Question

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

• A. $9 \,\Omega$
• B. $1111 \,\Omega$
• C. $0.9 \,\Omega$
• D. $111.1 \,\Omega$

Answer 1

Answer: (A)

$R_{1}\, \alpha_{1}+R_{2} \,\alpha_{2}=0$
$(100)\left(4.5 \times 10^{-3}\right)$
$=R\left(5 \times 10^{-2}\right)$
$0.9 \times 10=R$
$R=9\, r$