 Now let's talk about resistance. And I want to start by clarifying some terminology. So we've got three really close terms. Resistance, resistor, and resistivity. Our resistance is the ratio of voltage to current. A resistor is a device that creates resistance. And the resistivity is a material dependent property of the device. Now resistance was defined by Ohm's law. So that's how we know that it's the ratio of voltage to current. To work further on, we're going to temporarily go back and review what we've already learned about current density. Both of these equations, J, was my current density. In one case, it was the current per area. In the other case, it was the conductivity times the electric field. Since both of these things are equal to the current density, I can set them equal to each other. Well, why am I doing this? Well, this is part of how I define my resistance equation for a wire. See, if I start with this equation, then I can remember that the electric field is equal to a voltage over a length. If I substitute that in, I'm going to get a slightly different equation. Now for this equation, I want to just rearrange it. I want to move my current over to my right-hand side. And I want to move my sigma and my L over to the left-hand side. So if I cross-multiply, I'm going to end up with this. I got one more little shift to make because 1 over sigma is going to be a new quantity called rho. Putting that in here, I now have this equation. And this side of the equation over here, well, it's equal to the voltage over the current, which means this must be equal to my resistance. So let's take a better look at this equation. Capital R is resistance. The L was my length of wire, and the A was my cross-sectional area of that wire. And this rho is our resistivity. So the resistivity was a material-dependent property. The L and the A tell me something about the geometry of a particular wire. So I know something about the material and the geometry. Let's look at the resistivity in a bit more detail. So again, resistivity has this symbol here, which is the Greek letter rho. But remember, its name is resistivity. And don't confuse this usage of rho for resistivity with our previous usage of rho for charge density. We have to reuse the symbols in physics sometimes. So we brought this rho resistivity in because it was 1 over the conductivity, 1 over sigma. So that means the resistivity is the inverse of conductivity. For units, that means it's going to have units of ohm meters. You may remember that conductivity had units of 1 over ohm meters. So now we can look at our overall units for our resistance equation. Rho, we just said, has units of omega times meters, ohm meters. For my geometry, I've got length over area. So that's going to be meters per meter squared. Now, my meter squared on the bottom is going to cancel the 2 meters up on top, leaving me with units of ohms for my resistance. So resistance is measured in ohms. Resistivity is measured in ohm meters. So that's resistance, particularly the equation for resistance for a wire.