The temperature coefficients of resistivity αin Table 27.2 are based on a reference temperature

step 1 So for this problem, we have the temperatures, 20 degrees Celsius and 0 degrees Celsius. We have

The temperature coefficients of resistivity αin Table 27.2...

The temperature coefficients of resistivity $\alpha$ in Table 27.2 are based on a reference temperature $T_{0}$ of $20.0^{\circ} \mathrm{C}$ . Suppose the coefficients were given the symbol $\alpha^{\prime}$ and were based on a $T_{0}$ of $0^{\circ} \mathrm{C}$ . What would the coefficient $\alpha^{\prime}$ for silver be? Note: The coefficient $\alpha$ satisfies $\rho=$ $\rho_{0}\left[1+\alpha\left(T-T_{0}\right)\right],$ where $\rho_{0}$ is the resistivity of the material at $T_{0}=20.0^{\circ} \mathrm{C} .$ The coefficient $\alpha^{\prime}$ must satisfy the expression $\rho=\rho_{0}^{\prime}\left[1+\alpha^{\prime} T\right],$ where $\rho_{0}^{\prime}$ is the resistivity of the material at $0^{\circ} \mathrm{C} .$

The temperature coefficients of resistivity $\alpha$ in Table 27.2 are based on a reference temperature $T_{0}$ of $20.0^{\circ} \mathrm{C}$ . Suppose the coefficients were given the symbol $\alpha^{\prime}$ and were based on a $T_{0}$ of $0^{\circ} \mathrm{C}$ . What would the coefficient $\alpha^{\prime}$ for silver be? Note: The coefficient $\alpha$ satisfies $\rho=$ $\rho_{0}\left[1+\alpha\left(T-T_{0}\right)\right],$ where $\rho_{0}$ is the resistivity of the material
at $T_{0}=20.0^{\circ} \mathrm{C} .$ The coefficient $\alpha^{\prime}$ must satisfy the expression $\rho=\rho_{0}^{\prime}\left[1+\alpha^{\prime} T\right],$ where $\rho_{0}^{\prime}$ is the resistivity of the material at $0^{\circ} \mathrm{C} .$

Key Concepts

Reference Temperature and Base Resistivity

The reference temperature is the temperature at which the resistivity is defined or measured as a base value (?0). Changing the reference temperature alters the baseline resistivity value since the material’s properties are temperature?dependent. In problems involving resistivity, it is important to consistently account for the chosen reference temperature when applying the linear formula so that changes in temperature yield correct resistivity values.

Conversion of Temperature Coefficients

When the temperature coefficient is defined based on one reference temperature and needs to be converted to another (for example, from 20.0°C to 0°C), the resistivity expressions at both bases must be equated. This involves accounting for the shift in the base resistivity values and results in a conversion factor between the coefficients. Specifically, if the original coefficient is ? (with reference at 20°C) and the new coefficient is ?? (with reference at 0°C), then by equating the expressions for resistivity at a common temperature, one obtains a relation such as ?? = ?/(1 ? 20?), which adjusts the coefficient to reflect the change in reference point.

Resistivity Temperature Dependence

Resistivity in metals generally increases with temperature in a roughly linear fashion over common temperature ranges. This behavior is often modeled by simple linear equations relating the resistivity at any temperature to its value at a reference temperature using a temperature coefficient. The linear approximation is valid when temperature variations are modest, and it simplifies analysis and design in electrical applications.

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