Question

A temperature-stable resistor is made by connecting a resistor made of silicon in series with one made of iron. If the required total resistance is 1200 capital omega in a wide temperature range around 20degrees Celsius, what should be the resistances of the two resistors? The temperature coefficients of the resistivities for iron and silicon are:

Answer 1

Answer:

The resistance of the silicon has to be 80 Ω and the iron must be 1120 Ω

Explanation:

Lets take

Temperature coefficients of resistivities or iron = $5.\times 10^{-3} K^{-1}$

Temperature coefficients of resistivities or silicon = $75.\times 10^{-3} K^{-1}$

The resistance of the iron increases a little as the temperature rises

The resistance of the silicon decreases a lot as the temp rises.

So we want the iron to be most of the resistance and have its increase in resistance exactly equal to the drop in resistance of the silicon.  

Since the drop in the silicon is 15 times the rise in the iron ( 75 / 5 ) you want the iron to have 15 time the resistance of the silicon. And the total resistance has to be 1200Ω

1200/15 = 80

So

The resistance of the silicon has to be 80 Ω and the iron must be 1120 Ω