Hello!
I am having a bit of problem figuring out I given the set up with the zero resistance wire. I know the current moves through the wire with the least resistance, so does that mean the 2 ohm resistor is pretty much non existent? I tried getting Rtotal between an imaginary zero ohm resistor on the top wire in parallel with the 2 ohm resistor but that didn't work too well either. Unless Im mistaken, the current going through the 6 ohm resistor is I=V/R= 12/6= 2 A but im not sure if its counter or clockwise. Thank you for any help!

 

Yes, the 2 ohm resistor is shorted across with the wire so it's electrically invisible.

Conventional current flow is from positive to negative.

 

I know the current moves through the wire with the least resistance...

In this case the "least" resistance is a hypothetical zero, so there is no current or voltage across the shorted resistor.

But realize that any time there is a voltage drop, current moves through all paths, not just the one with lower resistance. Picture 120V across a 1KΩ resistor. Now you add a 10KΩ in parallel. Does it carry current? Of course it does, as predictable by Ohms' law. Do you care, for instance if the 10K resistor is you? You should!

 

A much better saying than, "current follows the path of least resistance" is that it "favors" the path of least resistance. This is what is meant by that saying and most people pick up on that implicitly, but it also causes a lot of misunderstanding for others.

A good exercise for you with this problem would be to show the current (magnitude and direction) in all six branches of the circuit.

 

A much better saying than, "current follows the path of least resistance" is that it "favors" the path of least resistance.

While true, I think this still minimizes a significant safety hazard that comes from people thinking they are somehow safe because some path of least resistance is nearby to protect them. It's the toaster-in-the-bathtub discussion, or this one, all over again. A toaster thrown into the bathtub shouldn't really hurt me, but it might, and I'm not going to rely on "current favors the path of least resistance" to save me.

 

But it's only meant to be a qualitative description of Ohm's Law. People that try to read that kind of conclusion into it generally have much bigger shortcomings to threaten their continued existence.

 

But it's only meant to be a qualitative description of Ohm's Law. People that try to read that kind of conclusion into it generally have much bigger shortcomings to threaten their continued existence.

Hi,

Ha ha, had to laugh at that one

Yeah if someone is that stupid they are in for trouble sooner or later.
What we dont look at here is the way electrical current travels through a thick and wide solid (or liquid) conductor (distance changes things too) and the electric field, but that should not be necessary for the toaster dilemma