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.
where
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.