Resistors and Ohm's Law Video Lessons

Concept

# Problem: A uniform wire of resistance R is stretched unit its length doubles. Assuming its density and resistivity remain constant, what's its new resistance?

###### FREE Expert Solution

Resistance:

$\overline{){\mathbf{R}}{\mathbf{=}}{\mathbf{\rho }}\frac{\mathbf{l}}{\mathbf{A}}}$ where ρ is the resistivity, l is the length, and A is the cross-sectional area.

When the wire is stretched to double its length, the cross-sectional area will be reduced by half.

Since the density remains constant, the volume will be constant after the wire is stretched.

This means that,

Vi = Vf

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###### Problem Details

A uniform wire of resistance R is stretched unit its length doubles. Assuming its density and resistivity remain constant, what's its new resistance?