Question

the temperature coefficient of resistance of tungsten is 4.5*10-³°C-¹ and that of germanium is -5*10-²°C-¹.A tungsten wire of resistance 100ohm 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.