Electric Circuits Legacy Problem #5 Guided Solution

An electrical wire offers resistance to the flow of charge, which therefore reduces the current. The amount of resistance offered by the wire depends upon three variables, the first one being the resistivity of the material, which is different for different materials. The second variable is the length of wire, with more wire offering more resistance to charge. And the third variable is the cross-sectional area of the wire, usually envisioned to be a circular cross-section, and it can be described by stating a diameter of that circular cross-section. With greater area, there is generally a lower resistance, and therefore a larger current value. Here we wish to calculate the resistance using the equation R equal resistivity, which is the number that differs for different materials, multiplied by length divided by cross-sectional area. So what I need to do here is I need to list the resistivity, it's going to be different for each part of the problem, I need to list that L equal 100 meters, and then I need to calculate the cross-sectional area of my wire. Now it's a circular cross-section, so you need to use the equation area equal pi R squared, where pi is just the 3.141592 value that you're accustomed to from your math classes, and the R is the radius, which is simply one-half the diameter. Now I need to give attention to units in this problem, because in the numerator I'm going to have an ohm times a meter for resistivity, multiplied by a meter, to give me an ohms times meters squared. So in the denominator, I'm going to need to have meters squared as well, so that the meters squared cancels, and I end up with ohms as a unit of resistance. So in that diameter, I need to convert the 0.163 centimeters diameter first to a radius, and then to a radius in units of meters. So to convert from diameter to radius, you need to divide by 2, and then to change from centimeters to meters, you need to divide by 100. Now once you've done that, multiply by, square the number and multiply by pi, and that gives you the denominator of that equation, the cross-sectional area. Now again, the equation is resistance equal resistivity, in ohms times meters, multiplied by length in meters, divided by area in meters squared. Now all you need to do is plug and chug into that equation four different times for the four different parts, and then round to three significant digits.