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Resistivity Constantan resistivity and temperature
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Resistivity
Constantan resistivity and temperature
Why does the resistivity of Constantan and Nichrome not change with temperature?
SEED Expert Tony Veneruso answers:
The resistivity of most pure metals increases with temperature. This can be a problem in electrical circuits that must operate in varying temperatures, such as inside Schlumberger measuring sensors that are lowered into boreholes deep underground. It can also be a problem in strain gauge sensors that are used to measure weight and pressure in many commercial applications. The problem is because resistors that change with temperature create errors in the measurements, which must be corrected depending upon the temperature.
Around the 1930's the search started to find a metal or a metal alloy to make wire resistors for sensors that did not vary with temperature. Constantan alloy was discovered by a process of trial and error. A 60% Copper, 40% Nickel alloy was found to give the least change in resistance with temperature. A few years later an alloy of Nickel and Chromium called Nichrome was also found to be stable with temperature.
Why does Constantan have that property? For an answer we need to understand why a metal has resistance.
Electricity involves the flow of electrons through the atoms of a metal. A metal like Copper (Cu) has atoms with 29 electrons and Nickel has 28. These electrons move in precise tracks (or orbits). Physicists call them shells. To explain the conduction (flow) of electrons through metal, I find it useful to think of their behaviour as similar to that of people in a crowed theater:
Imagine that you are an electron and you enter into a row of seats in a crowed theater. If all the people are very polite (low friction, low resistance) they will stand and move over to make room for you. They each move over one place until the one at the end is pushed out, has no seat and moves away. However, if is difficult for them to move away from their seats (high friction, high resistance), you will have a tough time to push into the seat and force someone out from the other end (high resistance).
Now imagine two types of theaters. The Copper and Nickel atomic theaters have the same seating arrangement but the Nickel Theater only allows 28 people while Copper allows 29 people. They both have two key shells or sections, which seat electrons; Physicists call these sections 3d and 4s. Section 3d is a bit closer to the stage (atomic nucleus) and is harder to get in and out of compared to 4s, which is further away. Section 3d has exactly 10 seats and section 4s has exactly 2 seats.
Nickel's 28 electrons are seated as follows: 18 are firmly stuck into their seats in the front of the theater near the stage in a section called the Ar (or Argon) section; 8 more are in section 3d (leaving two seats empty), and two fill section 4s in the upper row near the exit. Any new electrons have to go into the two seats in the 3d section.
Copper's 29 electrons are seated this way: 18 are firmly stuck in the Ar section, 10 fill section 3d, and one lone electron is up near the exit in section 4s, where it is easy to come and go. Copper's lone electron in section 4s moves about quite easily, making Copper a good conductor. A visiting electron finds it harder to get into and out of the two remaining seats in Nickel's 3d section, giving Nickel a higher resistance than Copper.
Unfortunately both of our atomic theaters are in a place where the ground shakes, and it shakes harder as temperature increase. This makes it harder for visiting electrons to get into and out of their seats i.e. resistance increases.
If the two theaters are joined together, the lone electron in Copper's 4s section can move down into the 3d section of Nickel. In fact as more and more Copper is added to Nickel this is exactly what happens. When there is about 60% Copper in the mixture, Copper's 4s electrons have all moved to fill all the available spaces in Nickel's 4d section, leaving its own 4s section empty most of the time. This means that there is no interference for visiting electrons to come down the aisle and find a seat. Of course they have to spend energy going up and down the aisle, so the alloy Constantan has a higher resistance than both Copper and Nickel, but it does not change with temperature.
Nickel and Chromium atoms have the same electron seating arrangement (shell structure) as Nickel and Copper - hence Nichrome also has a wide temperature range where resistance does not change.
Some resistivity values (ohm m x 10-8):
Copper 1.68
Nickel: 6.93
Chromium: 13.2
Constantan: 49
Nichrome: 100
A chart showing “the electrical resistance and conductance of some other materials at 20oC” is provided by Hyperphysics, Georgia State University, USA
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