Kirchhoff's Rules for analyzing this circuit with batteries and resistors

[nmsurobert]

Summary:: Choosing the direction of the loop and the current

I am attempting to work out Example 1 in the link provided. https://courses.lumenlearning.com/physics/chapter/21-3-kirchhoffs-rules/

When solving for loop aefgh, I get:
I₁R₁-I₃R₃-I₃r₂-E₂ =0

I chose the current to continue to move clock wise instead of have the current move counter clockwise. I feel that it will be easier to explain with the current and the loops moving in the same direction.

The example is worked out as:
I₁R₁+I₃R₃+I₃r₂-E₂ =0

The author has the loop and the current moving in opposing directions.

With that being said, when solving for I₁, I₂, and I₃ I get very different numbers from what is in the book. My I₂ = 9.9A, I₁ = -7.4A, and I₃ = 0.3A.

Can someone verify that the answers in the book are correct or not? OR verify that I am correct or not?

Thank you!

 

[Cutter Ketch]

The author has the loop and the current moving in opposing directions.

It’s a convention, and everything works if you negate the convention. However, you have to be sure to change everything. In all the diagrams you will ever see all the signs on all the voltages and all the arrows on all the currents are shown with the standard convention. What if you slip up and forget to change one of them? Why not stick with the convention? Positive charge gives positive voltage and positive charge running away from positive voltage toward negative voltage gives positive current and the arrows point in the direction of positive current. Not to mention field lines, labels on terminals of batteries and capacitors, etc. It seems like bucking the convention is only likely to hurt you.

 

[Cutter Ketch]

I have checked their calculations, and the results on the web page appear to be correct.

 

[kuruman]

With that being said, when solving for I1, I2, and I3 I get very different numbers from what is in the book. My I2 = 9.9A, I1 = -7.4A, and I3 = 0.3A.

You can see immediately that these currents cannot be correct. At the nodes the sum of a pair of currents must equal the third. Given your numbers, there is no pairing for which that happens. The values of your currents violate charge conservation.

 

[nmsurobert]

It’s a convention, and everything works if you negate the convention. However, you have to be sure to change everything. In all the diagrams you will ever see all the signs on all the voltages and all the arrows on all the currents are shown with the standard convention. What if you slip up and forget to change one of them? Why not stick with the convention? Positive charge gives positive voltage and positive charge running away from positive voltage toward negative voltage gives positive current and the arrows point in the direction of positive current. Not to mention field lines, labels on terminals of batteries and capacitors, etc. It seems like bucking the convention is only likely to hurt you.

I understand the convention. What is throwing me off is the second loop not moving the same direction as the assumed current. Everything I've found online has the currents moving in the clockwise direction. Of all the examples and videos I've looked at, the current moves in the same direction as the loop.

I have checked their calculations, and the results on the web page appear to be correct.

Ill work it out again. I figured I made a mistake but I wanted to make sure.

Thanks!

 

[nmsurobert]

You can see immediately that these currents cannot be correct. At the nodes the sum of a pair of currents must equal the third. Given your numbers, there is no pairing for which that happens. The values of your currents violate charge conservation.

ahh that makes total sense. that should've raised a few red flags lol.

 

[Cutter Ketch]

I understand the convention. What is throwing me off is the second loop not moving the same direction as the assumed current. Everything I've found online has the currents moving in the clockwise direction. Of all the examples and videos I've looked at, the current moves in the same direction as the loop.

Yep, it’s a little disconcerting. To do the analysis you have to guess a current direction. You draw an arrow and for all the calculations you assume the direction you randomly selected is correct. But don’t you think it’s kinda great that you don’t have to guess right? The calculation itself tells you (by the sign of the current) if you guessed wrong.