Assuming a constant temperature coefficient of resistivity, what is the maximum percent decrease

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Assuming a constant temperature coefficient of resistivity,...

Key Concepts

Temperature Coefficient of Resistivity

This coefficient (commonly denoted as ?) quantifies how much a material’s resistivity (and consequently its resistance) changes with temperature. For metals and alloys, the resistance at a temperature T can be approximated by a linear relation R = R?[1 + ?(T – T?)], wherein a positive ? indicates that resistance increases with temperature while a negative change in temperature decreases the resistance.

Linear Model of Resistance Variation with Temperature

The linear approximation of resistance variation assumes that over the range of temperatures in consideration the temperature coefficient remains constant. This model allows us to compute the percent change in resistance simply by multiplying the temperature coefficient by the change in temperature, which is especially useful for estimating the resistance change when cooling or heating a conductor from an initial temperature.

Absolute Zero as a Limiting Temperature

In problems addressing the maximum possible change in resistance from a given starting temperature, the limiting case often considers cooling the material all the way to absolute zero (0 K). Although the linear relationship may not hold near absolute zero in real materials, under the assumption of a constant temperature coefficient, absolute zero represents the theoretical lower bound on temperature, and thus it provides the maximum potential decrease in resistance relative to the starting temperature.

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