Engineering Solving unkown impedance in circuit

[x86]

Homework Statement

Homework Equations

V=IZ

The Attempt at a Solution

So my plan is as follows:
Find the current through the 1 ohm resistor, multiplying this by the combined impedance of the capacitor & 1 ohm resistor. Now I know the voltage across the unkown impedance Z. Subtract this voltage from the 12 V source, now I know the voltage through the 9 ohm resistor. Use KCL to find the current through Z, and use V=IZ to find the unknown impedance.

Current through 1 ohm resistor: 4(45d)
Voltage through 1 ohm resistor & capacitor: 4(45d)(1-j1)=5.66(0d)
Voltage through 9 ohm resistor: 12(0d)-5.66(0d) = 6.34(0d)
Current through 9 ohm resistor: 6.34(0d)/9 = 0.7044(0d)

By KCL:
-Ic + Iz + Io = 0
Iz = Ic - Io = 0.7044(0d) - 4(45d) = 3.54(53d)

V/Iz = 5.66(0d)/3.54(53d) = 1.6(-53d) = 0.963-1.278j

But this is wrong, and I've been trying to figure this out for a good hour now, but keep getting the same answer. So I conclude that there's something wrong with my approach.

 

[gneill]

I think you want to check your KCL. There is one current flowing into the node and two flowing out. Which is which?

 

[x86]

I think you want to check your KCL. There is one current flowing into the node and two flowing out. Which is which?

Yes. My sign convention is (-) for in, (+) for out. Iz is the current across Z, Io is the current through the resistor/capacitor, Ic is the current through the 9 ohm resistor.

 

[gneill]

The angle of your Iz looks suspicious. What was your rectangular version?

 

[x86]

The angle of your Iz looks suspicious. What was your rectangular version?

0.7044 - 2sqrt(2) - 2sqrt(2)j
-2.124-2.823j
3.537(53d)

 

[gneill]

0.7044 - 2sqrt(2) - 2sqrt(2)j
-2.124-2.823j
3.537(53d)

Yeah, both terms are negative. In what quadrant should the resulting angle lie?

 

[x86]

Yeah, both terms are negative. In what quadrant should the resulting angle lie?

The quadrant where x<0 and y<0, so this means that the answer is 3.537(-53d)

Even so, this doesn't change the real answer, it is still 0.963

But the complex part is correct. Perhaps I'll redo this problem tomorrow when I'm more awake. I really need to focus on the little things more!

Thanks

 

[gneill]

The quadrant where x<0 and y<0, so this means that the answer is 3.537(-53d)

-53° is in the 4th quadrant where x > 0...

 

[x86]

-53° is in the 4th quadrant where x > 0...

Yes you are right. Sorry about that, I was up very late last night and havent' slept well lately.