Finding the voltage in this AC circuit

[edsoneicc]

Homework Statement

Homework Equations

KVL at that loop

The Attempt at a Solution

I can easily solve all the individual current and voltages in this circuit using Mesh analysis and Gaussian Elimination. But how do I get Vx? I can simply add the voltages of the two 10uF capacitors if they are in series. But they are not in series. I thought maybe if I write a KVL equation on that loop, I can solve for Vx but that equation means simply adding the voltages. I'm confused.

 

[gneill]

The two capacitors you have in mind may not be in series in the sense of the topological definition for series components, but their potentials are certainly in series in the KVL sense. So you can simply sum them as you suggest.

 

[donpacino]

Vs is the voltage differential between that node on the far right and the node below the voltage source.If you can find the individual voltages at each node, you can simply subtract the node voltages. Alternatively, find the voltage drop across the two 10 uF caps at the bottom of the schematic.