For some applications, it is important that the value of a resistance not change
ID: 2120084 • Letter: F
Question
For some applications, it is important that the value of a resistance not change with temperature. For example, suppose you made a 6.50k%u03A9resistor from a carbon resistor and a Nichrome wire-wound resistor connected together so the total resistance is the sum of their separate resistances.
a.)
What value should the carbon resistor have (at 0 %u2218C) so that the combination is temperature independent
R0C=
b.)
What value should the Nichrome wire-wound resistor have (at 0 %u2218C) so that the combination is temperature independent?
R0N=
Explanation / Answer
Resistance change with temperature is given by
R = Ro( 1 + alpha Dt)
let RC = carbon resistance , RN = nichrome resistance
RC = R1o(1+ aplhaC Dt)
RN = R20(1+ aplha2 Dt)
total resistance,
RC + RN = R1 o + R2o + (R1o alpha1 + R2o alpha 2) Dt
if it is independent of temperature ,
RC alpha 1 = -RN alpha 2
alpha 1(Carbon) = 0.0005
alpha 2(Nichrome) = 0.0004
|RC/RN| = |alpha2/alpha1]
thus RC = Rn * 0.0004/0.0005
Rc = 0.8 Rn
but given Rc +Rn = 6500
Rn =3611.11 ohms = 3.611 kohms
RC = 2006 .172 = 2.889 K ohms