Question

Consider two copper wires. one has twice the length of the other. how do the resistivities of these two wires compare?

Answer 1

The resistivity
`\rho` of a wire is related to its length L by the following relationship:

`\rho = (RA)/(L)`
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
`\rho` becomes half of the original value. In fact, replacing L with 2 L we get

`\rho '= (RA)/(2L)= (1)/(2) (RA)/(L)= (\rho)/(2)`