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In an experiment, the resistance of a material is plotted as a function of temperature (in some range). As shown in the figure, it is a straight line. One may conclude that [Figure: graph of ln R(T) on the vertical axis against 1/T² on the horizontal axis; a straight line segment with negative slope, running from a high point just to the right of the vertical axis down to a low point just above the horizontal axis.]

Asked in JEE Main 10th April 1st Shift 2019 · Temperature dependence of resistance

Figure: Temperature dependence of resistance
Answer: (3) R(T)=R₀e^-T₀²/T²

Step-by-step solution

The graph says ln R=c-k 1/(T²) with k>0 (negative slope, positive intercept).

Write c=ln R₀ and k=T₀²: ln R=ln R₀-(T₀²)/(T²).

So R(T)=R₀e^-T₀²/T², option (c).

The printed key marks no option as correct, but the physics gives option (c).

Why the other options are wrong

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