A temperature-stable resistor is made by connecting a resistor made of silicon i

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 1100 in a wide temperature range around 20, what should be the resistances of the two resistors? For the temperature coefficients of resistivities for iron and silicon use the values:

i = 5.0 10-3 K-1

s = -75 10-3 K-1

(a) Resistance of the silicon resistor at 20, Rsilicon, 20:

[5 points] 0 attempt(s) made (maximum allowed for credit = 5)

[after that, multiply credit by 0.5 up to 10 attempts]

(b) Resistance of the iron resistor at 20, Riron, 20:

[5 points] 0 attempt(s) made (maximum allowed for credit = 5)

[after that, multiply credit by 0.5 up to 10 attempts]

Explanation / Answer

alpha(i) = 5.0e-3 K^-1
alpha(s) = -75e-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 you 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 1100

1100 / 16 = 68.75

The resistance of the iron has to be 1031.25 and the silicon must be 68.75

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