Question

A wire of resistance 5 ohm is stretched to double it's length. What will be it's new resistance and resistivity if temperature remains constant

Answer 1

the resistance will increase by 4 times since length is doubled by stretching therefore area remaining would be half.
so the answer is 20 ohm

Answer 2

Answer :

Let the length be l, area of cross section be A, resistivity be p and volume be V

Given, R = 5 ohm

As  increasing the length of the wire does not change its volume, so doubling the length to 2*l , area becomes half A/2

Resistance = Resistivity * length / area

R' =  resistivity * (2 * length) / (area/2)

R' =  (resistivity*length/area)*4

R' = 4*R

So, new resistance is 4 times the old resistance. And as the temperature is constant, there will be no change in resistivity.