# Analysing a 3-Loop RLC Circuit and Finding State Equations

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1. Jan 28, 2016

### Captain1024

1. The problem statement, all variables and given/known data
Obtain the state equations in Matrix form for the two-input and one-output circuit shown in the figure below where the output is $i_2$.

2. Relevant equations
Ohm's Law, KVL, KCL

3. The attempt at a solution

Currents i1, i2, i3 assumed clockwise. Is there a better assumption I could have made?

Nodes:
a: $i_1=i_2+i_\mathrm{L}$
b: $i_3=i_2+C\frac{\mathrm{d}v_C(t)}{\mathrm{d}t}$

Loops:
l1: $v_1-\mathrm{R}_1i_1-\mathrm{L}\frac{\mathrm{d}i_1(t)}{\mathrm{d}t}=0$
l2: $v_C-\mathrm{???}-\mathrm{R}_2i_2=0$
l3: $v_2-v_C-\mathrm{R}_3i_3=0$

Before I start solving for unknowns, I need a little help writing the loop equations. After that, I'm not sure how to choose my state variables.

-Captain1024

2. Jan 28, 2016

### axmls

Your first loop equation is incorrect. Notice that the current in the branch with the inductor is $i_1 - i_2$, so you would instead have $-L \frac{d}{dt} \left(i_1(t) - i_2(t)\right)$.

3. Jan 29, 2016

### Captain1024

My professor has posted the solution now. This thread may be deleted.

4. Jan 29, 2016

### Staff: Mentor

Threads are not deleted unless there is some extraordinary reason. You may mark it "Solved", however. See the "MARK SOLVED" icon at the top of the thread.

5. Jan 30, 2016

### Captain1024

I don't think marking a thread "solved" is an option anymore. I looked at the top of the thread and didn't find anything. Then, I searched the site for "mark solved" and found a thread from last year that mentioned that feature is gone. Thanks anyway.

-Captain1024

6. Jan 30, 2016

### Staff: Mentor

The feature is back. Go to the top of this page and look to the right of the thread title (all the way to the right of the page). Find the black icon:

Just hit that and it marks the thread "Solved".

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7. Jan 30, 2016

### Captain1024

I logged in with Chrome, FireFox, and IE and I did not see that button next to my thread title. Is it possible this is a moderator only feature?

8. Jan 30, 2016

### Staff: Mentor

No, it's supposed to be available to all.

Leave it with me, I'll report the issue. Thanks for pointing it out.