What is the Equivalent Resistance of Resistors in Series and Parallel?

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Discussion Overview

The discussion revolves around determining the equivalent resistance of a circuit with resistors arranged in series and parallel configurations. Participants explore the application of circuit analysis techniques and the implications of specific resistor arrangements, particularly focusing on a central "diamond" configuration.

Discussion Character

  • Homework-related
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant expresses difficulty in visualizing the series-parallel connections and identifies the top left resistors as being in parallel, while questioning the arrangement of the middle box.
  • Another participant suggests redrawing the circuit for clarity and encourages the first participant to articulate their reasoning regarding the classification of resistors as parallel or series.
  • A third participant questions whether the central "diamond" has zero resistance and raises concerns about its effect on the surrounding resistors.
  • A later reply confirms that the diamond does have zero resistance but refrains from providing a complete explanation, suggesting that the problem is designed to challenge students' understanding of series and parallel resistances.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the implications of the central diamond's resistance or the overall circuit configuration. Multiple viewpoints regarding the arrangement and analysis of the resistors remain present.

Contextual Notes

There are unresolved assumptions regarding the behavior of the circuit when a voltage source is applied and the specific role of the central diamond in the overall resistance calculation.

axleboy57
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Homework Statement



All resistors have the same value, 'R'

Homework Equations



I don't think mesh/loop analysis or nodal analysis is applicable here, I think I'm just having a hard time seeing how the series-parallel connections work.

The Attempt at a Solution



I know the top left two are in parallel and then they come back together, and I know all the corners are in series, it's just the middle box that throws me.
 

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My approach would be to redraw the circuit so it's a bit easier to see what's going on.

You are right that mesh and nodal don't apply- you have no need to find voltages or currents.

Now, lastly, why do you say the top left are in parallel and the rest are in series? Step through that thought process, it might help you. I'm not saying you're wrong, but I'm not saying you're right either- just walk through the process.
 
Welcome to PF!

Hi axleboy57! Welcome to PF! :smile:

I don't normally do electricity questions unless they're really easy :rolleyes: …

can someone tell me whether the centre "diamond" is supposed to have zero resistance, because if it is, why don't the right-hand sides of the "diamond" short-out the four right-hand resistances? :confused:
 


tiny-tim said:
Hi axleboy57! Welcome to PF! :smile:

I don't normally do electricity questions unless they're really easy :rolleyes: …

can someone tell me whether the centre "diamond" is supposed to have zero resistance, because if it is, why don't the right-hand sides of the "diamond" short-out the four right-hand resistances? :confused:

Yes, it has zero resistance (the diamond) but I don't want to say more lest I give away the answer. Think about when a source is applied, where is current going to flow?

This is a very common type of problem for intro courses to electronics. It's basically designed to force the student to think about parallel and series resistances (though, honestly, it's really just meant to confuse more than anything). I can PM you the solution, tiny-tim, so you can see what to do and I can explain what I can't in this thread if you want me to?
 


Fronzbot said:
Yes, it has zero resistance (the diamond) but I don't want to say more lest I give away the answer. Think about when a source is applied, where is current going to flow?

This is a very common type of problem for intro courses to electronics. It's basically designed to force the student to think about parallel and series resistances (though, honestly, it's really just meant to confuse more than anything). I can PM you the solution, tiny-tim, so you can see what to do and I can explain what I can't in this thread if you want me to?

Good hint, TT :wink:
 

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