Resistance,

$\overline{){\mathbf{R}}{\mathbf{=}}\frac{\mathbf{\rho}\mathbf{L}}{\mathbf{A}}}$

ρ is the resistivity, L is the length and A is the cross-sectional area.

Constant density implies that **V = AL** is constant.

Let the new length be L_{1} and area, A_{1}.

$\begin{array}{rcl}\mathbf{A}\mathbf{L}& \mathbf{=}& {\mathbf{A}}_{\mathbf{1}}{\mathbf{L}}_{\mathbf{1}}\\ \mathbf{A}\mathbf{L}& \mathbf{=}& {\mathbf{A}}_{\mathbf{1}}\mathbf{\left(}\mathbf{2}\mathbf{L}\mathbf{\right)}\\ \frac{\mathbf{A}}{\mathbf{2}}& \mathbf{=}& {\mathbf{A}}_{\mathbf{1}}\end{array}$

A wire of length *L* and cross-sectional area *A* has resistance *R*.

What will be the resistance *R*_{stretched} 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.

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