# Problem: A wire of length L and cross-sectional area A has resistance R.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.

###### FREE Expert Solution

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 L1 and area, A1.

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

85% (255 ratings) ###### Problem Details

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

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.