Which Form 2220 Respectively 2023-2024

If you haven't done so yet, make sure you pause the video and try to answer the question on your own first before listening on. As long as we assume that the current is uniform, then we can say that the current density (symbolized by J) is equal to the current divided by the cross-sectional area of the wire. The question gives us the current as 60 amps, so the numerator here is very easy. It's the area that we need to come up with an expression for because we were not given that directly. To do that, we note that resistance is equal to a quantity known as resistivity multiplied by the length of the wire divided by its cross-sectional area. We can solve this equation for the area (A) by multiplying both sides of the equation by A so that it cancels out on the right-hand side. Then, divide both sides of the equation by the resistance (R). We can see that the area is equivalent to this expression. Let's substitute that in for the area in our current density equation and we are left with a complex fraction, basically a fraction within a fraction. Let's multiply the denominator of our complex fraction by the resistance and also the numerator by the resistance, so it cancels out in the denominator. Now we have this expression for the current density, which is more useful. If we look carefully, we have the resistance per unit length in the expression, which is known to be 0.5 ohms per kilometer according to the question. It's useful to convert 0.5 ohms per kilometer to ohms per meter, so we'll say that 1 kilometer is equivalent to 1000 meters. Kilometers will cancel out, and this would equal 0.0015 ohms per meter. That's going to be the...