# Mesh analysis of AC circuits using matrices

#### picotrain

Joined Apr 12, 2013
32
I'm practicing various different methods of solving AC circuits, but I'm getting a bit stuck on mesh.
When I calculate using the other methods I get I1 = 6.94<-101.1° and I2 = 9.9 <50.8°.

When I'm doing mesh I'm plugging the equations for the loops into a matrix and using RREF to get the answer, however when I do that I get I1= I2 = 2.0<-113°

I'm wondering if it's my calculator or something I'm doing beforehand?
I've attached my working as an image.

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#### WBahn

Joined Mar 31, 2012
26,398
You have a note claiming that the voltage across the current source is zero.

What is that claim based upon?

Let's assume that it's true. What does that tell you about the current in the inductor? Does that make sense?

#### picotrain

Joined Apr 12, 2013
32
I was following a YouTube video that made that claim and I believed it.

If it were true, then the voltage across the inductor would be zero, which would not be possible with a non-zero AC supply.

So when I do loop I1, what do I do with the current source?

#### WBahn

Joined Mar 31, 2012
26,398
I was following a YouTube video that made that claim and I believed it.

If it were true, then the voltage across the inductor would be zero, which would not be possible with a non-zero AC supply.
It's not IMPOSSIBLE -- just unlikely. I could design an AC circuit such that the voltage across a particular inductor in the circuit turns out to be identically zero, but that would be the result of careful design.

Lots of YouTube stuff is pure crap, but it is also quite possible that you interpreted what was said incorrectly -- probably by overgeneralizing something that applied to the specific instance of the circuit they were analyzing in that particular video. You might go back and see if that was the case.

So when I do loop I1, what do I do with the current source?
Well, in terms of the mesh currents I1 and I2 what is the current in the current supply?

So then what is I1 and/or I2 in terms of the current in the current supply?

#### picotrain

Joined Apr 12, 2013
32
I was originally thinking that I1+I2 = current source, but then I realised that the voltage supply would also be contributing current as well.

#### WBahn

Joined Mar 31, 2012
26,398
I was originally thinking that I1+I2 = current source, but then I realised that the voltage supply would also be contributing current as well.
Does the mesh current I2 go through the current source?

Look at your diagram and how you have defined your two mesh currents.

#### picotrain

Joined Apr 12, 2013
32
Oh, I think I see what you're saying.
I1 is the current source.
Then I2 would be the current from the voltage supply.

#### WBahn

Joined Mar 31, 2012
26,398
Oh, I think I see what you're saying.
I1 is the current source.
Then I2 would be the current from the voltage supply.
Close.

The current from the voltage supply is the current leaving the positive terminal. I2 is the current entering the positive terminal. So I2 is the negative of the current from the voltage supply.

Now, if I1 is the current in the current source, what is the solution for I1?

See how, by inspection, we can solve half of the mesh equations for this problem?