Question

A wire of resistance and resistivity is stretched, so that its length becomes 3 times of its original length. Determine its new resistance.

Answer 1

The resistivity of any wire and its material does not change when subjected to a change that is physical, as is in this case with the shape of the wire. Resistance however a different issue.

R∝lA where l is length of conductor and A is the area of cross-section.

Since volume V remains constant and length is doubled,

A′=A2

If R′ is the new resistance,

R′R=2lA2Al

⇒R′=4R

Answer 2

$\tt \: \blue{Resistnace \: of \: the \: original \: wire } \\ \bf \: R = \frac{ ρL}{A}, \: \: \sf \: where \: A= \frac{V}{L} \\ \\ \bf ⟹ R = \frac{ρL²}{V} \\ \\ \cal \small { Now \: its \: length \: is \: stretched \: such \: that \: new \: length }\\ \rm L′ = 3L \\ \\ \tt \: {Thus \: resistance \: of \: the \: wire} \\ \rm \: R′ = \frac{ρ(3L)²}{V} = 9²R \\ \\ \red{ \small{ \bf Hence \: \: resistance \: becomes \: 9 \: times \: the \: initial \: resistance.}}$