Homework Help: AC nodal anaylsis to find V thevenin

1. Apr 25, 2015

Swagbinger

1. The problem statement, all variables and given/known data
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.

2. Relevant 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.

3. 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.

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Last edited: Apr 25, 2015
2. Apr 25, 2015

Hesch

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

3. Apr 25, 2015

Swagbinger

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

4. Apr 25, 2015

Staff: Mentor

What happened to VL?

5. Apr 25, 2015

Swagbinger

Sorry, a typo, the second Vth should be VL

6. Apr 25, 2015

Hesch

According to arrow and signs, it's wrong.