A wire 3.00 m long and 0.450 mm^2 in cross-sectional area has a resistance of 41.0 Ωat 20^∘ C.

step 1 In this question, we are given the following information for a wire. So the resistance, R0, is e

A wire 3.00 m long and 0.450 mm^2 in cross-sectional area...

A wire $3.00 \mathrm{~m}$ long and $0.450 \mathrm{~mm}^{2}$ in cross-sectional area has a resistance of $41.0 \Omega$ at $20^{\circ} \mathrm{C}$. If its resistance increases to $41.4 \Omega$ at $29.0^{\circ} \mathrm{C}$, what is the temperature coefficient of resistivity?

Key Concepts

Temperature Coefficient of Resistivity

The temperature coefficient of resistivity is a parameter that quantifies the change in a material's resistivity with temperature. It is defined as the fractional change in resistivity per degree of temperature change, indicating how sensitive the material's resistance is to temperature variations.

Temperature Dependence of Resistance

The resistance of a conductor typically increases with temperature due to increased atomic vibrations within the material, which scatter the charge carriers more. This effect is modeled by the linear relationship R = R0[1 + ?(T - T0)], where ? is the temperature coefficient of resistivity, and R0 is the resistance at a reference temperature T0.

Resistivity

Resistivity is a fundamental material property that measures the degree to which a material opposes the flow of electric current. It depends on both the nature of the material and its temperature, with higher resistivity indicating a greater opposition to current flow.

Physical Dimensions and Resistance

The resistance of a wire is also influenced by its physical dimensions, specifically its length and cross-sectional area, as described by R = ?L/A, where ? is the resistivity, L is the length, and A is the cross-sectional area. These dimensions are crucial in determining the baseline resistance before temperature effects are considered.

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