# Shorts in parallel - out of curiosity

Normally a current would take a simpler route, hence why a resistor in parallel with a short gets no share in current. Again two equal resistors in parallel get equal share in current.

These questions just crossed my mind:

1. What happens when you have two shorts in parallel? Do they get equal share as well?
2. Again, what happens when I place an inductor in parallel with a short? Would the inductor become a short (eventually)? You know how inductor behave under DC.

What others have to say?

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two shorts in parallel is effectively a single short (ignoring the practical fact that there is no perfect short) –  user13267 Apr 23 '14 at 2:49

A short is never actually a true short. It's a very low resistance. So even if you made two "shorts" one could be 0.25 Ohms and the other could be 0.001 Ohms. Depending on the circuit, they're both shorts, but they could act very differently depending upon the amount of current coming from the circuit. The difference in this case would make the 0.001 Ohms a much better path for current. Consequently, hardly any current would go through the 0.25 ohm short. In summary, it's likely too difficult to try and control two shorts to act in a balanced manner. If you are, you're not thinking of them as a short but rather as a current/low-resistance path.

The inductor would act like it's equivalent series resistance (ESR) once the current stabilizes to a steady state.

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There's no such thing as a mathematically perfect short. Usually there is some DC resistance, so it's the same as two resistors in parallel, after it settles down.

$I_{R1} = I_T(\frac{R2}{R1+R2})$

$I_{R2} = I_T(\frac{R1}{R1+R2})$

If there is no resistance (superconductors) the current is shared based on the inductance.

$I_{L1} = I_T(\frac{L2}{L1+L2})$

$I_{L2} = I_T(\frac{L1}{L1+L2})$

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These could also be circulating current in case of superconductors;) –  Vovanium Apr 22 '14 at 16:01
@Vovanium True. Assumption was that it was starting with zero circulating current, so none should arise. –  Spehro Pefhany Apr 22 '14 at 16:18
Hazardous assumption:) –  Vovanium Apr 22 '14 at 16:20
Perhaps, but have had no problems with it so far. SQUIDs are pretty much incremental measuring devices. –  Spehro Pefhany Apr 22 '14 at 16:21

A short circuit has resistance, just very much lower than a resistor. If you have two short circuits than the current will share between them based upon their resistance values. The same applies to the inductor which, in the real world, will have a dc resistance value.

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1. In theortical ideal circuits, every distribution of currents, giving right sum would be correct solution: (0.5 0.5), (0.0 1.0), or even (2.0 −1.0) where one current flows in opposite direction. (Under solution I mean mathematic solution on circuit model) You should not bother about it, because for remaining circuit these have no sense absolutely.

2. Ideal shorted inductor will keep its current constant (which was at moment of short). Current through short will be sum of inductor current and external current, obviously.

But you cannot get these results in practice.

In normal conditions these answers have no practival sense absolutely, because every conductor have non-zero resistance. (Good answers on convetional conductors are already there)

More closer are superconductors -- you can connect two superconductors in parallel of course. But superconductors not true shorts too, they have nonzero inductance. So they act more like two inductors in parallel. Simply, they take current proportional to reciprocal inductance plus constant circulating current. Look for SQUID magnetometer if you interested.

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