Question

electrical resistance and temperature conceptual question
the electrical resistance of most materials is dependent on temperature. for many materials, the resistance decreases as the temperature of the material decreases. the data below show the resistance of a disk of yba2cu3o7, a hard, brittle ceramic, at temperatures between 200 k and 240 k. (figure 1)
part a
based on the trend of these data, predict the expected resistance r of the sample at 160 k. express your answer in milliohms (10^(-3) ω).
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Explanation:

Step1: Assume linear - relationship approximation

Since we only have limited data and no specific formula given, we can assume a linear - relationship between resistance and temperature in the vicinity of the known data points. Let the resistance $R$ be a linear function of temperature $T$, $R = mT + b$. We can use two known points on the graph (for example, two adjacent points on the red - line segment) to find the slope $m$ and the intercept $b$. But since we don't have exact coordinate values from the graph, we can also estimate visually. The graph shows that as $T$ decreases from $200$ K to $240$ K, $R$ is in the range of approximately $8\times10^{-3}\Omega$ to $10\times10^{-3}\Omega$. If we assume a linear decrease, the rate of change of resistance with respect to temperature can be estimated. As the temperature decreases, the resistance decreases. Since the resistance decreases as the temperature decreases and we want to find the resistance at $160$ K (lower than the shown range), we expect the resistance to be lower than the values at $200 - 240$ K. By visual inspection and the trend of the line, we can estimate that at $160$ K, the resistance $R$ is around $4\times10^{-3}\Omega$.

Answer:

$4\times10^{-3}$