# B Why does current choose the short circuit path?

#### Kevin J

I've seen answers saying that electricity takes path of least resistance, I know this and there is no need to explain this for me.
A forum's answer told me that the electrons initially flow through to the path with resistance and eventually becomes congested (redirecting the remaining electrons to the ''short circuit path' where it offers no resistance.
What I don't understand is, in a normal parallel circuit, with resistors connected across the paths, don't the electrons get ''congested" and " stucked", then how do current/electrons even flow in through 2 paths? (Can anyone explain on how the electrons really move?)

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#### DaveE

Electrons don't "initially flow and become congested" they adjust their direction and magnitude through the resistor circuit paths almost instantaneously. Each path takes part of the current flow. Each resistor generates a voltage from the current flowing through it V = I*R. But in a parallel circuit the voltage across one resistor is the same as the voltage across the other. The amount of current that flows in each path is the amount that makes the resistor voltages equal. This is often called a current divider.
So, lets say we have 2 parallel resistors R1 and R2. R1 has current I1 flowing through it. R2 has I2 current. The total current I = I1+I2. Since the resistors share the same voltage when they are connected in parallel, then V = I1*R1 = I2*R2, so I2 = I1*R1/R2 and the total current must be I = I1*(1+R1/R2).

#### Kevin J

Electrons don't "initially flow and become congested" they adjust their direction and magnitude through the resistor circuit paths almost instantaneously. Each path takes part of the current flow. Each resistor generates a voltage from the current flowing through it V = I*R. But in a parallel circuit the voltage across one resistor is the same as the voltage across the other. The amount of current that flows in each path is the amount that makes the resistor voltages equal. This is often called a current divider.
So, lets say we have 2 parallel resistors R1 and R2. R1 has current I1 flowing through it. R2 has I2 current. The total current I = I1+I2. Since the resistors share the same voltage when they are connected in parallel, then V = I1*R1 = I2*R2, so I2 = I1*R1/R2 and the total current must be I = I1*(1+R1/R2).
So there is no congestion due to the resistor? And why no current flows through the resistance path in a short circuit(assume 5 Ohms and 0 Ohms), but it flows through the resistor in a usual parallel circuit (let's say 5 Ohms and 10 Ohms)?

#### DaveE

I'm not sure what congestion is with electrons. It's not how I would describe their behavior.
Current will absolutely flow through a short circuit. In fact all of it will. In practice short circuits don't have 0 ohms they are just very, very small valued resistors. Consider the equations I1*R1 = I2*R2, if R1 = 0, then I2 = 0, all of the current will flow through R1.

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#### sophiecentaur

Science Advisor
Gold Member
I've seen answers saying that electricity takes path of least resistance, I know this and there is no need to explain this for me.
No it doesn't . And you need to have it explained.
Water doesn't only flow down the widest pipe, does it? It's the same for electrical current; more current will flow via a lower resistance path but some current flows through every possible path.
I do hate water analogies in general but, in this case the analogy is a strong one..
Edit: As with all such phenomena, things take time to settle down and the usual calculations that we do for simple DC, resistive circuits only apply after the EM fields have propagated around the circuit (at a little under c)
In the case of water flow, there is also a delay due to the finite speed of sound (pressure waves) through the pipes.
Edit 2 When you hear that nasty Water Hammer effect, it's due to the finite time for pressure differences to propagate round your plumbing circuits.

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#### Dale

Mentor
Can anyone explain on how the electrons really move?
I would start here, it is a general overview of electron transport in materials with an application to conduction in carbon nanotubes:

http://nanotube.msu.edu/nt05/abstracts/NT05tutor-Nygard.pdf

However, I must warn you that the movement of individual electrons through resistive materials is complicated. I strongly discourage this as a route to understanding circuits. Personally, I don’t think that electrons should be discussed in a circuits class at all.

On average electrons through resistors behave according to Ohm’s law. For a large structure there are a lot of electrons so the average is all you need. So what you need to know is simply that $V=IR$. All of the details of individual electrons are complicated and unnecessary

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#### rbelli1

Gold Member
In practice short circuits don't have 0 ohms
Except for superconductors a short never has a resistance of 0 ohms.

BoB

#### sophiecentaur

Science Advisor
Gold Member
Personally, I don’t think that electrons should be discussed in a circuits class at all.
+1 But try to tell that to the mediocre Scientists who feel qualified to decide what kids should be taught and who sit on those committees. The occasional rare species of well informed Educationist is either not able to fight the mundane or is just unaware of the actual level of the target audience for Education.

#### anorlunda

Mentor
I agree with @Dale. It would be wonderful if an inspired educator developed smarter textbooks and curricula for studying electricity. I would even like to see an elementary circuits course that taught first using only power and energy, and introducing voltage and current as an additional degree of freedom at a second stage. But I should really sit down and write it rather than just advocate it.

