Q 12-03-252JEE MainJEE Main 2019 (10 Apr, Shift 1)Easy
In an experiment, the resistance of a material is measured as a function of temperature (in some range). A graph of $\ln R(T)$ against $\dfrac{1}{T^2}$ is found to be a straight line with a negative slope. One may conclude that
Answer: (D) $R(T) = R_0e^{-T_0^2/T^2}$
A straight line of negative slope means $\ln R = c - \dfrac{k}{T^2}$ with $k > 0$. Writing $c = \ln R_0$ and $k = T_0^2$:
$$R(T) = R_0e^{-T_0^2/T^2}$$
The other options give $\ln R$ linear in $T^2$ or in $\ln T$, not in $1/T^2$.
Solution by Sreeraj P, M.Sc Physics