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(A) The resistance $R$ of a wire is given by the formula $R = \frac{ho l}{A} = \frac{m l}{n e^2 	au A}$,where $m$ is the mass of an electron,$l$ is

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(A) The resistance $R$ of a wire is given by the formula $R = \frac{ho l}{A} = \frac{m l}{n e^2 	au A}$,where $m$ is the mass of an electron,$l$ is the length,$A$ is the cross-sectional area,$e$ is the charge of an electron,$n$ is the free electron density,and $	au$ is the relaxation time.Given that $l$,$A$,$m$,$e$,and $	au$ are constant,the resistance $R$ is inversely proportional to the free electron density $n$,i.e.,$R \propto \frac{1}{n}$.It is given that $n \propto T$,therefore $R \propto \frac{1}{T}$.This relationship $R = \frac{k}{T}$ (where $k$ is a constant) represents a rectangular hyperbola,which corresponds to the graph shown in option $A$.

Assume a hypothetical wire in which free electron density changes with temperature in proportionality $n \propto T$,assuming $\tau$ (relaxation time of collision) and dimensions of the wire remain unchanged with increasing temperature. Which one of the resistance $v/s$ temperature graphs is true?

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