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 1300 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: alphairon = 5.0times 10-3 K-1

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aristocles aristocles · Answer 1 · 2019-11-08T02:07:32+01:00

Answer:

[tex]R_{Si} = 81.25 ohm[/tex]

[tex]R_{Fe} = 1218.75 ohm[/tex]

Explanation:

As we know that the two resistors are made to combine so that we will get temperature stable resistor

so we will have

[tex]\alpha_i = 5.0 \times 10^{-3}[/tex]

[tex]\alpha_s = -75 \times 10^{-3}[/tex]

now we know that

[tex]R_1\alpha_1\Delta T + R_2\alpha_2\Delta T = 0[/tex]

[tex]R_1 (5 \times 10^{-3}) - R_2(75 \times 10^{-3})= 0[/tex]

[tex]R_1 = 15 R_2[/tex]

also we know that

[tex]R_1 + R_2 = 1300 [/tex]

[tex]R_{Si} = 81.25 ohm[/tex]

[tex]R_{Fe} = 1218.75 ohm[/tex]