Is it Possible for a Short Circuit to Contradict Voltage in a Parallel Circuit?

[Kevin J]

Assume a superconducting parallel circuit being shorted, a 10V ideal battery, and a 5 Ohms resistor connected on one of its path. This means the shorted path has a 0 Ohm resistance, which also means it has no potential difference, how is this even possible if voltage across in a parallel circuit should be the same, in this case one path has 10V, the other one has 0V?
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Or is an ideal voltage source/battery is impossible to be connected with a superconducting wire?

 

[willem2]

Ideal voltage sources that can source unlimited current do not exist. Superconductors have a current limit.

 

[CWatters]

+1

Ideal voltage sources are simplified models of real voltage sources, models in which the internal resistance is assumed to be zero so its effect can be ignored. It's up to you to decide if it's reasonable to use that model in any particular circuit.

You might also like to think about what happens you open circuit an ideal current source (compared to a real current source).

 

[Lord Jestocost]

Or is an ideal voltage source/battery is impossible to be connected with a superconducting wire?

Regarding "Zero electrical DC resistance" questions, it is always better to physically rethink analyzing the circuit under constant current conditions in the following sense:

"The simplest method to measure the electrical resistance of a sample of some material is to place it in an electrical circuit in series with a current source I and measure the resulting voltage V across the sample. The resistance of the sample is given by Ohm's law as R = V / I. If the voltage is zero, this means that the resistance is zero." (from https://en.wikipedia.org/wiki/Superconductivity#Zero_electrical_DC_resistance)

 

[Dale]

Or is an ideal voltage source/battery is impossible to be connected with a superconducting wire?

It is impossible. It is a logical self contradiction since the ideal voltage source asserts $V\ne 0$ and the ideal short asserts $V=0$. The one contradicts the other.

Since ideal voltage sources don’t exist that is the assumption that usually fails and the current will be limited by the real source’s internal resistance. However, you could also consider the inductance of the short, which can be nonzero even for a superconductor. Superconductors also have a maximum current density at which point they stop superconducting and become resistive.