# Finding the thevenin equivalent using Vo and Io

• Evales
In summary, 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.
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

#### Attachments

• Working Out.pdf
202.5 KB · Views: 326
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

Last edited:
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

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.

Last edited:
Is this correct?
i3=3i=-3io

I wouldn't think so, 3i is the value given to a dependant 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.

Evales said:
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

Jony130, I came up with the same results using

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

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.

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

Jony130 said:
But it is impossible to use superposition when we have dependant 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.

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.

## 1. What is thevenin equivalent circuit?

Thevenin equivalent circuit is a simplified circuit that represents a complex network of resistors, voltage sources, and current sources. It is used to analyze the behavior of a circuit and determine the voltage and current at any point in the network.

## 2. How do you find the thevenin equivalent using Vo and Io?

To find the thevenin equivalent, you need to follow these steps:1. Disconnect all the voltage and current sources from the original circuit.2. Calculate the open-circuit voltage (Vo) across the terminals where the load resistor was connected.3. Calculate the short-circuit current (Io) by connecting a short circuit between the two terminals.4. Use the calculated Vo and Io to determine the thevenin equivalent voltage (Vth) and the thevenin equivalent resistance (Rth).

## 3. What is the purpose of finding the thevenin equivalent?

Thevenin equivalent is used to simplify complex circuits and make them easier to analyze. It can also be used to determine the maximum power transfer from a circuit to a load, and to find the voltage and current at any point in the circuit.

## 4. Can thevenin equivalent be used for non-linear circuits?

No, thevenin equivalent can only be used for linear circuits which follow Ohm's Law. Non-linear circuits, such as those containing diodes and transistors, cannot be simplified using thevenin equivalent.

## 5. What are the limitations of using thevenin equivalent?

Thevenin equivalent can only be used for DC circuits, not AC circuits. It also assumes that the behavior of the circuit does not change with different loads. Additionally, it can only be used for networks that can be reduced to a single voltage source and a single resistor.

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