In an experiment the resistance R of a sample is measured against temperature T over a range, and ln R plotted versus 1/T² turns out to be a straight line. Which relation does the data support?

R(T) = R0/T²
R(T) = R0 e^(-T²/T0²)
R(T) = R0 e^(-T0²/T²)
R(T) = R0 e^(T²/T0²)

Correct answer: R(T) = R0 e^(-T0²/T²)

Solution

For R = R0 e^(-T0²/T²), ln R = ln R0 - T0² * (1/T²), which is linear in 1/T²; resistance rises with T as expected for the standard form.

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