A carbon resistor is to be used as a thermometer. On a...

A carbon resistor is to be used as a thermometer. On a winter day when the temperature is $4.0^{\circ} \mathrm{C},$ the resistance of the carbon resistor is $217.8 \Omega$. What is the temperature on a spring day when the resistance is $215.5 \Omega$ ? (Take the reference temperature $T_{0}$ to be $4.0^{\circ} \mathrm{C}$.)

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Key Concepts

Temperature Coefficient of Resistance

This concept refers to how the resistance of a material changes with temperature. In many materials, especially in resistors used as sensors, resistance changes approximately linearly with temperature over a limited range. The coefficient quantifies this change and is fundamental for converting resistance measurements into temperature readings.

Linear Temperature-Resistance Relationship

For many temperature sensors, the relationship between resistance and temperature can be approximated as linear, meaning that a change in temperature produces a proportional change in resistance. This linear approximation simplifies calculations and is widely used in temperature measurement and calibration, especially when the temperature variations are small.

Reference Temperature Calibration

Calibration involves establishing a known resistance at a specific, known temperature (the reference temperature). This initial condition is crucial because it provides a baseline from which changes in resistance can be directly correlated to changes in temperature, allowing for accurate temperature determination in subsequent measurements.

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