But the OP @Kevin J , if you insist on a visual analogy, consider the flow of water through an island archipelago. Water follows the path of least resistance, yet in the islands, some water flows via every possible path.

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#### sophiecentaur

Science Advisor
Gold Member
Water flows according to the path of least resistance
Your use of English here makes this statement misleading. It flows according to the inverse of resistance. Using the word "least" implies the selection of just one path.The thread has already established that this is not the case.
Edit: Sorry to be picky but people can easily grab the wrong message about electrical matters.

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#### anorlunda

Mentor
Your use of English here makes this statement misleading.
You're absolutely right. I edited it to say "water follows the path of least resistance." While mathematically imprecise, that is the common language phrase most often used.

#### Kevin J

First of all please neglect wire's resistance(assume it is a superconducting wire), second neglect the batteries internal resistance.
My question is in a short circuit where one path has resistance and the other does not, we all assume that the whole current flows through the 0 resistance path, what I don't understand is how the electrons even know which one has resistance and which one doesn't?

#### Bystander

Science Advisor
Homework Helper
Gold Member
Your use of English here makes this statement misleading. It flows according to the inverse of resistance. Using the word "least" implies the selection of just one path.The thread has already established that this is not the case.
Edit: Sorry to be picky but people can easily grab the wrong message about electrical matters.

#### Drakkith

Staff Emeritus
Science Advisor
2018 Award
First of all please neglect wire's resistance(assume it is a superconducting wire), second neglect the batteries internal resistance.
My question is in a short circuit where one path has resistance and the other does not, we all assume that the whole current flows through the 0 resistance path, what I don't understand is how the electrons even know which one has resistance and which one doesn't?
How do the links in a chain know when the ends are connected and pulled on? The information, if we choose to call it that, is transmitted from link to link through the EM force. Similarly, everything that happens in a circuit happens because of the EM force and what happens in one part of the circuit, or what properties that part may have, affects the rest of the circuit because charged particles are self-interacting through the EM force. In essence, they 'transmit' the 'information' through the circuit. I don't mean that they are beaming ones and zeroes to each other with little antennas, I only mean that there is a propagation of cause and effect via the EM force and the charge carriers.

#### Dale

Mentor
what I don't understand is how the electrons even know which one has resistance and which one doesn't?
Did you read the material I posted earlier about resistance at the electron level? I think electrons are not helpful for understanding circuits, but if you insist on learning about how electrons actually behave in resistors then that is the sort of thing you have to learn.

I recommend that you stop asking about electrons until you get to a class on quantum electrodynamics. Everything you learn about electrons before such a class is probably a lie. And it is completely unnecessary, just use Ohm’s law.

#### Mister T

Science Advisor
Gold Member
First of all please neglect wire's resistance(assume it is a superconducting wire), second neglect the batteries internal resistance.
Okay.

My question is in a short circuit where one path has resistance and the other does not, we all assume that the whole current flows through the 0 resistance path,
So, like if you shorted out the battery with both a superconducting wire and a regular wire at the same time? I don't believe such a scenario is possible. With that superconducting path between the terminals of a real battery, the battery voltage would have to drop. I can't describe how an ideal battery would behave in this situation because my understanding of ideal battery behavior is rather like my understanding of ideal gas behavior. I know there's no such thing as an ideal gas, but I recognize that real gases can under some circumstances come close to exhibiting this ideal gas behavior. Likewise, I realize that under some circumstances real batteries can come close to exhibiting ideal battery behavior, even though there is no such thing as an ideal battery.

So in my mind your question looks like this. Is it possible to short a battery with a superconductor and have the battery exhibit ideal battery behavior? The answer is no.

what I don't understand is how the electrons even know which one has resistance and which one doesn't?
When the battery is first connected an electric field travels through the conducting paths at nearly the speed of light. The electrons respond to the field. They don't "know" anything. Humans taking measurements on a circuit might make the mistake of thinking the electrons use the same process as they do to determine the resistance of a path, but they don't.

#### sophiecentaur

Science Advisor
Gold Member
I don't mean that they are beaming ones and zeroes to each other with little antennas,
Haha. It's a strictly Analogue Radio Link but there's very little difference - except for the spectrum of the analogue.
PS Amazing that we now take it for granted that 'Information' is assumed to be Digital.

#### tech99

Gold Member
My view is that at switch-on, guided EM waves travel away from the switch in both directions, the waves being 180 degrees out of phase. The ratio of B and E depends on the characteristic impedance of the wire. When a wave reaches a resistor, it is reflected or attenuated depending on the resistance. A set of standing waves then exist on the system until losses cause the initial high frequency energy to be dissipated. Things then settle down to the steady state, or plumbing, explanation.

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