Simplifying a resistance circuit

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Discussion Overview

The discussion revolves around finding the Thevenin resistance (Rth) of a specific circuit involving multiple resistors. Participants explore the configuration of the resistors, particularly focusing on how to combine them correctly to determine the total resistance.

Discussion Character

  • Homework-related
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant initially proposes combining two 1-ohm resistors in series, then the 4-ohm and 12-ohm resistors in parallel, leading to a total resistance of 10 ohms, but expresses uncertainty about the configuration of the 1-ohm resistors.
  • Another participant clarifies that the two 1-ohm resistors share the same nodes and are therefore in parallel, not series.
  • A participant acknowledges confusion about the connections and questions how the top resistors are considered parallel, despite being connected to other resistors.
  • It is noted that as long as two components share two nodes, they are parallel-connected, while series connections require exclusive ownership of the nodes.
  • One participant recalculates the resistance of the two 1-ohm resistors in parallel as 0.5 ohms and combines this with the 4-ohm and 12-ohm resistors to arrive at a total resistance of 8.5 ohms.

Areas of Agreement / Disagreement

Participants generally agree on the parallel connection of the 1-ohm resistors, but there is some confusion regarding the overall configuration and calculations, leading to different interpretations of the total resistance.

Contextual Notes

Some assumptions about the circuit configuration and the definitions of series and parallel connections are discussed, but these remain unresolved as participants work through their understanding.

GBA13
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Homework Statement


Hi guys,

I am trying to find the Thevein resistance of a circuit, I'm only stuck on finding Rth. Can you help?

I have included a screen shot.

Homework Equations

The Attempt at a Solution


Well I thought that I could combine the two bottom 1 ohms in series, the 4 and 12 in parallel and then combine the three remaining for a total of 10 ohms. But I am starting to think that the two 1 ohm resistors don't actually share the same to nodes so I am now a bit stuck! Any help would be greatly appreciated.
 

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GBA13 said:

Homework Statement


Hi guys,

I am trying to find the Thevein resistance of a circuit, I'm only stuck on finding Rth. Can you help?

I have included a screen shot.

Homework Equations

The Attempt at a Solution


Well I thought that I could combine the two bottom 1 ohms in series, the 4 and 12 in parallel and then combine the three remaining for a total of 10 ohms. But I am starting to think that the two 1 ohm resistors don't actually share the same to nodes so I am now a bit stuck! Any help would be greatly appreciated.
The two 1 Ohm resistors do indeed share the same nodes; That makes them parallel connected, not serial.
 
Opps.. my mistake! I'm a little bit confused though, I can see that the two 1ohm obviously share the same bottom node, but I'm not really sure how the top ones are the same, I see they are connected by a wire but as the nodes are also connected to other resistors I thought they wouldn't be in parallel..

So then that makes then that means that their combined resistance is 1 ohm. So then the 4 and 12 are is parallel for a resistance of 3 ohms, making the total resistance 9 ohms?

Thanks for the help!
 
GBA13 said:
Opps.. my mistake! I'm a little bit confused though, I can see that the two 1ohm obviously share the same bottom node, but I'm not really sure how the top ones are the same, I see they are connected by a wire but as the nodes are also connected to other resistors I thought they wouldn't be in parallel..
As long as two components share two nodes they are parallel-connected regardless of what other components may also connect to those nodes. It's series connections that are finicky that way -- components that are in series must be the "sole proprietors" of the node that they share.
So then that makes then that means that their combined resistance is 1 ohm. So then the 4 and 12 are is parallel for a resistance of 3 ohms, making the total resistance 9 ohms?
Ah, so close. Two 1 Ohm resistors in parallel is how many Ohms?
 
Oh thanks! makes much more sense!

Once again, Opps! 1/1 + 1/1 = 2 so its 1/2. So the total resistance is 8.5 Ohms! :)
 
GBA13 said:
Oh thanks! makes much more sense!

Once again, Opps! 1/1 + 1/1 = 2 so its 1/2. So the total resistance is 8.5 Ohms! :)
Ta da! Yup. :smile:
 
Yay! Thanks very much, you've been really helpful! :)
 

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