Question

The temperature coefficient of resistance of tungsten
is 4.5 * 10-3 °C-1 and that of germanium is
-5 x 10-2 °C-1. A tungsten wire of resistance 100 22
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​

Answer 1

Answer:

$9\Omega$

Explanation:

1) We have ,

thermal coefficient of resistance of tungsten and that of germanium as

$\alpha _T=4.5 \times 10^{-3} units\\ \\\alpha_G=-5 \times 10^{-2}$

Let $\Delta T$ be the rise in temperature.

2) Since,

both the wires are connected in series.

$R_{eq}=R_T+R_G\\ \\ =>\Delta R=\Delta R_T+\Delta R_G\\ \\=>0=\alpha _T*R_T\Delta T+\alpha _G*R_G\Delta T\\ \\=>0=4.5*10^{-3}*100*\Delta T-5*10^{-2}*R*\Delta T\\ \\=>R=9\Omega$

Hence,The value of R for which the resistance of combination does not change with temperature is 9 ohms.