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You are an expert witness, having been hired by an attorney who is defending a wire manufacturing company in a lawsuit. The company is being sued by a firm that manufactures electronic measurement devices. The wire company provides copper wires with precision lengths and radii to be used in thermal measurement devices manufactured by the device firm. The device firm lost a major contract due to inaccuracy of their thermal measurement device. This firm is claiming that the precision of the wires provided by the wire company was not sufficient. You have inspected the wires in the laboratory and have found the lengths to be precise and the radii to be uniform, well within the specifications provided by the device firm. You report this information during the trial, and the legal team for the device firm looks frustrated. The lawyer confers with his client, jumps up, and says, "The wire company did not allow for thermal expansion of the wire! Thermal expansion could make a difference of several percent in the resistance of the wire!" A recess in the trial is called until the next day while you perform some calculations to determine the fraction by which thermal expansion would change the resistance of a wire so that you can report your result. (Use the following as necessary: AT, a, for the coefficient of linear expansion, and a, for the temperature coefficient of resistivity.) AR "RAT %3D R

You are an expert witness, having been hired by an attorney who is defending a wire manufacturing company in a lawsuit. The company is being sued by a firm that manufactures electronic measurement devices. The wire company provides copper wires with precision lengths and radii to be used in thermal measurement devices manufactured by the device firm. The device firm lost a major contract due to inaccuracy of their thermal measurement device. This firm is claiming that the precision of the wires provided by the wire company was not sufficient. You have inspected the wires in the laboratory and have found the lengths to be precise and the radii to be uniform, well within the specifications provided by the device firm. You report this information during the trial, and the legal team for the device firm looks frustrated. The lawyer confers with his client, jumps up, and says, "The wire company did not allow for thermal expansion of the wire! Thermal expansion could make a difference of several percent in the resistance of the wire!" A recess in the trial is called until the next day while you perform some calculations to determine the fraction by which thermal expansion would change the resistance of a wire so that you can report your result. (Use the following as necessary: AT, a, for the coefficient of linear expansion, and a, for the temperature coefficient of resistivity.) AR "RAT %3D R

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### Thermal Expansion and Resistivity in Copper Wires **Case Overview:** You have been hired as an expert witness by an attorney defending a wire manufacturing company in a lawsuit. This company is being sued by a firm that manufactures electronic measurement devices. The wire company provides copper wires with precision lengths and radii to be used in thermal measurement devices manufactured by the device firm. The device firm lost a major contract due to the inaccuracy of their thermal measurement device, claiming that the precision of the wires provided by the wire company was not sufficient. **Investigation Findings:** Upon inspection, the lengths and radii of the wires were found to be precise and uniform, well within the specifications provided by the device firm. This information was reported during the trial, causing frustration within the legal team for the device firm. Their lawyer suggested the possibility that thermal expansion of the wire was not accounted for, which could impact the resistance of the wire significantly. **The Issue:** Thermal expansion can affect the electrical resistance of wires. A recess was called in the trial to allow for calculations on how thermal expansion might affect the wire's resistance. The goal is to determine the fraction by which thermal expansion would change the resistance of the wire. **Formula for Calculation:** The relevant formula is: \[ \frac{\Delta R}{R} = \alpha_R \Delta T \] - \( \Delta R \): Change in resistance - \( R \): Original resistance - \( \alpha_R \): Temperature coefficient of resistivity - \( \Delta T \): Change in temperature ### Explanation: This equation suggests that the change in resistance (\( \Delta R \)) relative to the original resistance (\( R \)) is directly proportional to the change in temperature (\( \Delta T \)) and the material’s temperature coefficient of resistivity (\( \alpha_R \)). **Considerations for the Calculation:** - **Coefficient of Linear Expansion:** Represents how much the wire expands per degree change in temperature. - **Temperature Coefficient of Resistivity:** Indicates how the resistivity of the material changes with temperature. ### Conclusion: To accurately evaluate the impact of thermal expansion on the resistance of copper wires, consider the specific coefficients and changes in temperature. These calculations will help determine if the precision issues could have been caused by thermal expansion, which might exonerate the wire manufacturing company.
Transcribed Image Text:### Thermal Expansion and Resistivity in Copper Wires **Case Overview:** You have been hired as an expert witness by an attorney defending a wire manufacturing company in a lawsuit. This company is being sued by a firm that manufactures electronic measurement devices. The wire company provides copper wires with precision lengths and radii to be used in thermal measurement devices manufactured by the device firm. The device firm lost a major contract due to the inaccuracy of their thermal measurement device, claiming that the precision of the wires provided by the wire company was not sufficient. **Investigation Findings:** Upon inspection, the lengths and radii of the wires were found to be precise and uniform, well within the specifications provided by the device firm. This information was reported during the trial, causing frustration within the legal team for the device firm. Their lawyer suggested the possibility that thermal expansion of the wire was not accounted for, which could impact the resistance of the wire significantly. **The Issue:** Thermal expansion can affect the electrical resistance of wires. A recess was called in the trial to allow for calculations on how thermal expansion might affect the wire's resistance. The goal is to determine the fraction by which thermal expansion would change the resistance of the wire. **Formula for Calculation:** The relevant formula is: \[ \frac{\Delta R}{R} = \alpha_R \Delta T \] - \( \Delta R \): Change in resistance - \( R \): Original resistance - \( \alpha_R \): Temperature coefficient of resistivity - \( \Delta T \): Change in temperature ### Explanation: This equation suggests that the change in resistance (\( \Delta R \)) relative to the original resistance (\( R \)) is directly proportional to the change in temperature (\( \Delta T \)) and the material’s temperature coefficient of resistivity (\( \alpha_R \)). **Considerations for the Calculation:** - **Coefficient of Linear Expansion:** Represents how much the wire expands per degree change in temperature. - **Temperature Coefficient of Resistivity:** Indicates how the resistivity of the material changes with temperature. ### Conclusion: To accurately evaluate the impact of thermal expansion on the resistance of copper wires, consider the specific coefficients and changes in temperature. These calculations will help determine if the precision issues could have been caused by thermal expansion, which might exonerate the wire manufacturing company.
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