Kirchoff Rule Sign Conventions, Need Clarity.

[Dgray101]

Hey all, I am just doing Kirchoffs rules right now. So we have a couple sign conventions we were taught. I just need to make sure my reasoning makes sense for the 3 and 4 rule.

1. When we travel through a source of emf from + --> - we get a - voltage.
2. When we travel through a source of emf from - ---> + we get a + voltage
3 When we travel through a resistor in the same direction as the assumed current we get a -RI because current goes in the same direction as decreasing potential.
4. When we travel through a resistor in the opposite direction as the assumed current, we get a +RI.

So for 3, because we are going in the direction of the assumed current, current always flows from the high potential to the low potential, just as when we consider a positive point charge the potential gradient weakens as we move further away. So the RI term is - which indicates the potential difference at that location is decreasing.

for 4, because we are going opposite the direction of current, we are moving further away from a lower potential difference and closer to a higher potential difference. Like transversing a Potential gradient from infinity to the source, it gets stronger and stronger and the potential is higher.

I really need to make sure my use of potential difference and potential is not convoluted because I tend to misuse the terms.

 

[Redbelly98]

I have re-ordered your post somewhat, on grounds that it's important to address your last statement first.

I really need to make sure my use of potential difference and potential is not convoluted because I tend to misuse the terms.

And then there is potential gradient as well.

Potential is analogous to elevation, and we can talk about the potential at a specific location. There is the complication that we can add an arbitrary constant to the potential, as long as we add the same constant at all locations. Imagine asking for the elevation at the top of a building: do you mean relative to the ground just outside the building, or relative to sea level? You'll come up with different values for the elevation depending on which reference point is used. So there has to be an implied or understood reference point if you are going to give a numerical value to the potential or elevation at some specific location.

Potential difference (P.D.) means we are comparing the potentials at two locations. It would be nonsensical to talk about the P.D. at a single location -- unless there is some implied or understood reference point that the potential at the location in question is being compared to, in which case we are really talking about the P.D. between the location of interest and the location of the reference point.

(For P.D., that arbitrary-constant-issue we have with potential is no longer an issue, because any constant value added to two locations will cancel when we do the subtraction to calculate the P.D. between those locations.)

Potential gradient is simply the rate of change or slope of the potential, and we can talk about the potential gradient at a single location. (It's equal in magnitude to the electric field, which points toward lower potential.)

So for 3, because we are going in the direction of the assumed current, current always flows from the high potential to the low potential,...

Yes, correct (for resistors anyway).

. . . just as when we consider a positive point charge the potential gradient weakens as we move further away. So the RI term is - which indicates the potential difference at that location is decreasing.

It's more a matter of how the potential itself, not the gradient, is changing. In a typical resistor, the potential gradient is pretty constant -- i.e., the potential itself has a pretty constant slope -- and current is from higher potential "down the slope" to a lower potential.

for 4, because we are going opposite the direction of current, we are moving further away from a lower potential difference and closer to a higher potential difference. Like transversing a Potential gradient from infinity to the source, it gets stronger and stronger and the potential is higher.

Actually, it is that we are moving from a lower potential to a higher potential. As I mentioned before, the actual potential gradient (i.e. the slope of the potential) is pretty constant within the resistor material.

Hope that helps.