# Definition of current?

While doing some questions using Kirchhoff's laws, I came across this problem, as shown in the picture.
Obviously, no current passes through the 5 ohm resistor. But then I get confused.

1) If "no current" passed through the branch, wouldn't that be as if the branch weren't there? that would mean that two 1ohm resistors are connected in series and then parallel to each other.

However, we could also see the circuit as if the two middle nodes were collapsed together, leaving us with a parallel combination of two 1 ohm resistors on the left and two on the right.
This would work, because there is no potential difference across the 5 ohm resistor---but does that mean there isn't any current flow?

2) Take a piece of wire AB (in the picture) for example, there is no potential difference between the two points, but does that mean there is no current flow?

Current flow happens only when there is a difference in potential, but the definition of current is Coloumbs per second which has no reference to potential at all...

So could someone who's good with definitions help me out? Thank you.

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I think what you're missing is ohm's law, that relates current, potential, and resistance: E = I * R
Basically, ohm's law says that if there's no potential, there's no current, period. You are right that this can be solved without kirchoff's laws, though you may want to practice using them anyways.

For your second question, consider rearranging Ohm's law, such that it's now E / R = I. Between A and B, there is no potential, but also no resistance, so you end up with 0 / 0, which is undefined; it tells you nothing. You have to consider the voltage drop across a component, rather than a random piece of wire.

Andrew Mason
Homework Helper
While doing some questions using Kirchhoff's laws, I came across this problem, as shown in the picture.
Obviously, no current passes through the 5 ohm resistor. But then I get confused.

1) If "no current" passed through the branch, wouldn't that be as if the branch weren't there? that would mean that two 1ohm resistors are connected in series and then parallel to each other.
There is no current because there is no voltage. If you are trying to determine the resistance of this configuration you have to pretend there is a voltage applied somewhere and work out the current that flows. I am not sure what you are trying to do.

However, we could also see the circuit as if the two middle nodes were collapsed together, leaving us with a parallel combination of two 1 ohm resistors on the left and two on the right.
This would work, because there is no potential difference across the 5 ohm resistor---but does that mean there isn't any current flow?
Where is the applied voltage?

2) Take a piece of wire AB (in the picture) for example, there is no potential difference between the two points, but does that mean there is no current flow?
If there is current and no potential difference then there is 0 resistance. That is just Ohm's law: R = V/I

Current flow happens only when there is a difference in potential, but the definition of current is Coloumbs per second which has no reference to potential at all...
Current does not strictly require a potential difference. Current consists of moving charges. Once charges start moving if there is no resistance to flow, they keep moving. You can keep a current flowing in a superconductor after you remove the voltage.

AM

There is no current because there is no voltage. If you are trying to determine the resistance of this configuration you have to pretend there is a voltage applied somewhere and work out the current that flows. I am not sure what you are trying to do.

Current does not strictly require a potential difference. Current consists of moving charges. Once charges start moving if there is no resistance to flow, they keep moving. You can keep a current flowing in a superconductor after you remove the voltage.
Well, what I'm trying to do...is actually what i couldn't wrap my head around in my former question "Kirchoff's Loop Rule--Direction of Current?", which you helped me answer for the most part, thank you very much.
however, i still have a slight problem, and I posted it on the other question, hopefully you'll answer if you have time.
the superconductor is an interesting way of thinking of things, that helps me clear up some of the confusion. physics is so abstract for me, and i keep trying to delve into all the miniscule details.