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Equivalent Circuits

Mohammad Al-Hiyali

Apr 8, 2015
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I am studying Thevenin's Theorem. In one of the slides introducing the theory. The slide states that circuits below are equivalent.
How are the circuits below equivalent?


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(*steve*)

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What is their open circuit voltage and short circuit current of each?
 

(*steve*)

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For the purpose of the question, equivalence is determined by what happens at the output.
 

Kabelsalat

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equivalent-circuits-svg-png.43479


Image you have a load that have a certain resistance (you are to decide it's value).

Then ask yourself this question:
- Will the voltage over the load be the same in both cases?
- Will the current through the load be the same in both cases (?)
- If the terminals is shorted, will there flow the same amount of current in both cases
- If you remove the load and let the termnals open, will there be the same voltage in both cases.

If yes is the answer on all those questions, then the circuits are equivalent.

Normally, the two first questions can be omitted, but by answering those - espechially if you take your time to actually calculate on a couple of examples - that should prove the concept for you.
 

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Harald Kapp

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One circuit will have current flow and the other won't.
That is no help here. If the open circuit voltage and the short circuit current of a linear source are equal, the sources are equivalent. For any linear passive load the voltage across the load (aka output voltage of the source) and the current through the load (aka output current of the source) will be the same.
@(*steve*) 's question to the op is to check whether this is the case here. The answer to this question is also the answer to the op's original question.
 

(*steve*)

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In fact, since this is a linear circuit, showing that the output of both circuits is equal at any two different points is sufficient to show that it is the same at all points.

Short circuit and open circuit are the conventional points to test because they are typically simpler. There's no reason you couldn't use 43Ω and 270kΩ.

In this case the results for open and short can be determined by inspection (i.e. no more than simple math you can do in your head).
 
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