A Malleable Wire

Electricity and Magnetism Level 1

A copper wire conducts with some resistance $R$ . The wire is then flattened and stretched so that the length doubles and the cross-sectional area goes down by a factor of $\frac14$ , without changing the resistivity. By what factor does the resistance of the wire change?

1 2 4 8

2 solutions

Vincent Sijben
Feb 18, 2018

This example is physically rather 'strange': as the copper material is (almost) incompressible, a wire that is stretched to double length would have a 0,5 factor area reduction, not 0.25 .

Fair, I didn't really think about that. But I hope that if you know enough to consider that a problem, that you understood the point of the exercise. If you like some of the copper wire was also removed during the process.

Matt DeCross - 3 years, 3 months ago

Aditya Narayan Sharma
Apr 4, 2016

$\begin{aligned}R=\rho\frac{l}{A}\end{aligned}$ & $\text{Given that resistivity doesn't change}$

$\text{Let the new resistance be }\mathfrak{R}$

$\large \mathfrak{R} = \rho\frac{\color{#3D99F6}{2}l}{\color{#D61F06}{\frac{1}{4}}A}=8.\rho\frac{l}{A} = 8R$

$\text{So the resistance changes by 8 times.}$

A Malleable Wire

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