Circuit reduction/Thevenin's equvalent resistance question.

In summary, the conversation discussed finding the Thevenin equivalent of a circuit and the difficulties faced when trying to reduce the circuit to just the Zth value. The suggested approach was to use resistance series and parallel equations, as well as converting from a star to delta configuration. Ultimately, the final resistance (impedance) for Zth was determined to be 2Z/3.
  • #1
braceman
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0

Homework Statement



I have a question to find the thevenin equivalent of a circuit (attached). I have found the Vout but am struggling when trying to reduce the circuit to just the Zth value. All the examples I have don't show an impedance between the terminals and I can't find any examples to try and follow through on how to reduce it. it doesn't help that I've got one book saying look at the circuit from the terminals side, and another saying work FROM the other side (where the Vin was and is now short-circuited) towards the terminals. This configuration is proving problematic for me.

Homework Equations



Resistance series and parallel equations.

Re = R1+R2 etc...Re = R1R2/R1+R2

The Attempt at a Solution



I want to work this one out myself and don't want the answer (no point in blagging it if I can't do it again in the future!) but need some pointers.
Can anyone talk me through how to reduce a circuit like this or point me to a webby with some good examples. I've seen a suggestion to use the left hand side in a 'star' config and convert it to a 'delta', but my books haven't covered these so I'm guessing there's another normal way to do it. I'm betting it's just staring me in the face, but I haven't done this type of thing for a good few years. Any pointers would be greatly appreciated!
 

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  • #2
Can you post your circuit diagram as a gif or jpg? My (ancient, creaking) software can't sort out the format of your .docx.doc attachment, and I'm always leery of opening an unknown file with an application that has enough smarts to read/write my hard disk and run macros...
 
  • #3
is this pic any good for you?
 

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  • #4
braceman said:
is this pic any good for you?
Much better, thanks. I'll take a look...

...Looks like the top rail and bottom rail are connected by the wire on the far left. That makes the top and bottom a single node, and you can move the connections all to one rail (the equivalent of "folding" the circuit along the central line). Does that help you out?
 
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  • #5
hopefully this is close...If it is, then next step would be to reduce the 2 parallel resistor pairs.

Then add the left and top middle resistors to make a single resistor, which would then sit in parallel with the final right resistor,,,and this would give us the final resistance (impedance) for Zth??
 

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  • #6
braceman said:
hopefully this is close...


If it is, then next step would be to reduce the 2 parallel resistor pairs.

Then add the left and top middle resistors to make a single resistor, which would then sit in parallel with the final right resistor,,,and this would give us the final resistance (impedance) for Zth??

Sounds like an excellent plan :smile:
 
  • #7
R1R2/R1+R2 = (2 x 10/7)/2+10/7 = 5/6
 

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  • #8
R1+r2 = 5/6 + 5/2 = 10/3
 

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  • #9
R1R2/R1+R2 = (10Z/3 x 5Z/6) / (10Z/3 + 5Z/6) = 2Z/3

Therefore Zth - 2Z/3 (hopefully!)
 
  • #10
braceman said:
R1R2/R1+R2 = (10Z/3 x 5Z/6) / (10Z/3 + 5Z/6) = 2Z/3

Therefore Zth - 2Z/3 (hopefully!)

Yup. Looks good.
 
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FAQ: Circuit reduction/Thevenin's equvalent resistance question.

What is circuit reduction and why is it important?

Circuit reduction, also known as Thevenin's equivalent resistance, is a method used to simplify complex electrical circuits into a single equivalent circuit. This is important because it allows for easier analysis and understanding of the circuit's behavior.

2. How is Thevenin's equivalent resistance calculated?

Thevenin's equivalent resistance is calculated by first finding the open-circuit voltage and short-circuit current of the original circuit. Then, the equivalent resistance is equal to the open-circuit voltage divided by the short-circuit current.

3. What are the benefits of using Thevenin's equivalent resistance?

Thevenin's equivalent resistance allows for easier analysis of complex circuits, as well as the ability to predict the behavior of the circuit under different load conditions. It also allows for easier troubleshooting and designing of circuits.

4. Can Thevenin's equivalent resistance be used for all types of circuits?

Thevenin's equivalent resistance can only be used for linear circuits, which means that the relationship between current and voltage remains constant. Non-linear circuits, such as those containing diodes or transistors, cannot be reduced using this method.

5. What are some real-world applications of Thevenin's equivalent resistance?

Thevenin's equivalent resistance is commonly used in the design and analysis of electronic circuits, such as in computers, mobile phones, and other electronic devices. It is also used in power systems to model the behavior of electrical grids and in telecommunications to analyze signal transmission.

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