What Is the Maximum Power on an Impedance Z?

[crom1]

Homework Statement

Find the maximum power on a impedance Z.

Homework Equations

The Attempt at a Solution

I got as Thevenin impedance Zt=4+j4 and Ut= 32 V, but since my solution for power is wrong, something is wrong with either impedance or voltage (or both).
If point A is above Z, and point B is under Z, looking from A to B I get for impedance:
First j4 , then since I have current source in of the branches, I ignore impedances in that branch and get j4+(j4-j4+4) and since there is voltage source I ignore 2-j12.
For Thevenin voltage, I tried with superposition, and if potential of B=0, I get that for A:
$$ \varphi_A= 16 \angle 0 + 4 \angle 0 \cdot 4 + 4 \angle 0 \cdot j4 + 4 \angle 0 \cdot (-j4)=32 $$

 

[gneill]

Your Thevenin values look okay. How did you calculate the maximum power?

 

[crom1]

I=Ut/(Z+Zt)=2-j2 , P=I^2 Z = 32-32i = 32 sqrt(2) , And the solution says 64.

 

[gneill]

What value did you give to the load impedance Z?

 

[crom1]

Z=Zt=4+j4

 

[gneill]

Z=Zt=4+j4

Check the maximum power theorem for complex impedance. I think you'll find that the imaginary part of the load should nullify the source impedance's imaginary component.

 

[crom1]

You're right. I now get P=64-j64, do I now just take real part to get P=64?

 

[gneill]

You're right. I now get P=64-j64, do I now just take real part to get P=64?

Yup.