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

[Emo_Jesus]

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

Any help is highly appreciated, thank you :)

 

[Gavran]

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?

 

[DaveE]

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.

 

[DaveE]

https://www.khanacademy.org/science...-circuits-with-resistors/a/ee-kirchhoffs-laws

 

[Emo_Jesus]

Thank you both for the Help, i solved it now! :)