The resistance of a coil of copper wire is 3.35 Ωat 0 ^∘ C....

The resistance of a coil of copper wire is $3.35 \Omega$ at $0{ }^{\circ} \mathrm{C}$. What is its resistance at $50^{\circ} \mathrm{C}$ ? For copper, $\alpha=4.3 \times 10^{-3}{ }^{\circ} \mathrm{C}^{-1}$ $$ R=R_{0}+\alpha R_{0}\left(T-T_{0}\right)=3.35 \Omega+\left(4.3 \times 10^{-3}{ }^{\circ} \mathrm{C}^{-1}\right)(3.35 \Omega)\left(50^{\circ} \mathrm{C}\right)=4.1 \Omega $$

The resistance of a coil of copper wire is $3.35 \Omega$ at $0{ }^{\circ} \mathrm{C}$. What is its resistance at $50^{\circ} \mathrm{C}$ ? For copper, $\alpha=4.3 \times 10^{-3}{ }^{\circ} \mathrm{C}^{-1}$
$$
R=R_{0}+\alpha R_{0}\left(T-T_{0}\right)=3.35 \Omega+\left(4.3 \times 10^{-3}{ }^{\circ} \mathrm{C}^{-1}\right)(3.35 \Omega)\left(50^{\circ} \mathrm{C}\right)=4.1 \Omega
$$

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Key Concepts

Electrical Resistance

Electrical resistance is a measure of how strongly a material opposes the flow of electric current. It depends on the material's intrinsic properties, its geometry, and external factors such as temperature. Understanding resistance is fundamental in circuits and electrical engineering as it determines current flow under a given voltage.

Temperature Dependence of Resistance

This concept explains how the resistance of a material changes with temperature. In many conductive materials, especially metals, an increase in temperature causes an increase in resistance due to enhanced atomic vibrations that scatter electrons. This relationship is often approximated linearly over small to moderate temperature ranges.

Temperature Coefficient of Resistance

The temperature coefficient of resistance is a constant that quantifies the change in resistance per unit change in temperature. It is expressed in units of per degree Celsius (or Kelvin) and is crucial for predicting how a material's resistance will vary with temperature. This concept allows the use of linear formulas to estimate resistance at different temperatures based on a known reference value.

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