A length of #8 copper wire (radius = 1.63 mm) has a mass of 24.0 kg and a resistance of 2.061 ohm per km (Ω / km). What is the overall resistance of the wire?

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welcome back everyone a zinc wire with 1.27 millimeter radius weighs 17 kg, calculate the overall resistance of the wire if it has a resistance of 1. omega per kilometer recall that our unit for resistance is actually omega here and omega or the 1.39 omega per kilometer is a conversion factor that we're going to use. And we have our resistance related to kilometers which is a distance unit. But we're given information in the prompt for the radius and mass of ours inquire. So what we can begin with is recalling our formula to solve for the volume of this wire where we would recall that volume is equal to mass divided by density. Now we have our mass, millions of kilograms and we have our density of zinc which will need to actually look up. So in our textbooks or online we would find our density of zinc equivalent to a value of 7.133 g per cubic centimeter. So as you can see density utilizes grams and so we actually want to convert this mass from kilograms to grams. So what we'll have is that our volume is equal to in our numerator, we have 17 kg and we're going to multiply with kilograms in the denominator and grams in the numerator where our prefix kilo tells us that we have 10 to the third power grams. So canceling out kilograms, we have grams in the numerator for mass and then in our denominator are density for zinc being 7.133 g per cubic centimeter where now we can just cancel out grams with grams in the numerator. And so for our final unit of volume we have cubic centimeters which is what we prefer. And so in our calculators we would find the volume of this zinc wire equal to a value of 2383. cubic centimeters. So now we have the volume of our think wire. And as we stated earlier, we want to relate this volume in terms of unit of distance. And so we're going to need to find now for step two the length of the wire. And so we can recall our next formula. And sorry, this says why you're here. The length of our wire for our next formula we're going to recall is where we would relate volume to length times pi times the radius squared. And to find the length of the wire we want to isolate for length. So we would divide this formula by pi or squared. So that would cancel out here. And so what we would have is that volume is equal to or sorry, the length is now equal to volume divided by pi r squared. And so we are given that radius value in the prompt in units of millimeters. But as we see our volume is in units of centimeters specifically cubic centimeters. So let's take that radius that were given 1.27 millimeters and convert two centimeters. So we would have millimeters in the denominator and we're going to go two m first. So for one millimeter recall we have 10 to the negative third of our base unit meter, canceling out millimeters. We can now go from meters two centimeters so meters in the denominator centimeters in the numerator and recall that our prefect senti tells us that we have an equivalent of 100 centimeters to one m, canceling out meters will be left with centimeters and will now have a radius equal to a value of 10. 27 centimeters which we can now plug in. And so what we would have is that our length is equal to our volume in our numerator, we found that to be 2.383 point 29 cubic centimeters. And sorry, that's 2383 . cm. And then in our denominator we have pie Multiplied by a radius, which we just calculated as .127 cm, which is squared here. So let's keep things coordinated. We have a square power here. And so be sure that the square power is only applying to our radius. And what we'll find is that our length of our wire is equal to a value of 47,034 0.8. And as far as our units, we have cubic centimeters which will be canceled out with r squared centimeters. Leaving us with one power of centimeters. So we would just technically have centimeters as our final unit for length. Now that we have this length or distance of our zinc wire, we can now get to that conversion factor given in the prompt to get to the overall resistance of this wire. And so beginning with getting from our length and centimeters to kilometers, we have again 47,034 0. centimeters. We're going to multiply to go from centimeters to meters where recall that we have for 100 centimeters and equivalents of one m. So now canceling out centimeters, we will go from now meters, two kilometers. Recall that we have an equivalent for one kilometer being 10 to the third power meters canceling out meters. We're now going to incorporate the conversion factor given in the prompt where for one kilometer we have an equivalent of 1.39 omega. So oh hmm. And this will allow us to now be left with omegas as our final unit for our overall resistance of the zinc wire. And this is going to yield the results of points, I'm sorry. So the result is equal 2.488 We'll say 4886. So we can round this to about .489 Omega. And this would be the overall resistance of ours inquire. So what's highlighted in yellow here is our final answer to complete this example. I hope that everything I went through was clear. If you have any questions, please leave them down below and I'll see everyone in the next practice video.

A length of #8 copper wire (radius = 1.63 mm) has a mass of 24.0 kg and a resistance of 2.061 ohm per km (Ω / km). What is the overall resistance of the wire?

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Key Concepts

Resistance

Ohm's Law

Cross-sectional Area