Network Analysis, Kirchhoff's Laws, changing current source to voltage

AI Thread Summary
The discussion focuses on applying Kirchhoff's laws to analyze a circuit with a current source. The original poster is unsure about including the current source in their loop equations and whether to convert it to a voltage source. Key points emphasize the importance of correctly identifying nodes and branches in the circuit, as well as ensuring all linearly independent equations are included. It is clarified that the current source should be included in the loop for Kirchhoff's Voltage Law (KVL) and that careful attention must be paid to definitions and polarities in the equations. Ultimately, the poster successfully resolved their issue with the help of the community.
Emo_Jesus
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Homework Statement
The voltage U1, U2 the current I3 and the resistors R1, R2, R3 are given.
a) Write down the equations needed to calculate U3 using Kirchhoffs Laws and Ohms Laws.
b) calculate U3 using the Network-equations
Relevant Equations
Kirchhoffs 1. and 2. Law, U = R*I
I tried setting up 4 equations using Kirchoffs laws, but the current source is throwing me off, as i dont know wether to include it in the loop, and if it would be smart to transform it into a voltage source.
The equations i have so far are:
I1 + I2 + I3 = I(R3)
I(R3) = I1 + I4
I4 = I2 + I3
U1 = U(R1) + U3

I(R3) being the current through R3, I2 through R2, R1 through R1, and I4 being the one going "right" at the knot under R3

Screenshot_2.png


Any help is highly appreciated, thank you :)
 
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Emo_Jesus said:
The equations i have so far are:
I1 + I2 + I3 = I(R3)
I(R3) = I1 + I4
I4 = I2 + I3
U1 = U(R1) + U3

I(R3) being the current through R3, I2 through R2, R1 through R1, and I4 being the one going "right" at the knot under R3
This is the wrong approach.

Nodes and branches in the circuit must be identified correctly.
What is a node in an electrical circuit? What is a branch in an electrical circuit?

All linearly independent equations written by using the first and the second Kirchhoff’s laws must be included.
How many linearly independent equations can be written by using the first Kirchhoff’s law? How many linearly independent equations can be written by using the second Kirchhoff’s law?
 
Yes, you include it in the loop for KVL, sort of. It doesn't matter what the circuit element is for KVL you are simply defining the voltages across each and adding them up.

So KVL for the right most loop (clockwise) is simply ##(-U_3) + (U_3 - U_2) + (U_2) = 0##.
You can then substitute using the circuit element definitions. For example ##(U_3-U_2)=R_2 I_{R2} ##.
You don't have to substitute anything for ##U_2##, it is a known value or independent variable.
You can't substitute anything for ##U_3## since the current source circuit element doesn't define it's own voltage, that is one of the things you need to solve for.

KCL is similar, of course, but with nodes instead of loops.

Be very careful with your definitions and polarities. You must be consistent in all of the equations.
 
Thank you both for the Help, i solved it now! :)
 
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