The resistance of a bulb filmanet is $100\,\Omega$ at a temperature of $100\,^o C$. If its temperature coefficient of resistance be $0.005$ per $^o C$, its resistance will become $200\,\Omega$ at a temperature of ................ $^oC$
AIEEE 2006, Medium
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$R_{1}=R_{0}[1+\alpha \times 100]=100$ ...$(1)$
$R_{2}=R_{0}[1+\alpha \times T]=200$ .......$(2)$
On dividing we get
$\frac{200}{100}=\frac{1+\alpha T}{1+100 \alpha} \Rightarrow 2=\frac{1+0.005 T}{1+100 \times 0.005} \Rightarrow T=400\,^{o} \mathrm{C}$
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