Question

A wire of resistance R is stretched so that it's radius decrease by factor n calculate it's new resistance and resistivity

Answer 1

Given:

Resistance of a wire = R

To find:

New resistance and resistivity of the wire when the radius is decreased by factor n.

Solution:

Since, we know that the formula of resistivity of the wire is pV/A²

Where p is its resistance, V is the volume of the wire and A is the area of the wire.

We chose this formula because volume of the wire does not vary in the wire.

Resistivity = pV/π²r^4

= pV/ π²(r/n)^4

Therefore the resistivity of the wire increases by a factor of n^4.

There will be no change in resistivity.

Therefore, the resistance of the wire increases by a factor of n^4 and resistivity will remain unaffected.