The temperature coefficient of resistance of tungsten is $4.5 \times 10^{-3}{ }^{\circ} C ^{-1}$ and that of germanium is $-5 \times 10^{-2}{ }^{\circ} C ^{-1}$. A tungsten wire of resistance $100 \,\Omega$ is connected in series with a germanium wire of resistance $R$. The value of $R$ for which the resistance of combination does not change with temperature is .......... $\Omega$
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(a)
$R_1 \alpha_1+R_2 \alpha_2=0$
$(100)\left(4.5 \times 10^{-3}\right)=R\left(5 \times 10^{-2}\right)$
$0.9 \times 10=R$
$R=9 r$
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