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

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Discussion Overview

The discussion revolves around the implications of short circuits in parallel circuits, particularly in the context of superconductors and ideal voltage sources. Participants explore the theoretical aspects of voltage consistency across parallel paths and the limitations of ideal models in practical scenarios.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant questions how a shorted path with 0 Ohm resistance can coexist with a 10V potential in another path of a superconducting parallel circuit.
  • Another participant asserts that ideal voltage sources capable of sourcing unlimited current do not exist and that superconductors have a current limit.
  • A participant elaborates on the nature of ideal voltage sources as simplified models, suggesting that the model's applicability depends on the specific circuit conditions.
  • One participant emphasizes the need to analyze circuits under constant current conditions, referencing Ohm's law to illustrate the relationship between voltage and resistance.
  • A later reply states that connecting an ideal voltage source with a superconducting wire leads to a logical contradiction, as the ideal source asserts a non-zero voltage while the short asserts zero voltage. They also mention the limitations of real voltage sources and the role of inductance and maximum current density in superconductors.

Areas of Agreement / Disagreement

Participants express differing views on the feasibility of connecting ideal voltage sources to superconducting wires, with some asserting contradictions while others focus on the limitations of ideal models. The discussion remains unresolved regarding the implications of these contradictions.

Contextual Notes

Participants highlight the assumptions underlying ideal voltage sources and superconductors, including the implications of zero resistance and the existence of maximum current density, which may not be universally applicable.

Kevin J
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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?
*
Or is an ideal voltage source/battery is impossible to be connected with a superconducting wire?
 
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Ideal voltage sources that can source unlimited current do not exist. Superconductors have a current limit.
 
+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).
 
Kevin J said:
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)
 
Kevin J said:
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.
 

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