# Measuring resistance in a superconductor

1. Jul 25, 2012

### chutes123

I am currently an intern at a superconductor lab and have been faced with a personal curiosity. I work with a device that determines the critical temperature at which the material stops superconducting. This device is composed of an electric temperature probe and two coils of wire which are positioned on either side of the sample. I run a MATLAB program which graphs the Voltage vs. the Temperature over time. It seems to me that there is a voltage produced in one coil and the inducted current is measured in the second. The signal is provided and recovered from a "Signal Recovery" device which displays the real time voltage in and voltage out. I am pretty sure that an AC voltage is applied since there is this sort of induction. Does anyone know what properties and equations would be used to measure the varying superconducting properties in this device? If I was not clear about anything, please ask.

2. Jul 25, 2012

### the_emi_guy

My guess is that it is detecting the presence of the Meissner effect. When a material transitions into superconducting state, any static magnetic field lines that were passing through it are suddenly expelled. One coil may be creating static B field, and the other looking for induced voltage due to sudden change in B field (Faraday's law).

Ask someone there and report back, include photo if you can!

3. Jul 26, 2012

### chutes123

the_emi_guy you were right! I figured it out with lot of help from Wikipedia shortly after posting this. The second coil is measuring the voltage induced from the emfs allowed through the superconductor. However, while the superconductor is in the Meissner state, it will create circular currents that oppose the applied emfs similar to a coil of wires according to Faraday's Law. Therefore when the superconductor changes phase out of the Meissner state, a sharp change in voltage induced in the second coil will be noted on the graph. The calculated critical temperature is the midpoint of the transition period. I will provide a picture of the MATLAB GUI, the test equipment, and an artsy picture of liquid nitrogen tomorrow morning when I get into the lab.

NOW I need help explaining this to one of my coworkers. The program that we use displays the graph I mentioned before as R[V] vs T[K]. Before I understood the test, I assumed R stood for resistance in Voltage (strange but plausible considering the field of science), but now I am sure that it stands for something else. The only two concepts I could think fitting would be Reluctance or Reactance. I am not very familiar with either of the concepts, but I can describe how "R" was derived in the MATLAB code (rather cryptically though). If at all possible, I could use some help determining what the variable "A" meant as well.

Two variables: xx and yy were taken from the measurement equipment
I suspect that xx is the Voltage in and yy is the Voltage out
The variable RV was defined as: xx + i(yy)
The variable R was defined as: abs(RV)
The variable A was defined as phase(RV)*180/pi
The function phase(G) "computes the phase of a complex vector" where "G is a complex-valued row vector"

Thanks for the help

4. Jul 26, 2012

### f95toli

"R" is just the magnitude of the signal.
The "signal recovery device" is a lock-in amplifer (Signal Recovery is the name of the company) which gives the in-phase (X) and quadrature phase (Y) of the signal out; i.e. it measures a complex signal X+iY.

Any complex signal can also be written in polar form, with R being the magnitude(=radius) and theta the phase.

The reason the signal is complex is that here is also a phase-shift beween the input and output signal, i.e. both the voltage and the phase matters (although in this case there is probably no addition information in the phase).

Also, in a setup like this the y-scale is arbitrary so it has no real meaning (it is almost impossible to convert the voltage from the lock-in to somehng with physical meaning); one is usually just interested in the Tc and and width of the transition.

5. Jul 26, 2012

### chutes123

Thank you f95toli and the_emi_guy. Both of your answers were helpful and well stated. I will post the pictures in case anyone is still interested.

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