Solving for multiple unkowns using KVL and KCL equations

[fredro]

Homework Statement

I am asked to solve for v_X, P_{DEV BY} i_S1, P _{ABS BY} v_S3 (please see attached figure). We have only covered KCL, KVL, Ohm's law and Power in class. No Thevinen theorem, so it can't be used to help solve.

The Attempt at a Solution

I know that current will not pass through the 4 Ohm resistor or v_S4. My initial hunch was to solve for i_Q in terms of v_S1 (upper left of figure) and then use that equation to help solve for a KVL with the 3 and 7 ohm resistors and v_S3. The result was not pretty and very wrong.

 

[gneill]

Yeah, it's going to get messy. There are a lot of interrelationships to account for with all the controlled sources. However, to make a start, choose a ground node, label the other important nodes, and see what you can do about writing equations for their voltages in terms of the given information. Here's a suggestion:

The voltage at node D (which is the same as -v_Q) will be important. You can write a KCL equation for that node.

 

[fredro]

Here's what I have so far. Unfortunately, I keep running into nonsensical, trivial answers where my systems keep having coefficients of zero. I've spent several hours on this problem.

 

[gneill]

Watch out for the polarities of things. The diagram shows v_Q to be the negative of the voltage at your KCL1 node (note the +/- sign locations).

Suppose you take the voltage at node D to be v_D. Then [itex] v_Q = -v_D[/itex]. Can you write expressions for the node voltages at A and B (with respect to the ground node that I indicated) in terms of this v_D ? (You may need to keep v_x as a variable for now).

 

[fredro]

Here's what I have so far. Unfortunately, I keep running into nonsensical, trivial answers where my systems keep having coefficients of zero. I've spent several hours on this problem.