A ductile metal wire has resistance R. Then the wire is stretched to three times its original length. The stretching shrinks the diameter of the wire, but does not affect its density or resistivity. What is the resistance of the stretched wire

Explanation:

Let us assume that the final resistance after stretching is . Since, the volume of rod does not change and the initial and final volume will be the same as follows.

           V =

It is given that, .

Therefore,      

We know that relation between resistance and area is as follows.

          R =

             =

             = 9  

             = 9R

Thus, we can conclude that the resistance of the stretched wire is 9R.