# F5 Phy resistance

A resistor is to have a constant resistance of R = 30。Ω, independent of temperature. For this, an aluminium resistor with resistance R01 at 0℃ is connected in series with a carbon resistor with R02 at 0℃. Evaluate R01 and R02. Given that linear temperature coefficient α1= 3.9×10^-3 for aluminium and α2 = -0.5×10^-3 for carbon.

Could you please tell me the method to do it? Thanks.

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Since you did not give a unit to the temperature coefficients, I suppose they are in unit of C^-1

It is required that: R01 + R02 = 30 ohms --------------------- (1)

Suppose the temperature rises by T degrees C

change of resistance of R01 = (R01) x (3.9x10^-3) x T

change of resistance of R02 = (R02) x (-0.5x10^-3) x T

For the total resistance to be kept at 30 ohms, we need to have,

change of resistance of R01 + change of resistance of R02 = 0

i.e. [(R01) x (3.9x10^-3) x T] + [ (R02) x (-0.5x10^-3) x T] = 0

[(R01) x (3.9x10^-3) = (R02) x (0.5x10^-3)

(R02) = (R01) x [3.9x10^-3/0.5x10^-3] = 7.8(R01)

Substitute into equation (1)

R01 + 7.8(R01) = 30

hence, R01 = 3.409 ohms

and R02 = 7.8 x 3.409 ohms = 26.59 ohms

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