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Explain why R=R0(1+αΔT) for the temperature variation of the resistance R of an object is not as accurate as rho=rho 0(1+αΔT), which gives the temperature variation of resistivity rho.

a) Temperature affects resistance and resistivity differently.

b) The formula for resistance is outdated.

c) Resistivity is not affected by temperature.

d) Both formulas are equally accurate.

User Kikea
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1 Answer

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Final answer:

The formula for resistivity as a function of temperature is more accurate than that for resistance because resistivity is a fundamental material property unaffected by object dimensions, and it directly relates to how temperature affects the material's inherent resistance to electron flow.

Step-by-step explanation:

The equation R = R0(1 + αΔT) represents the temperature variation of the resistance R of an object, where R0 is the original resistance, α is the temperature coefficient of resistance, and ΔT is the change in temperature. This relationship is based on the assumption that the dimensions of the object do not change significantly with temperature. However, the equation ρ = ρ0(1 + αΔT) for the temperature variation of resistivity ρ is generally considered more accurate because resistivity is a fundamental material property that does not depend on the object's dimensions, and temperature has a direct effect on it.

Furthermore, the resistance of an object is proportional to its resistivity; for a cylindrical object, we know R = ρL/A, where L is the length, A is the cross-sectional area, and ρ is the resistivity. For relatively small temperature changes where the dimensions of the object (L and A) do not change significantly, the resistance will show the same temperature dependence as resistivity. Therefore, the formula for resistivity as a function of temperature is preferred because it directly relates to the material property affected by temperature and is not substantially influenced by changes in the object's geometry.

User Kerwyn
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