Solving for I2 in a Circuit: What Am I Doing Wrong?

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In summary, the conversation is about solving a circuit for three currents (I1, I2, I3). The person is using loop equations and a junction at B to solve for I2. There is a discrepancy between the measured I2 value and the calculated one. After some discussion, it is determined that the nodes A and C are incorrect and need to be corrected in order to solve for the unknown currents.
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radji
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Homework Statement


I am attempting to solve the circuit for three currents (I1, I2, I3). I am starting with I1 in terms of I2, then using a third equation to solve for I2 in terms of E and R. I wrote my loops at the bottom of the page. I am using Loop 1 @ B, Loop 2 @ B, and Junction at B to solve for I2.
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Homework Equations


ΣIin=ΣIout
∫dv=0

The Attempt at a Solution


Page 2 has all my algebra to solve for I2 first. I reversed the sign of Loop 3 at B, but I don't think that is what is throwing off my answer. I have a measured I2 value to compare against and my answer is nowhere near it. Not sure what I am doing wrong.
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  • #2
The first issue is that A is not a junction. Also the system looks over determined. There are only two loops so you only need two currents.
 
  • #3
Thank you for your reply. This is a lab experiment so I have to follow (i.e. use) the circuit diagram I am given. You are absolutely right, I need only the two loops and one junction at B to solve for the 3 currents. I am more looking to see if my loop equations are setup correctly. Then I can move on to what I did wrong in my calculations.
 
  • #4
Okay, in that case the nodes A and C are incorrect.
 
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  • #5
Thank you for your observation. I was able to correct the nodes and solve for each unknown current. Even found out how to solve using only one node!
 

FAQ: Solving for I2 in a Circuit: What Am I Doing Wrong?

What is EMF?

EMF stands for electromotive force, and it refers to the energy per unit charge that is provided by a power source, such as a battery or generator. It is measured in volts (V) and represents the potential difference between two points in a circuit.

What are Kirchhoff's rules?

Kirchhoff's rules are two laws that govern the behavior of currents and voltages in an electrical circuit. The first rule, known as Kirchhoff's current law, states that the sum of all currents entering a node in a circuit must equal the sum of all currents leaving that node. The second rule, known as Kirchhoff's voltage law, states that the sum of all voltage drops around a closed loop in a circuit must equal the sum of all voltage rises.

Why are Kirchhoff's rules important?

Kirchhoff's rules are important because they allow us to analyze and solve complex electrical circuits. By applying these rules, we can determine the unknown currents and voltages in a circuit, and predict how a circuit will behave under different conditions. These rules are essential for designing and troubleshooting electrical circuits.

How do Kirchhoff's rules relate to conservation of energy?

Kirchhoff's rules are based on the principle of conservation of energy. The first rule, which states that the sum of all currents entering and leaving a node must be equal, is a direct result of the conservation of charge. The second rule, which states that the sum of all voltage drops and rises in a loop must be equal, is a consequence of the conservation of energy, as voltage can be thought of as energy per unit charge.

Are Kirchhoff's rules always accurate?

Yes, Kirchhoff's rules are always accurate as long as the assumptions of a simple electrical circuit are met. These assumptions include the absence of magnetic fields, constant temperature, and linear elements (such as resistors) in the circuit. In real-world situations, these assumptions may not hold, but Kirchhoff's rules are still a useful approximation in most cases.

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