Help! Different results from different analysis methods!

Hello!

This is an exercise which my Electrotecnics I course teacher gave me weeks ago:



Find the current in the branches of the circuit and the tension in its elements with:

a) Kirchhoff's circuit laws (Current and Voltage Law) -- from what I read on the internet I think this method is called the Branch Current method.
b) Mesh current method
c) Nodal voltage analysis

So basically, we must find the current and voltage each time with a different method, and the results should be the same every time.
I solved the circuit with all the 3 methods, I checked the arithmetic and the logic and started the calculations from scratch dozens of times, and still the results aren't the same. For every method I use, I get a completely different set of results which aren't even close with each other. I tried a QUCS simulation of the circuit and the values don't correspond with either of the results of the 3 methods.

Please help me! I don't know what I'm doing wrong!

Thanks in advance!

Elton.

Obviously, you are doing all the methods wrong!

Post your work as we can see where you are doing bad.

This is solved with the first method, only with Kirchoff's laws.
As you can see, none of the currents is equal or close to the QUCS simulation.
I shall upload the Mesh Current analysis of this circuit as soon as possible.

Here are the Mesh Current analysis and the Nodal Voltage analysis.
In the Nodal Voltage analysis, the results are the same as those of the QUCS simulation but the currents don't correspond to those of the Mesh Current analysis or Kirchoff's laws method.
This time I noticed that Kirchoff's laws analysis results matched those of Mesh Current analysis, but both don't match Nodal Voltage analysis results, which in turn matches to those of QUCS. Such a mess!!!

Not that it will make much of a difference, but on your last page where you a trying to check your results from nodal analysis with the mesh analysis results you wrote,

\(\frac{V_{2} - V_{4}}{5}\)

but did,

\(\frac{V_{2} - V_{3}}{5}\)

jegues said:

Not that it will make much of a difference, but on your last page where you a trying to check your results from nodal analysis with the mesh analysis results you wrote,

\(\frac{V_{2} - V_{4}}{5}\)

but did,

\(\frac{V_{2} - V_{3}}{5}\)

Click to expand...

Thanks but do you have any idea what I am doing wrong that my results aren't the same?

I got an idea: please look at the first page of a) Kirchoff's laws.
Could it be that when we write the KVL equations we don't take into account the direction of the current to a resistor?
So the equation -8 + I1 + 5*I2 + 15 + 3*I5 + 4*I4 = 0 is wrong and has to be -8 + I1 + 5*I2 + 15 + 3*I5 - 4*I4 = 0 ?

How should I fix this in the second method?

So in the Mesh Current Analysis the supermesh equation should be: -8 + I1 + 5*I2 + 15 + 3*(I2-I4) - 4*(I3-I1) = 0 ?

I tried to solve the matrices with these changes and they correspond to each other and the QUCS simulation.
So the problem in the first method would be that I added a (-) in front of the I4 thinking that the direction of the I4 current should be read as negative and in the second method the polarity of the 4 Ohm resistor was chosen from the I3 current perspective not from I1 and so the voltage drop would be -4*(I3-I1) (reading in the direction chosen in the supermesh), or else if we wanted to write 4*(I1-I3) we should reverse the polarity of the 4 Ohm resistor.

Is it safe to say this thread is solved?