Weird Science

Resistance Drop at Low Temperatures

Polish ver­sion is here

Elec­tri­cal Resi­stance

Resi­stance, also known as elec­tri­cal resi­stance, is a quan­tity that cha­rac­te­ri­zes the rela­tion­ship between vol­tage and cur­rent in DC cir­cu­its. It is repre­sen­ted by the Greek let­ter Ω.

In the 1830s, Georg Ohm stu­died the rela­tion­ship between the cur­rent flo­wing thro­ugh a con­duc­tor and the applied vol­tage. He disco­ve­red that the cur­rent thro­ugh a con­duc­tor is direc­tly pro­por­tio­nal to the applied vol­tage. This pro­por­tio­na­lity became known as Ohm’s Law and is expres­sed by the well-known equ­a­tion:

U = R * I

The pro­por­tio­na­lity con­stant R is cal­led resi­stance. This law holds true only for cer­tain mate­rials, pri­ma­rily metals. Such con­duc­tors are refer­red to as linear (see here), as oppo­sed to non­li­near con­duc­tors, where the rela­tion­ship is dif­fe­rent.

What fac­tors affect the resi­stance of metals? It undo­ub­te­dly depends on the type of metal; resi­sti­vity is a cha­rac­te­ri­stic pro­perty of each ele­ment. Resi­stance also depends on the con­duc­tor's cross-sec­tio­nal area and length: the smal­ler the cross-sec­tio­nal area and the lon­ger the con­duc­tor, the gre­a­ter the resi­stance.

As it turns out, tem­pe­ra­ture also affects elec­tri­cal resi­stance.

Mate­rials Nee­ded

To exa­mine the effect of tem­pe­ra­ture on the elec­tri­cal resi­stance of metal, you will need the fol­lo­wing mate­rials:

War­ning: Nitro­gen is not toxic, but in its liquid state, it is extre­mely cold. Han­dle it with great care. The author assu­mes no respon­si­bi­lity for any inju­ries or dama­ges resul­ting from buil­ding or using this device; pro­ceed at your own risk!

The type of coil and the wire para­me­ters are not cri­ti­cal; it sho­uld sim­ply have a mea­su­ra­ble resi­stance. I used the small toro­i­dal coil shown below:

Ilustracja:

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Expe­ri­ment

Due to its low tem­pe­ra­ture (-196°C or -320.8°F at its boi­ling point), liquid nitro­gen must be sto­red in spe­cia­li­zed Dewar fla­sks. For the expe­ri­ment, a smal­ler ther­mos is more prac­ti­cal. Con­nect the coil to the mul­ti­me­ter so it can display the coil’s resi­stance. The assem­bled expe­ri­men­tal setup is shown below:

Ilustracja:

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Ini­tially, the coil's resi­stance is about 6.15 kilohms.

Next, immerse the coil in liquid nitro­gen. At first, the nitro­gen boils upon con­tact with the war­mer coil, pro­du­cing clo­uds of con­den­sed water vapor from the air, which cre­a­tes fog. Simul­ta­ne­o­u­sly, the wire’s elec­tri­cal resi­stance decre­a­ses signi­fi­can­tly. This con­ti­nues until the coil’s tem­pe­ra­ture drops to -196°C and the nitro­gen stops boi­ling, as shown in the image below:

Ilustracja:

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As you can see, the coil's resi­stance has signi­fi­can­tly decre­a­sed to 1.2 kilohms.

Expla­na­tion

To explain this phe­no­me­non, we need to under­stand the nature of elec­tri­cal con­duc­ti­vity in metals. Elec­tric cur­rent is defi­ned as the orde­red motion of charge car­riers within an elec­tric field.

In metals, the charge car­riers are elec­trons, which have a nega­tive charge. Metals have a cry­stal­line struc­ture, con­si­sting of ions arran­ged in a lat­tice. Valence elec­trons, being loo­sely bound to ato­mic nuc­lei, can move fre­ely within the cry­stal lat­tice, for­ming what is known as an elec­tron gas. As a result, the posi­ti­vely char­ged metal ions (atoms without valence elec­trons are refer­red to as ion cores or ato­mic cores) can­not move fre­ely and form a cha­rac­te­ri­stic spa­tial cry­stal lat­tice:

Ilustracja

An exter­nal elec­tric field cau­ses the elec­trons to move in an orderly man­ner due to the Cou­lomb for­ces, resul­ting in the flow of elec­tric cur­rent.

But can elec­trons truly move fre­ely thro­ugh the metal lat­tice? Altho­ugh the posi­ti­vely char­ged ions can­not move, they do vibrate aro­und their equ­i­li­brium posi­tions above abso­lute zero. These vibra­tions are known as ther­mal vibra­tions. Moving elec­trons col­lide with these ions, cau­sing a scat­te­ring effect. The macro­sco­pic result of these col­li­sions is elec­tri­cal resi­stance.

Lowe­ring the tem­pe­ra­ture redu­ces the vibra­tions of the ions, allo­wing elec­trons to move more fre­ely. As a result, the resi­stance of the coo­led metal decre­a­ses. When the tem­pe­ra­ture rises, the oppo­site effect occurs.

The obse­rved decre­ase in resi­stance is even gre­a­ter than expec­ted for cop­per, which was used to make the coil wire. Addi­tio­nal fac­tors, pos­si­bly inc­lu­ding ther­mo­e­lec­tric effects, may con­tri­bute to this phe­no­me­non.

Enjoy expe­ri­men­ting! :)

Fur­ther rea­dings:

Marek Ples

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