PLEASE ANSWER CORRECTLY I WILL RATE YOU HIGH! For some applications, it is impor

Question

PLEASE ANSWER CORRECTLY I WILL RATE YOU HIGH!

For some applications, it is important that the value of a resistance not change with temperature. For example, suppose you made a 90 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.

Part A

What value should the carbon resistor have (at 20C) so that the combination is temperature independent?

Express your answer to one significant figure and include the appropriate units.

R0c =

Part B

What value should the Nichrome wire-wound resistor have (at 20 C) so that the combination is temperature independent?

Express your answer to one significant figure and include the appropriate units.

R0N=

Explanation / Answer

We make the combined resistor from a carbon resistor (Roc at 20°C) in series with a nichrome resistor (Ron at 20°C).
Rtot = Roc+Ron=90000 (equation 1)

Since in general R = R(1+(T-0)):

Rtot = Roc[1 - 0.0005(T-20]+ Ron[1 + 0.0004(T-20)]
. . . . = Roc - 0.0005T*Roc+0.01 + Ron+ 0.0004T*Ron -0.008
. . . . = R1 + R2 +0.002+ 0.0004T*Ron - 0.0005T*Roc
. . . . = 90000 + 0.0004T*R2 - 0.0005T*R1

For Rtot to be independent of temperature need 0.0004T*Ron - 0.0005T*Roc to be zero, so that the resistance remains 90000 whatever the temperature.

0.0004T*Ron - 0.0005T*Roc = 0
0.0004Ron = 0.0005Roc
Ron/Roc = 5/4
Ron = 1.25Roc

Since Ron+Roc = 90000
1.25Roc + Roc = 90000
2.25Roc = 90000

Roc = 40000 (=40k) to 1 significant figures

Ron = 90000-40000
. . . = 50000 = 50k to 1 significant figures

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