Mastering Physics Solutions: A Stretchable Resistor

A Stretchable Resistor

Part A = 4R

Solution Below:

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

Part 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.
Express your answer in terms of the wire’s original resistance R.

Resistance is equal to ρ * l/A, where ρ is resistivity, l is length, and A is the cross sectional area. A cylinder has a volume of πr2h. Doubling the length (h) while holding volume constant means that the cross sectional area will be cut in half. Since the length doubles and the cross sectional area is cut in half, the overall resistance increases by a factor of 4.

4R

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