The resistance of a conductor is $5\, ohm$ at $50\,^oC$ and $6\, ohm$ at $100\,^oC$. Its resistance at $0\,^oC$ is ................ $ohm$
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$\frac{{{R_1}}}{{{R_2}}} = \frac{{(1 + \alpha {t_1})}}{{(1 + \alpha {t_2})}} \Rightarrow \frac{5}{6} = \frac{{(1 + \alpha \times 50)}}{{(1 + \alpha \times 100)}}$$ \Rightarrow \alpha = \frac{1}{{200}}\,{\rm{ per}}\,{{\rm{ }}\,^o}C$
Again by ${R_t} = {R_0}(1 + \alpha t)$
$ \Rightarrow \,\,5 = {R_0}\left( {1 + \frac{1}{{200}} \times 50} \right) \Rightarrow {R_0} = 4\,\Omega .$
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