A 1.50 m cylindrical rod of diameter 0.500 cm is connected to a power supply that maintains a

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A 1.50 m cylindrical rod of diameter 0.500 cm is connected...

$\mathrm{A} 1.50 \mathrm{~m}$ cylindrical rod of diameter $0.500 \mathrm{~cm}$ is connected to a power supply that maintains a constant potential difference of $15.0 \mathrm{~V}$ across its ends, while an ammeter measures the current through it. You observe that at room temperature $\left(20.0^{\circ} \mathrm{C}\right)$ the ammeter reads $18.5 \mathrm{~A}$, while at $92.0^{\circ} \mathrm{C}$ it reads 17.2 A. You can ignore any thermal expansion of the rod. Find (a) the resistivity at $20.0^{\circ} \mathrm{C}$ and (b) the temperature coefficient of resistivity at $20^{\circ} \mathrm{C}$ for the material of the rod.

Key Concepts

Temperature Dependence of Resistivity

The resistivity of most materials changes with temperature. Typically, for conductors, resistivity increases as temperature increases. This temperature dependence can often be approximated as a linear relationship for small temperature ranges, which is key to understanding and predicting material behavior in varying thermal environments.

Geometric Considerations in Electrical Conduction

The geometry of a conductor, specifically its length and cross-sectional area, plays a critical role in determining its resistance. A longer conductor increases the resistance, while a larger cross-sectional area decreases it. Calculating the cross-sectional area from diameter or radius measurements is a common step in applying the resistance formula R = ?L/A.

Temperature Coefficient of Resistivity

The temperature coefficient of resistivity is a parameter that quantifies how the resistivity of a material changes with temperature. It is defined in the linear approximation of resistivity variation as ? = ?0[1 + ?(T - T0)], where ? represents the temperature coefficient. This concept is important for designing and analyzing electrical systems that operate over a range of temperatures.

Ohm's Law

Ohm's Law states that the voltage across a conductor is directly proportional to the current through it, with the constant of proportionality being the resistance. This fundamental relationship, expressed as V = IR, is crucial for analyzing electrical circuits and understanding how changes in resistance affect current when a constant voltage is applied.

Resistance and Resistivity

Resistance is an intrinsic property of a material that quantifies how strongly it opposes the flow of electric current. The resistance of a conductor is related to its resistivity, length, and cross-sectional area by the formula R = ?L/A. This relationship is essential in predicting how changes in physical dimensions or material properties influence the overall resistance.

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