Resistivity & Resistors in Circuits

by Patrick Ford
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Alright guys. So we talk about resistance is in conductors. We want to talk about two related concepts in this video which is the rest festivity of the material and also how we deal with resistors in circuits. All right, let's go ahead and check it out. So any material has a property called the resistive ity. So this resistive, it 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 row and the units for that are in omega 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 of this material, I need to know the resistive iti, 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 row times l over a where I just want to reiterate that this resistive ity depends on Lee on the material that it's made of. So, basically it's just a constant that's gonna be given to you for instance, row lead has a resistive ity of this number right here. But 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 homework's. But this is basically the relationship between resistance is and resistive ITI, 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 toe 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. Resistance is, 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 were always gonna consider or assume that wires have zero resistance and really they have some, you know, non zero. It's like very, 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. This little squiggly lines were going to say that this resistor here are 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. Second. So you've got these wires here have zero resistance. Okay, so let's go ahead and check out a new example Problem right here. Who? You got a wire that's 25.1 m long and six millimeters in diameter. It's got a resistance off 15 millones. This number is actually pretty small already on. We can see that a wire that's 25 m 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 potential difference right here. We're supposed to figure out what the resistive ity of this wire material is. So in other words, we're supposed to be figuring out what row is equal to. So let's go ahead and set up our equation. The relationship between resistance row the length over the area is row is R equals row L over A. So we have with 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 pi times r squared where I just want to reiterate this are 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 got l. That's gonna come down. And that means that our times a over l is gonna be equal to row. So, in other words, the resistance right here, which is 15 million homes 15 times 10 to the minus three. Now we have to figure out what the area is. The area is just gonna be pi times 0.3 because we're giving it 6 million m 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. Now we have two divided 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. OK, so you go ahead and work this out in your calculators, plugging everything carefully. You should get a row. A resistive ity. That is 1.69 times 10 to the minus seven. And that is gonna be ohm meters. Now, this corresponds to a material that's copper, which is usually what MOCs wires are made of. So this is copper. So we need a wire that's 25 m long. It's like 75 ft long just to get a resistance. That's 15 millones, which is very, very small. Okay, so again, this is sort of reiterating that wires have zero resistance in the circuit. All right, so now we're supposed to do is we're supposed to figure out what the current in the wire is. How do we do that? Well, we're told specifically that the voltage across this wire is volts. And now we have with the resistance is so we can figure out the current using homes law. So if we need to figure out, I we just have to relate it back to V equals I times are now I know again, we're supposed to assume that this has zero assistance, 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 didn't have to worry about it. Okay, so we've got V over R is gonna equal toe I So we've got that 23 divided by 15 times. 10 to the minus three is going to give us the currents, and that's equal to 1.53 times 10 to the third. And that's gonna be it's not cool arms. That's gonna be an apse. Alright, so that is the current due to the resistance and the voltage. Let me know if you guys have any questions and I'll see you guys the next one