# Using Kirchoff's Loop Rule to Determine Currents in a Circuit

• JessicaHelena
In summary, the conversation discusses a problem with determining the current at two resistors, r_2 and R_3, in a circuit using Kirchoff's Rule. The original attempt at solving the problem was incorrect and the correct answer involves grouping like current terms and using the clockwise direction to apply the loop rule.
JessicaHelena

## Homework Equations

Kirchoff's Rule
The sum of all V = 0

## The Attempt at a Solution

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I think I'm having a problem determining the current at r_2 and R_3. I had originally thought the currents at both resistors would be I_3, writing E_2 — r_2 I_3 — R_3 I_3 — I_1 R_1 = 0, but I got it wrong, so I thought that the current at both must've been I_1, getting the answer as screenshotted above, but that is wrong as well...

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JessicaHelena said:
I think I'm having a problem determining the current at r_2 and R_3. I had originally thought the currents at both resistors would be I_3, writing E_2 — r_2 I_3 — R_3 I_3 — I_1 R_1 = 0, but I got it wrong, so I thought that the current at both must've been I_1, getting the answer as screenshotted above, but that is wrong as well...
You are correct that the current through ##r_2## and ##R_3## is ##I_3## ; they are in series and only ##I_3## is in that branch of the circuit. Your answer in the above quote looks okay to me. Are there any special rules regarding the answer formatting that you might have overlooked? For example, do you need to enter a complete equation (with an equals sign), or group like current terms ( writing ##-~(r_2 + R_3)I_3## rather than ##-~r_2 I_3 - R_3 I_3## )?

The problem statement says "Apply the loop rule to loop aefgha". So my guess is they expect you to start at node "a" and go clockwise. So the first term would be +I1R1. The plus sign is optional.

## 1. What is Kirchoff's loop rule?

Kirchoff's loop rule, also known as Kirchoff's voltage law, states that the sum of all voltages in a closed loop must equal zero. This means that in a circuit, the sum of all voltage drops must equal the sum of all voltage sources.

## 2. How do I apply Kirchoff's loop rule?

To apply Kirchoff's loop rule, you must first identify all the loops in a circuit. Then, you can write an equation for each loop by summing up all the voltage drops and equating it to zero. This equation can then be solved to find unknown voltages or currents.

## 3. Why is Kirchoff's loop rule important?

Kirchoff's loop rule is important because it allows us to analyze and solve complex circuits. By applying this rule, we can determine the voltage and current at any point in a circuit, which is crucial for designing and troubleshooting electrical systems.

## 4. Can Kirchoff's loop rule be applied to any circuit?

Yes, Kirchoff's loop rule can be applied to any circuit, as long as it is a closed loop. It is a fundamental law in circuit analysis and is applicable to both DC and AC circuits.

## 5. What happens if Kirchoff's loop rule is violated?

If Kirchoff's loop rule is violated, it means that there is an error in the circuit analysis or that the circuit is not functioning properly. This violation could be due to incorrect calculations, faulty components, or an open circuit. In any case, it is important to review and double-check the analysis to ensure accurate results.

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