The length of an aluminum wire is quadrupled and the radius is doubled. by which factor does the resistance change?

The resistance of a conductive wire is given by:

where
is the material resistivity
is the wire length
is the cross-sectional area of the wire

The length of the wire is quadrupled, so if we call L the original length and L' the new length, we can write 


Similarly, the radius of the wire is doubled (r'=2r), so the new area is


And if we substitute into the equation, we find that the new resistance of the wire is

Therefore, R=R': this means that the resistance of the wire did not change.

Ibelieve your answer is b.hope this : )