A wire of length L and cross-sectional area A has resistance R.
a) What will be the resistance Rstretched of the wire if it is stretched to twice its original length? Assume that the density and resistivity of the material do not change when the wire is stretched.

The resistance R stretched of the wire if it is stretched to twice its original length is [Δ(2L) / A ]* 2

Explanation:

Original Resistance R = ΔL / A

Given length is doubled

New length  L' = 2L

New Volume is constant, resistivity and density of material is also assumed to be constant

AL = A'L'

AL = A'(2L)

A' = AL / 2L

A' = A / 2

∴ new Resistance R' = ΔL' / A'

                                 =  Δ(2L) / A/2

                                  = [Δ(2L) / A ]* 2

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