 Now we're ready to tackle resistivity and resistance and do some example problems. I have another video that covered the equation itself so you can watch that one to understand it a little better. But our equation here tells us that the resistance can be calculated if we know the resistivity, the length, and the area. And this is the row symbol which is the resistivity. It's a material constant. For example, for copper, you might have a value of the resistivity which is 1.68 times 10 to the minus eighth ohm meters. So let's actually plug this in and take a look at an actual calculation. So let's say I've got copper, so I put in my value for copper for the resistivity or the row value. Let's say I have a 100 meter long piece of copper and it's just a little cable so it's cross-sectional area is just 0.001 meters squared. When I calculate this, I'm going to find I've got a resistance of 0.00168 ohms. That's also known as 1.68 milli ohms. Now in comparison, let's think about a rubber plate. Now rubber has a much higher resistivity, 1 times 10 to the 14th ohm meters. So if I have a sheet of rubber and it's only 0.02 meters thick, which is like 2 centimeters, and I've got 0.2 meters squared, so that's just a slab of it, I'd find that that has an electrical resistance of 10 tera ohms. So that's a whole lot higher resistance than you would have from a wire, which is why a piece of rubber can electrically isolate you effectively from any current going through because it has such a high resistivity giving it a very high resistance. In most cases, what we're actually going to be dealing with are, again, those wires. And a lot of times in the wire, you don't know the area directly, you have to calculate the area based on the radius of the wire. So we've got lots of R words here. You've got the resistance, the resistivity, and now the radius. If you're given the diameter, remember to take half of that to find your resist, to find your radius. So the diameter, take it in two, that gives you your radius, which allows you to calculate the area. So as an example here, if you had something which was 4 centimeters diameter or 2 centimeters in radius, then your area would be 0.00126 meters squared. If instead of being 4 centimeters, it was just 4 millimeters in diameter, then the radius would be 0.002 meters, and the area would be the 1.26 times 10 to the minus fifth meter squared. So a very small wire, something that might have a radius of 2 millimeters, is going to have a very small area. When we go to plug this into our equation, let's say we've got 100 meters of copper wire, but it has just this very, very small radius, that's going to actually increase our resistance by having a smaller number on the bottom. And you might actually have a resistance of 0.133 ohms. Now compared to most resistors you might put into a circuit, this wire doesn't have a huge resistance, but it does show us that if we have a long stretch of wire, because the longer the wire gets, the higher the resistance is going to be, you have to actually take that resistance into account when you're looking at the circuit. But if you were to have a similar equation and you had a very short section of wire, maybe just 0.1 meters, well that will change your answer and instead you would end up getting 0.00013 ohms. So when you've got a short section of wire, you can typically neglect the resistance of that short wire. So these are some example problems for solving for the resistance if you know the resistivity, the length and the area, or if you don't know the area but you know the radius, you can calculate the area and then be able to find your resistance. You could also rearrange this equation to find the area, the length or the resistivity, but we'll leave that for another example video.