The V-I graph for a conductor at temperature $T_{1}$ and $T_{2}$ are as shown in the fig. The term $(T_{2} - T_{1})$ is proportional to

\frac{s i n 2 θ}{s i n^{2} θ}

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\frac{c o t 2 θ}{s i n^{2} θ}

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\frac{c o s 2 θ}{s i n 2 θ}

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\frac{t a n 2 θ}{s i n^{2} θ}

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Solution

The correct option is C $\frac{c o s 2 θ}{s i n 2 θ}$
$V_{2} = t a n (90 - θ) I_{2} V_{1} = t a n θ I_{1}$
$\Rightarrow V_{2} = c o t θ I_{2} \Rightarrow R_{1} = t a n θ$
$R_{2} = c o t θ$
$\Rightarrow (R_{2} - R_{1}) = R_{1} α (T_{2} - T_{1})$
$\Rightarrow (T_{2} - T_{1}) \propto (R_{2} - R_{1})$
$\Rightarrow (T_{2} - T_{1}) \propto (\frac{c o s^{2} θ - s i n^{2} θ}{s i n θ c o s θ})$
$\Rightarrow (T_{2} - T_{1}) \propto \frac{c o s 2 θ}{s i n 2 θ}$

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