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Anderson Video - Resistance Example

Professor Anderson
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 Okay, let's try an example. And let's do aluminum wire and a copper wire. And let's say that these things have the same dimensions. Okay, the aluminum wire and the copper wire are the same thickness and also the same length. And let's tell you that the resistance of the aluminum wire is 0.2 ohms and let's ask the question, what is the resistance of the copper wire? Okay. Let's go back to our definition of resistance, right. Resistance was resistivity Rho times L over A. L over A is the same for both. Okay, same L over A, if all those dimensions are the same. And so we can rewrite this equation slightly as the following: L over A equals R over Rho. And now we can write this for aluminum: L over A equals R for aluminum over Rho for aluminum, and for copper: L over A is equal to R for copper over Rho for copper, and now we can put these things together, right? L over A is the same so we can equate the right sides, and what we're looking for is R of copper. So let's write it like this: R of copper divided by the resistivity of copper, is equal to R of aluminum divided by the resistivity of aluminum. So what is R of copper? It is Rho of copper divided by Rho of aluminum times R of aluminum. What we told you was resistance for aluminum. What we need is the resistivity for aluminum and copper right there. And that you have to look up in the textbook. Okay, so if you flip open the textbook and you find the correct table in this chapter, you should get the following: resistivity of copper is 1.72 times ten to the minus 8 ohm meters. Those are SI units. Aluminum is 2.82 times 10 to the minus 8, also ohm meters, and we have a resistance now of 0.2 ohms, which was given to us. So if you plug in all those numbers, I did it earlier, you get 0.12 ohms. All right, R of copper we just found was 0.12 ohms. So which of these makes a better extension cord? Does aluminum or copper make a better extension cord? Okay, copper right? Everything else was the same, same length same width and yet the copper has a resistance that is much smaller than the aluminum, right? It's on the order of half the resistance of aluminum, and so when you go to Home Depot and you buy a big long extension cord, those cables that are inside the thing, those are going to be made of something like copper, a good conductor. Aluminum turns out to be not a very good conductor. Alright. If you spend more money on your extension cable it will also be thicker. So what you'll notice is in the extension cord aisle there will be a 25-foot extension cord for ten dollars and then next to it there'll be a 25-foot extension cord for twenty dollars. Look at the cross-sectional area A and what you'll notice is the more expensive one is thicker, it has a bigger A, which is ultimately going to get you a lower overall resistance.