AC nodal anaylsis to find V thevenin

[Swagbinger]

Homework Statement

Here is the circuit. I have to solve for V Thevenin

I am having trouble figuring out what I am doing wrong here. I need to solve for Vth and I do, but it does not match with what my TA posted as the solution. [/B]

Homework Equations

The equations I set up are the same as the above. VL is the node voltage on the jΩ inductor and Vth is the voltage on the right.

The Attempt at a Solution

1. -1∠0° + (VL)/j + (Vth)/(-.5j) = 0

2. Vth - VL = .25Ic

3. Ic = Vth/(-.5j)Substitute 3 into equation 2.

4. Vth - VL = .5iVth

Now solve the system of equations for 1. and 5.
1. -1∠0° + (VL)/j + (Vth)/(-.5j) = 0
5. Vth(1-.5i) -Vth = 0

Vth = -0.4-0.8i

VL = -0.8-0.6i

Am I doing this correctly? The solutions my TA posted does not get this answer for Vth. She got Vth = .4 -.8i.

 

[Hesch]

Your TA has forgotten the "-" in front of ".4".

 

[Swagbinger]

Your TA has forgotten the "-" in front of ".4".

He used VL-Vth = .25Ic. That is wrong correct?

 

[gneill]

2. Vth - VL = .25Ic

3. Ic = Vth/(-.5j)Substitute 3 into equation 2.

4. Vth - Vth = .5iVth

What happened to VL?

 

[Swagbinger]

What happened to VL?

Sorry, a typo, the second Vth should be VL

 

[Hesch]

He used VL-Vth = .25Ic. That is wrong correct?

According to arrow and signs, it's wrong.