The resistance of a platinum wire is to be calibrated for...

The resistance of a platinum wire is to be calibrated for low-temperature measurements. A platinum wire with resistance $1.00 \Omega$ at $20.0^{\circ} \mathrm{C}$ is immersed in liquid nitrogen at $77 \mathrm{K}\left(-196^{\circ} \mathrm{C}\right) .$ If the temperature response of the platinum wire is linear, what is the expected resistance of the platinum wire at $-196^{\circ} \mathrm{C} ? \quad\left(\alpha_{\text {platinum }}=3.92 \times 10^{-3} /^{\circ} \mathrm{C}\right)$

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Key Concepts

Temperature Coefficient of Resistance

This is a proportionality constant that indicates how much the resistance of a material changes per unit change in temperature. It is typically expressed in per degree Celsius and is essential for predicting how the resistance will vary as the temperature changes, which is particularly important for sensor calibration and design.

Linear Resistance-Temperature Relationship

This concept involves the assumption that the change in resistance of a material is directly proportional to the change in temperature, following the formula R = R?(1 + ??T). This linear approximation simplifies calculations and is valid over moderate temperature ranges, making it a fundamental tool in electrical and materials engineering.

Calibration of Resistive Sensors

Resistance calibration is the process of precisely determining the resistance of a sensor, like a platinum resistor, under varying temperature conditions. By using known coefficients such as the temperature coefficient of resistance, engineers can accurately translate measured resistance changes into temperature readings, ensuring reliable performance in temperature measurement applications.

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