00:01
Our question says that we have a wire that has a resistance of r.
00:05
And then it tells us that we have another wire that has a length.
00:09
So we're going to call this other wire, wire two, and the original wire, wire, one.
00:15
So the other wire has a length that is one -half the length of the original wire.
00:20
So l2 is one -half l -1.
00:22
And it has a thickness, which i call d, that is one -half the thickness of the original wire.
00:28
So d -2 is equal to one -half d -1.
00:31
We want to find the resistance of the second wire based upon the fact that we know this information and we know the resistance of the first wire r1 is equal to r so we'll write that as well just so we're clear on that r1 is equal to r okay well we're going to use the fact that the resistance of a wire is proportional to the length divided by area and the area is equal to one -fourth pi squared, well, we don't really care about the constants, because we're going to be using ratios and constants are going to cancel out these ratios, so we can just consider the fact that this is proportional to d squared.
01:22
Okay, so now we can go ahead and calculate the resistance of r2.
01:26
R2 is equal to r times the ratio of the areas, a1 over a2, this is times l2 over l1.
01:46
And this comes from just taking the ratio of r2 to r1 and using the information that was given in these two equations here...