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

• nmsurobert
In summary: It’s a little disconcerting.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.
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!

nmsurobert said:
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.

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

nmsurobert
nmsurobert said:
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
Cutter Ketch said:
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.

Cutter Ketch said:
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!

kuruman said:
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.

nmsurobert said:
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.

## 1. What are Kirchhoff's Rules?

Kirchhoff's Rules, also known as Kirchhoff's Circuit Laws, are fundamental principles in circuit analysis that allow us to determine the currents and voltages in a circuit. These rules are based on the principles of conservation of charge and energy.

## 2. What is the first rule of Kirchhoff's Rules?

The first rule, also known as Kirchhoff's Current Law (KCL), states that the sum of currents flowing into a node in a circuit must be equal to the sum of currents flowing out of that node. In other words, the total current entering a node must be equal to the total current leaving that node.

## 3. What is the second rule of Kirchhoff's Rules?

The second rule, also known as Kirchhoff's Voltage Law (KVL), states that the sum of voltage drops around a closed loop in a circuit must be equal to the sum of voltage rises. In other words, the total voltage dropped across all the components in a closed loop must be equal to the total voltage supplied by the battery or source.

## 4. How do Kirchhoff's Rules help in analyzing circuits with batteries and resistors?

Kirchhoff's Rules provide a systematic method for analyzing complex circuits with multiple batteries and resistors. By applying KCL and KVL, we can determine the currents and voltages in each component, which helps us understand the behavior of the circuit and troubleshoot any issues.

## 5. Are there any limitations to Kirchhoff's Rules?

While Kirchhoff's Rules are very useful for analyzing circuits, they have some limitations. These rules assume ideal conditions, such as perfect conductors and no magnetic fields, which may not always hold true in real-world circuits. Additionally, these rules do not account for capacitance and inductance, so they cannot be used to analyze circuits with these components.

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