Having a bit of trouble with Electric currents and resistance

[Divergent13]

Hey there! This question has be a bit confused as to where to start---

Suppose you made a 4.70 k-Ohm resistor from a carbon resistor and a Nichrome wire wound resistor connected together so the total resistance is the sum of their separate resistances. What value should each of these resistors have (at 0 degrees Celsius) so the combination is temperature independent?

My question is how can we make it temperature independent? I am having trouble in general---- understanding what that means...

Any help would be greatly appreciated thank you.

A lot of the ideas in this chapter play a big role in materials science so I am quite interested in this part of the course--- more so than mechanics :]

 

[turin]

Off the top of my head, I don't know. Apparently, the resistivity of one material will increase with temperature while the other will decrease. Then, you would want the resulting increase in resistance to compensate for the resulting decrease in resistance. You are probably just supposed to determine this for small variations around 0^oC. I will look into this further and come back to share what I have found.



What I found (source: http://hyperphysics.phy-astr.gsu.edu/hbase/electric/restmp.html):

R = R₀ {1 + αΔT}

Where R is the resistance, R₀ is the resistance at 0^oC in your case, α is the temperature coefficient of resistance, and ΔT is the temperature in ^oC in your case.

carbon: α_C = -5E-4 per C^o

nichrome: α_N = 4E-4 per C^o

Then, you want

R_total = constant = R_C + R_N

where R_C = R_0,C {1 + α_CΔT}

and R_N = R_0,N {1 + α_NΔT}

 

[rayjohn01]

Agree with Turin -- these cancellations only are valid over a small range of temerature and you cannot expect carbon to be very stable or repetitive from one resistor to the next.

 

[Divergent13]

Interesting, we have not learned what is shown on the site that turin has found. If you have any more suggestions please post. But if not then Ill try to work with what turin has stated.

 

[turin]

divergent,
You may have learned a simple and straighforward equation into which you simply plug the temperature coefficients. The crap that I have listed is the next level down in the derivation.

 

[Theelectricchild]

What you posted doesn't seem like its bad, I was able to get solution that both Rs added get 4.5...

 

[turin]

After thinking somemore about it, I think it would be better to connect the resistors in parallel, rather than series. You want:

R_total = R_NR_C / (R_N + R_C) = constant.

That way, you alleviate more of the heating effect that would take the resistors far away from the 0^oC point by reducing the current that goes through them.