Finding the thevenin equivalent using Vo and Io

[Evales]

Hey,

I'm trying to find the thevenin equivalent of a particular circuit so that I can calculate the current across an inductor.

I've attached a pdf with the circuit and the working out I've done so far.

When I'm talking about i₀ I'm talking about the Thevenin equivalent current and voltage at the nodes near the 1V power source.

I have done this question over and over (and admittedly I do keep getting different answers).
I know that the correct i₀ is 3A however the closest I've gotten is -5A (the rest have been divisible by 7 or something).

I have a feeling it has something to do with my signs around the circuit, but it'd be a huge help if someone could look over it and let me know where I'm going wrong/ how to get it right lol.

The yellow part is attempt 1 with the orange part being attempt 2.
Anything that is yellow but is circled in orange I've used in attempt 2.

Also the matrix at the bottom is cut off a bit.
It should be: R₂-2*R₁

 

[Jony130]

I have a question, which current control this current control voltage source ?
And which direction this control current must flow to make CCVS voltage positivity.
Also I assume that you need Io to find Rth ?
Rth = Vth/Io

 

[Carl Pugh]

Maybe I'm not getting what the problem is, but isn't

Voltage across 4 ohm resistor 4 ohm X 3 amp = 12 volt
Current through 2 ohm resistor 1 volt/2 ohm = 0.5 amp

 

[Evales]

Apologies, the current controlled voltage source is defined by i which is in the location of i₀, in the opposite direction i = -i₀.
Carl I'm trying to find i₀, would you suggest nodal analysis? I use mesh analysis normally just because I find it easier to understand the sign conventions.

 

[Carl Pugh]

Is this correct?
i3=3i=-3io

 

[Evales]

I wouldn't think so, 3i is the value given to a dependent voltage source.
That is the current i₃ is the current passing through the dependent voltage source which = 3i Volts.

I wouldn't be surprised it my lecturer had put in a voltage source instead of a current source though. If nobody else has any ideas I might just put this down to image error.

It was an example in a lecture and I'm pretty bad at circuit calculation so I wanted to be able to do it and get the same answer.

 

[Jony130]

Apologies, the current controlled voltage source is defined by i which is in the location of i₀, in the opposite direction i = -i₀.

If so, we can write one equation

Io = 1V/2Ω + (1V - (-3*Io)/4Ω

Solving this for Io I get this result

Io = 3A

 

[Carl Pugh]

Jony130, I came up with the same results using

Io+I3=0.5
3Io+4*I3+1=0

 

[psparky]

Using superpostion (open current sources and short voltage sources) You can find currents, voltages and thevinin equivalents...by quick inspection.

Superposition and thevenin are you friend. Embrace them.

 

[Jony130]

But it is impossible to use superposition when we have dependent source in the circuit.

 

[psparky]

But it is impossible to use superposition when we have dependent source in the circuit.

I don't see why not. Nodal analysis will work too I think. KCL...

But super position usually requires no math equations, just simple V=IR stuff.

 

[Evales]

Thanks guys, I thought there was a way for me to thank you, but I'm not able to see it.

This has helped a lot.