistance. Okay? So we're told there's a potential difference right here. We're supposed to figure out what the resistivity of this wire material is. So in other words, we're supposed to be figuring out what rho is equal to. So let's go ahead and set up our equation. The relationship between resistance, rho, the length over the area is R = rhoL / A. So we have what the resistance of the material is. I know how long this wire is. And if I can figure out if I'm assuming that this wire is cylindrical, then I can figure out the area by πr2. Where I just want to reiterate, this r right here is the radius of the wire and not the resistance, just so you don't get those two things confused. Okay? So let's go ahead and manipulate this equation. I've got A that's gonna go over. We've got L that's gonna come down. And that means that R * A / L is gonna be equal to rho. So in other words, the resistance right here, which is 15 milliohms, 15 times 10 to the minus 3, now we have to figure out what the area is. The area is just gonna be pi times 0.003 because we're given 6 millimeters in diameter, but we need the radius. So that means we need half of this number right here, and then we need to put it in the right units. Now we have to square that. And now we have to divide it by the length of the wire, which is gonna be 25.1. And this is in meters, so we don't have to change anything about that. Okay? So if you go ahead and work this out in your calculators, plug everything carefully, you should get a rho, a resistivity that is 1.69 times 10 to the minus 8, and that is gonna be ohm meters. Now this corresponds to a material that's copper, which is usually what most wires are made of. So this is copper. So we need a wire that's 25 meters long. That's like 75 feet long just to get a resistance that's 15 milliohms, which is very very small. Okay? So again, this is sort of reiterating that wires have zero resistance in a circuit. Alright. So now what we're supposed to do is we're supposed to figure out what the current in the wire is. Now how do we do that? Well, we're told specifically that the voltage across this wire is 23 volts, and now we have what the resistance is we can figure out the current using Ohm's law. So if we need to figure out I, we just have to relate it back to V = I * R. Now, I know, again, we're supposed to assume that this has 0 resistance, but we're told specifically that this thing does have some resistance. So we have to plug that in. Okay? If this was a circuit problem, we wouldn't have to worry about it. Okay? So we've got, V / R is gonna equal to I. So we've got that 23 divided by 15 times 10 to the minus 3 is gonna give us the current, and that's.equal to 1.53 times 10 to the 3rd, and that's gonna be in amps. Alright. So that is the current due to the resistance and the voltage. Let me know if you guys have any questions.
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Resistors and Ohm's Law
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