For some applications, it is important that the value of the resistance not chan
ID: 1552748 • Letter: F
Question
For some applications, it is important that the value of the resistance not change with temperature. For example, suppose you made a 3.7k resistor from a carbon resistor and a Nichrome wire-wound resistor connected together so the total resistance is the sum of their individual resistances. What value should each of these resistors have at 0oC so that the combination is temperature independent? The temperature coefficient of the resistivity at 0oC for Carbon and Nichrome is C0 =0.0005Co1, N0 =0.0004Co1 , respectively. Note that here you have to formulate the temperature dependence of the resistivity in reference to the value at 0oC rather than at room temperature as defined in lecture.
Explanation / Answer
given
Rc+Rn = 3700
Rc+Rn=Rco[1+ac*dT]+Rno[1+an*dT]
Rc+Rn=Rco+Rno+dT[ac*Rco+an*Rno]
for temperature to be independent
Rc+Rn=Rco+Rno =3700
Rco+Rno =3700-------------1
dT[ac*Rco+an*Rno]=0
ac*Rco+an*Rno=0
temperature coefficents ar
ac=-0.0005 /C
an =0.0004 /C
-0.0005Rco +0.0004Rno=0
-5Rco+4Rno=0----2
solving 1 and 2 we get
a)
Rco =1644.28 ohms or 1.644 Kohms
b)
Rno=2055.35 ohms or 2.055 kohms