The $V-i$ graph for a conductor at temperature ${T_1}$ and ${T_2}$ are as shown in the figure. $({T_2} - {T_1})$ is proportional to
Diffcult
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(c) As we know, for conductors resistance $\propto$ Temperature.
From figure $R_1 \propto T_1$
From figure $R_1 \propto T_1$
$ \Rightarrow \tan\theta \propto T_1$
$ \Rightarrow \tan\theta = kT_1 $… $(i)$
and $ R_2 \propto T_2$
$\Rightarrow \tan (90^o -\theta) \propto T_2$
$ \Rightarrow \cot\theta = kT_2$ ….$(ii)$
From equation $(i)$ and $(ii)$ $k({T_2} - {T_1}) = (\cot \theta - \tan \theta )\,$
$\,({T_2} - {T_1}) = \left( {\frac{{\cos \theta }}{{\sin \theta }} - \frac{{\sin \theta }}{{\cos \theta }}} \right) = \frac{{({{\cos }^2}\theta - {{\sin }^2}\theta )}}{{\sin \theta \cos \theta }}$$ = 2\cot 2\theta $
$ \Rightarrow $ $(T_2 -T_1) \propto \cot 2\theta$
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