Find Thevenin equivalent circuit

[leroyjenkens]

Homework Statement

Find Thevenin equivalent circuit as seen across terminals A and B for each circuit.

Homework Equations

$$V=IR$$

The Attempt at a Solution

Those resistors are in parallel because not all of the current going through the top one is going to go through the next one, right?
So I add the resistors to make an equivalent resistance, but I'm not sure what to do after that.

I need to find the open-circuit voltage, but I don't know how to do that mathematically.

And I need to find the short circuit current, which is $$I=\frac{V_T}{R_T}$$.

Is the $$V_T$$ just the voltage source? And is the $$R_T$$ just the equivalent resistance that I found?

Thanks.

 

[rude man]

Homework Statement

Find Thevenin equivalent circuit as seen across terminals A and B for each circuit.

Homework Equations

$$V=IR$$

The Attempt at a Solution

Those resistors are in parallel because not all of the current going through the top one is going to go through the next one, right?
So I add the resistors to make an equivalent resistance, but I'm not sure what to do after that.
Wrong argument.

I need to find the open-circuit voltage, but I don't know how to do that mathematically.
What's the voltage across terminals A and B? That's your open-ckt voltage.

And I need to find the short circuit current, which is $$I=\frac{V_T}{R_T}$$.
If you short those same terminals, what's the current? That's your short-ckt current.Is the $$V_T$$ just the voltage source? And is the $$R_T$$ just the equivalent resistance that I found?
No. The thevenin voltage is the open-ckt voltage and the thevenin series resistance is the open-ckt voltage divided by the short-ckt current.
Thanks.

See above.

 

[leroyjenkens]

What do you mean by wrong argument? That's not the reason they're in parallel? There's a different reason they're in parallel? Or are they not in parallel at all?

The open circuit voltage would be $$V_{Th}=\frac{(2)(100)}{100+100}=1$$ right?

And the short circuit current would just ignore the middle resistor and that would be $$I=\frac{2}{100}=0.04A$$ right?

Ok so $$R_{Th}=\frac{1}{0.04}=25$$

So to answer the question posed, I would make a circuit replacing the $$V_{in}$$ with $$1V$$ and replace the two resistors with a 25 Ohm resistor?

Thanks for the response.

 

[rude man]

What do you mean by wrong argument? That's not the reason they're in parallel? There's a different reason they're in parallel? Or are they not in parallel at all?

The open circuit voltage would be $$V_{Th}=\frac{(2)(100)}{100+100}=1$$ right?
Right. But call it 1V.

And the short circuit current would just ignore the middle resistor and that would be $$I=\frac{2}{100}=0.04A$$ right?
Wrong. 2/100 does not equal 0.04. And, you're not "ignoring the middle resistor", you are shorting out the resistor across the output terminals.

Ok so $$R_{Th}=\frac{1}{0.04}=25$$

So to answer the question posed, I would make a circuit replacing the $$V_{in}$$ with $$1V$$ and replace the two resistors with a 25 Ohm resistor?

Correct your mistake and you're on the right track.

There are two kinds of Thevenin equivalent circuits. One is a voltage source in series with a resistor. The other is a current source in parallel with the same resistor. If you do it right and derive both, you will see that both have the same open-circuit voltage and short-circuit current.


Thanks for the response.

See above.

 

[Nickie]

As a scientist, my response to this content would be to provide guidance on how to solve the problem. First, it is important to understand the concept of Thevenin's theorem, which states that any linear circuit can be replaced by an equivalent circuit consisting of a voltage source in series with a single resistor. This equivalent circuit will have the same voltage-current relationship as the original circuit when viewed from two terminals, in this case terminals A and B.

To find the Thevenin equivalent circuit, follow these steps:

1. Identify the load resistance, which is the resistance between terminals A and B.

2. Remove the load resistance from the circuit and determine the equivalent resistance of the remaining circuit. This can be done by combining resistors in series and/or parallel.

3. To find the open-circuit voltage, reconnect the load resistance and measure the voltage between terminals A and B. This will be the Thevenin voltage (V_T).

4. To find the short-circuit current, replace the voltage source with a short circuit and determine the current flowing through the short circuit. This will be the Thevenin current (I_T).

5. Finally, construct the Thevenin equivalent circuit by placing the Thevenin voltage source in series with the Thevenin resistance (R_T).

In summary, to find the Thevenin equivalent circuit, you need to determine the Thevenin voltage and Thevenin resistance. The Thevenin voltage is the open-circuit voltage across terminals A and B, and the Thevenin resistance is the equivalent resistance of the circuit when the load is removed. I hope this helps in solving the problem.