A length of wire is cut in half and the two lengths are wrapped together side by side to make a thicker wire. How does the resistance of this new combination compare to the resistance of the original wire?
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This is Giancoli Answers with Mr. Dychko. Resistance initially is gonna be the resistivity of the material times the original length one of the wire divided by its original area one. Resistance in the second case, after you cut the wire and put it side by side, is the same resistivity because it's the same material, multiplied by a new length divided by new area. The new length after you cut it in half and put the two pieces beside each other, you can-- Well, originally, you had this length, L one, and now when you cut it in half, you're gonna have two pieces, and this length here is gonna be L one over two. Area two, I'm showing a cross-section on view here where, initially, it had some area one, the cross-sectional area of the wire. After you cut in half and placed the two segments side by side, you have total cross-sectional area equal to A one plus A one which is two times A one. So area two can be twice the area initially, and the length two is gonna be half the length they had initially. So let's make substitutions for L two and A two now. So R two is gonna be resistivity times L one over two divided by two times A one which is resistivity times L one over four A one. This is R one. So we have one quarter R one. So R two over R one is one quarter. We have one quarter of the resistance after you cut the wire in half and put the two segments side by side.
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