The resistivity [tex]\rho[/tex] of a wire is related to its length L by the following relationship:
[tex]\rho = \frac{RA}{L} [/tex]
where R is the resistance of the wire, and A its cross-sectional area.
Assuming that the resistance R and the area A are the same for the two wires, we can see from the formula that, if the length L is doubled, then the resistivity [tex]\rho[/tex] becomes half of the original value. In fact, replacing L with 2 L we get
[tex]\rho '= \frac{RA}{2L}= \frac{1}{2} \frac{RA}{L}= \frac{\rho}{2} [/tex]
