For some applications, it is important that the value of a resistance not change

Question

For some applications, it is important that the value of a resistance not change with temperature. For example, suppose you made a 18 k resistor from a carbon resistor and a Nichrome wire-wound resistor connected together so the total resistance is the sum of their separate resistances. The temperature coefficients of resistivity of carbon and Nichrome at 20C are -0.0005 (C)1 and 0.0004 (C)1, respectively. What value should the carbon resistor have (at 20C) so that the combination is temperature independent? What value should the Nichrome wire-wound resistor have (at 20 C) so that the combination is temperature independent?

Explanation / Answer

Let the resistors have values Rc & Rn (for carbon and nichrome respectively), and let the temperature coefficients of resistance be Cc & Cn.

Then Rc + Rn = 15000 ====> Rc = 15000 - Rn.............. (1)

Rn*Cn + Rc*Cc = 0 ............... (2)

Rn*0.0004 + (15000 - Rn)*(-0.0005) = 0

Rn = 8333.33 ohm

And  Rc = 15000 - 8333.33 = 6666.67 ohm

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