00:01
In this question, we're given a ductile wire, a ductile wire, which means that you can stretch it without breaking it.
00:10
It has a resistance r, and you're told that the length is stretched from the original length l to three times l.
00:20
So let's go ahead and write the new length, which we'll call l prime, is 3l.
00:30
You're also told that the density and resistivity remains constant as you stretch this wire.
00:38
So actually, the density remaining constant is there's a critical point.
00:43
We're actually going to make use of this effect explicitly.
00:50
And you're also told that the amount of metal in the wire stays the same, so it doesn't change as you're stretching it.
00:58
And they want to know what is the resistance now after you've stretched this wire.
01:06
So if you're stretching the wire, obviously the length is going to go up, but then the cross -sectional area of the wire will actually decrease.
01:20
So with the information that we have on hand, the equation that we'll use to solve this problem.
01:27
So we have a resistance, we have length, but we don't have resistivity, but we actually don't need a particular value for it, as you will see, because we can find stuff in terms of r and l and resistivity.
01:53
So we can use equation 2510, which says that the resistance is the resistivity times the length divided by the cross -sectional area.
02:15
So let's say this is for the original unstretched wire, and now for the stretched wire, that's called that resistance r -prime...