Question

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 :

• A. $R\left(T\right) = \frac{R_{0}}{T^{2}} $
• B. $R\left(T\right) = R_{0} e^{-T^2/T_{0}^2} $
• C. $R\left(T\right) = R_{0} e^{-T^2_0/T^2} $
• D. $R\left(T\right) = R_{0} e^{T^2/T_{0}^2} $

Answer 1

Answer: (C)

$\frac{\frac{1}{T^{2}}}{\frac{1}{T^{2}_{0}}} + \frac{\ell n\left(T\right)}{\ell nR\left(T_{0}\right)} = 1 $
$ \Rightarrow \ell nR\left(T\right) =\left[\ell nR\left(T_{0}\right) \right]\left(1- \frac{T^{2}_{0}}{T^{2}}\right) $
$ \Rightarrow R\left(T\right) =R_{0}e^{\left(- \frac{T^2_{0}}{T^{2}}\right)} $