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 1.8 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.

1. 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.

2. 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.

For some applications, it is important that the value of a resistance not change with temperature. For example, suppose you made a 0.9 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.

1. 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.

2. 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.

Explanation / Answer

1. given Rc = 1800 ohms

alphac = -0.0005 /C

alphan = 0.0004 /C

1. let reisstance of nichrome resistor be Rn

then

Reff = Rc' + Rn'

Rc' = Rc(1 + alphac*(T - 20))

Rn' = Rn(1 + alphan(T - 20))

where T is in degree C

hence

Reff = Rc(1 + alphac(T - 20)) + Rn(1 + alphan(T - 20))

now,

d(Reff)/dT = 0

hence

Rc(alphac) + Rn(alphan) = 0

Rc/Rn = -alphan/alphac = 0.8

hence

for temperature independence

Rc = 1800 ohm = 0.8Rn

2. Rn = 2250 ohm

2. 1. for Rc = 900 ohm

2. Rn = 900/0.8 = 1125 ohms

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