Alright, guys. Look at it. We're going to work this one out together. So we have a cylindrical resistor and we're told a bunch of information about it. What's the resistivity, the dimensions of that resistor, and also how much EMF or voltage is across it. We're supposed to figure out what is the current across this resistor right here. So if we wanted to figure out the current and its relationship to the resistance and voltage, first, we have to go ahead and relate it to Ohm's law. So if we wanted to figure out what the current is, we have to relate it to V=IR. So if we just divide over the R, then V/R just becomes the current. I have the voltage. I'm told that the EMF or the voltage is 5 volts. Now what I need to do is figure out the resistance. I'm told what the resistivity is and some of the properties of this resistor, but I don't have the resistance. So I have to go and use another equation. This resistance, remember, for any resistor of some resistivity is going to be ρ×l/A. And we assume that it's cylindrical. We have that it's going to be ρ times the length divided by the area of the cylinder, which is going to be, by the way, this is the cross-sectional area. So if we have a cylinder like this, so if we have a cylinder, then this area right here is actually the cross-sectional area of the specific cylinder, not the actual surface area. That's actually a common pitfall that students run into, so it's going to be the cross-sectional area. So I'm going to write that, cross-section area. So that means that the cross-sectional area is just going to be the area of a circle, which is π×r2, which is the radius. Okay. Cool. So let's go ahead and calculate where the resistance is. It's going to be ρ, which is 2.2×10-7. Now we have the length of this particular resistor, which is 2 centimeters or 0.02. Now we have to divide it by the area, which is going to be π×0.0052, and then all that stuff that's going to go in the denominator. Right? So we get a resistance of 5.6×10-5, and that's going to be in ohms. So now we can stick it back into Ohm's law and figure out what the current is. So that means that the voltage, which is 5 volts, divided by the resistance, 5.6×10-5, is going to be equal to the current. In other words, we have a current of 8.9×104 and it's amps. So actually a lot of current right there. So that is the current. That's how we figure out these kinds of things. We use our resistance, resistivity equations, and use Ohm's laws. Okay? Let me know if you guys have any questions.
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Resistors and Ohm's Law
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