I Paradox of Superconductivity

[Karmyogi01]

TL;DR Summary

Inductance of a superconductive coil

For a series R-L circuit that uses superconductive components, how long would it take for current to build up after the power is turned on?

 

[berkeman]

TL;DR Summary: Inductance of a superconductive coil

For a series R-L circuit that uses superconductive components, how long would it take for current to build up after the power is turned on?

Why are you putting a resistor in series with a superconducting inductor? That kind of defeats the purpose, no?

 

[Karmyogi01]

Why are you putting a resistor in series with a superconducting inductor? That kind of defeats the purpose, no?

There is no resistor in series. All components are superconductive. R is vanishingly small

 

[berkeman]

What is the source impedance of the power supply that you are using to build the current? How is it connected to the superconducting coil?

 

[Karmyogi01]

What is the source impedance of the power supply that you are using to build the current? How is it connected to the superconducting coil?

I am assuming an ideal power source with zero impedance for clarity. However, the fundamental logic will not change even if it were not an ideal power source.

 

[Karmyogi01]

I am assuming an ideal power source with zero impedance for clarity. However, the fundamental logic will not change even if it were not an ideal power source.

For a series circuit the power supply is connected in series.

 

[Dale]

The time constant will depend on the radiation resistance of the superconductor. Superconductors have no resistance at DC, but at high frequencies they do have resistance and effective resistance.

 

[Karmyogi01]

The time constant will depend on the radiation resistance of the superconductor. Superconductors have no resistance at DC, but at high frequencies they do have resistance and effective resistance.

Good insight indeed! However, here we do not have the high frequency situation.

 

[renormalize]

Good insight indeed! However, here we do not have the high frequency situation.

Are you sure? The idealized version of "the power is turned on" is a step-function in time, which contains Fourier components with arbitrarily high frequency.

 

[Dale]

Good insight indeed! However, here we do not have the high frequency situation.

As @renormalize mentioned, you have arbitrarily high frequencies for switching on an ideal source.

 

[Baluncore]

For a series R-L circuit that uses superconductive components, how long would it take for current to build up after the power is turned on?

The series R+L will need a return circuit, that has not yet been defined.

In effect, R1+L1 is a transmission line operating against an unspecified environment. The superconducting resistor R1, will become a second series inductor, L2. The length of the combined L1+L2 surface, and the dielectric insulation, will determine the transit time, t. The open (or maybe closed) far end will reflect the initial turn on transient back to the input at t2 = 2*t.

The current through L1+L2 will continue to rise in 2t long steps forever, as the reflected wave bounces back and forth along the impedance of the transmission line, between the mismatched terminal impedances.

It will actually be more complex since the impedance of the R1 and L1 transmission lines may differ and so form different resonators. Also, the coupling between the turns of conductor on the inductor, and maybe wire wound resistor, could form a faster capacitor coupled ladder network.

 

[Karmyogi01]

Are you sure? The idealized version of "the power is turned on" is a step-function in time, which contains Fourier components with arbitrarily high frequency.

The radiation resistance is supposed to be very small and does not change the logic in a fundamental way. The time constant (TC) does not match what we observe. In addition, the question is not constrained to only an ideal power source.

 

[Dale]

the question is not constrained to only an ideal power source

I am assuming an ideal power source

Hmmm.

The time constant (TC) does not match what we observe.

What makes you think that? Do you have a reference that shows an experiment where it doesn’t match?

 

[Karmyogi01]

Hmmm.

What makes you think that? Do you have a reference that shows an experiment where it doesn’t match?

As stated above, I mentioned "ideal source" for the sake of clarity only and mentioned already that we do not necessarily have to assume that. I stated this already. To answer your question regarding TC, please tell me your estimate of "radiation resistance."

 

[berkeman]

As stated above, I mentioned "ideal source" for the sake of clarity only and mentioned already that we do not necessarily have to assume that.

Who is "we"? If we knew the actual application, that would help us to focus our responses.

 

[Dale]

, please tell me your estimate of "radiation resistance."

This depends on the geometry but is typically in the range of 50 to 300 ohms.