Current Electricity: Resistance and Resistivity

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A wire of initial length L0 and radius r0 has a measured resistance of 1.56 ohm. The wire is drawn under tensile stress to a new uniform radius of r = 0.420r0. What is the new resistance of the wire?

The resistance of a conductor is given by

Here  is the resistivity, L is the length (thickness) and A is the area of the conductor.
As initially the length is L0 and the radius is r0 the resistance is given by
------------------------------ (1)
When the wire is stretched, its volume remains the same and thus

Substituting value of new radius r the new length L is given by

Gives
Hence the new resistance of the wire is given by

Or
Substituting the value of LHS from equation (1) in above equation we get

Thus the new resistance of the wire will be 50.1 .

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