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 kΩ 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 20∘C are -0.0005 (∘C)−1 and 0.0004 (∘C)−1, respectively.

1. What value should the carbon resistor have (at 20∘C) 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 kΩ 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 20∘C are -0.0005 (∘C)−1 and 0.0004 (∘C)−1, respectively.

1. What value should the carbon resistor have (at 20∘C) 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.

Answer 1

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