Questions about Klitzing constant of resistance.

[dhimokritis]

                    Questions about Klitzing constant of resistance.

 

Klitzing constant RK = 25812.807572(93) Ohm  or RK = 25812.887557(18) Ohm, after sources of data constants, first attire my interest, because is a constant in space (or of space?), and is a constant that not depend by length, cross section, or material, as we common people are seeing in resistors.

The second it attire my intention because:

 1-   RK = μ0 * c / (2 * α)  is depend by another constant that has to do with mass.

 I find a few connections that depend by mass, radius, and C = e, but strange enough, in the result radius is eliminated.

Z0  = 4 * pi * M * R * c / e^2  = 376 7303138 ohm.  This is too a constant of space linked with :

2--RK  =  Z0 / 2 * α = 25812.80762 ohm.

 

3 -- RK = (M * R * c * 2 *pi * / α ) / e^2 = h / e^2 = 25812.80757 ohm

 

4 – RK =  ( U1 * R1 ) / Rc / ( e * c / (2 * pi  R1 / α ) * Rc =

 

           = ( U1 * R1 ) / ( I1 / R1) = (1.439964393 * 10^-9) * (5.578488068*10^-14) =

     

           = 25812.80762 ohm

May any helper give me the formula from quanta mechanic theory about this constant, that result with the same value?

               

[Strange]

Could you explain:

1. Where these equations came from (or show how you derived them):

• RK = μ0 * c / (2 * α)
• RK  =  Z0 / 2 * α 
• RK = (M * R * c * 2 *pi * / α ) / e^2
• RK =  ( U1 * R1 ) / Rc / ( e * c / (2 * pi  R1 / α ) * Rc

2. Can you define what the following symbols mean: M, R, U₁, R₁, R_c

_Thanks

[studiot]

Here is some useful information on these formulae.

 

https://www.ptb.de/cms/en/ptb/fachabteilungen/abt2/fb-26/ag-262/the-quantum-hall-resistance.html

 

Quote

The tasks of the working group 2.62 are notably based on the so-called quantum Hall resistance which is characterised by quantised values of the Hall resistance R_H:

R_H = R_K/i    with  R_K = h/e2  and   i = 1, 2, 3, 4, …

i.e., the quantum Hall resistance is an integer fraction i of the von-Klitzing constant R_K. The von-Klitzing constant depends only on the Planck constant h and the charge of the electron e. Klaus von Klitzing discovered this effect in 1980 und was honoured in 1985 with the Nobel Prize in Physics.

 

[dhimokritis]

21 hours ago, Strange said:

Could you explain:

1. Where these equations came from (or show how you derived them):

• RK = μ0 * c / (2 * α)
• RK  =  Z0 / 2 * α 
• RK = (M * R * c * 2 *pi * / α ) / e^2
• RK =  ( U1 * R1 ) / Rc / ( e * c / (2 * pi  R1 / α ) * Rc

2. Can you define what the following symbols mean: M, R, U₁, R₁, R_c

_Thanks

• The first and second, from:Physics.nist.gov / constant.

• The third from conversion of electric constant that depend from charge “e”, in constant that depend from my Hypothetic charge : “M”
•  
•  
•  
•  The forth, by hypothetic potential (voltage) of : “e / e” in a distance 1 m. (that is unity of distance).

•  “I” from the charge “ e “ moving with velocity c in spherical trajectory which create appropriate frequency for radius 1m.

• ”

19 hours ago, studiot said:

Here is some useful information on these formulae.

 

https://www.ptb.de/cms/en/ptb/fachabteilungen/abt2/fb-26/ag-262/the-quantum-hall-resistance.html

 

 

Thanks Studiot.  I don’t go too dip, I am not able swimming. But I am satisfied that treating this constant classically I “re-found” in this post - speculation the link of von Klitzing constant from the “h” Planck and  “e”. What satisfied me, is that constant “h” came accidentally when I tried to find the link of the “μ0” with other Planck constants.