Question

The temperature coefficient of resistance of tungsten is $4.5\times {10}^{-3}$ ${}^o{C}^{-1}$ and that of germanium is $-5\times {10}^{-2}$ ${}^o{C}^{-1}$. 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

The correct option is A $9\Omega$

Let $\Delta t^{o}C$ the change in temperature initially sum of resistance = $(100+R)$

$R_{tungsten}=(1+4.5\times {10}^{-3})$

$R_{germanium}R(1+(-5\times {10}^{-2}\left)\right)$

$=R(1-5\times {10}^{-2})$

$R_{net}=R_1+R_2$

As in question given resistance does n'r change with temperature

$\Rightarrow (100+R)=100(1+4.5\times {10}^{-3})+R(1-5\times {10}^{-2})$

$\Rightarrow 100\times 4.5\times {10}^{-1}=R\times 5\times {10}^{-2}$

$R=\frac{4.5\times {10}^{-1}}{5\times {10}^{-2}}=9\Omega$