Consider two copper wires with the same cross-sectional area. Wire a is twice as long as wire b. How do the resistivities and resistances of the two wires compare?

from the equation 1 below, the ratio of the resistivity of wire b to its resistance is twice the ratio of the resistivity if wire A to its resistance.

Explanation:

R = (ρL) / A

A = (ρL) / R

Where A is cross sectional area,

ρ is the resistivity

L is length of wire

R is resistance of wire.

from the question the two wires have same cross sectional area.

Aa = Ab; hence

(ρaLa) / Ra = (ρbLb) / Rb

La = 2Lb

(ρa*2Lb) / Ra = (ρbLb) / Rb

(2ρa) / Ra = (ρb) / Rb

ρb/Rb = 2 * ρa/Ra ... equ 1