Mesh Analysis Method for Finding Current in a Circuit with Dependent Source

[Zack K]

Homework Statement

Find the current in each resistor. (refer to uploaded diagram)

Homework Equations

$Kirchhoff's Law: I_s=I_1 + I_2$
Mesh analysis method

The Attempt at a Solution

I'm calling $I_s$ the total current before and after the current splitting up, and $I_1$ and $I_2$ are the mesh currents. Though I'm not sure if that's how it works.
Anyways, my setup:
I'll call the upper loop mesh 1 and the lower loop mesh 2
We have on dependent source, which is at $R_3$, so I'll label the current there $I_x$
$$mesh 1: -V_s+I_1R_1+I_1R_2+R_3(I_1-I_2)=0$$
$$mesh 2: -V_s+I_2R_4+R_3(I_2-I_1)+I_2R_5=0$$
$$Dependent Source: I_x=I_1-I_2$$
$$Kirchhoff's Law: I_s=I_1+I_2$$

I'm not entirely sure from here on. I could substitute each of these equations, but I don't see how it would let me solve for one variable, it would seem just as messy.

 

[scottdave]

For starters, can you label the resistors (in the diagram) R₁ R₂ etc. to assist following your equations?
Then can you put in an actual symbol for this dependent source. Is that Vs ? If so, how are Vs and Ix related? I don't follow how you get that I1 and I2 add to get Ix. Are I1 and I2 the loop currents?

 

[Zack K]

For starters, can you label the resistors (in the diagram) R1 R2 etc. to assist following your equations?

Sorry about that, I made a lot of clumsy mistakes. I uploaded a proper picture now.

Then can you put in an actual symbol for this dependent source. Is that Vs ? If so, how are Vs and Ix related?

I defined Vs now as the potential from A to B.

I don't follow how you get that I1 and I2 add to get Ix. Are I1 and I2 the loop currents?

Again, my bad. I modified it so $I_x=I_1-I_2$, so it would be the sum of the currents.

If I made any other errors, then it would be form my misunderstanding of the problem/method. I just learned this form a wikipedia page since my professor gave us a very shaky lecture on it.

 

[scottdave]

So the way you have defined it, the Vs ia not in either of the loops that you drew. Also look at the junction where Is and I1 meet. What is the current in R2 ?

 

[Zack K]

So the way you have defined it, the Vs ia not in either of the loops that you drew. Also look at the junction where Is and I1 meet. What is the current in R2 ?

I have no clue how I would get that. Circuits in parallel would have different currents, and that's what I'm trying to find using the mesh method.

 

[scottdave]

Maybe it will help you if you draw a voltage source and hook it up to A and B to visualize what is going on in the circuit, and how you need to set up the equations. I still don't see where the dependent source is.