Calculating Equivalent Resistance in a Hexagonal Prism Circuit

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Homework Help Overview

The discussion revolves around calculating the equivalent resistance in a circuit formed by a hexagonal prism, where resistances are assigned to various wires connecting the hexagonal faces. Participants are exploring the implications of symmetry and the concept of balanced Wheatstone bridges in this context.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking, Mixed

Approaches and Questions Raised

  • Participants discuss the redundancy of certain wires based on the assumption of balanced Wheatstone bridges, while others challenge this assumption by noting that current can still flow through the circuit. There are mentions of using symmetry and Y-Δ transformations to simplify the analysis. Some participants express uncertainty about their calculations and seek validation from others.

Discussion Status

The discussion is active, with various interpretations of the circuit being explored. Some participants have offered potential methods for analysis, such as nodal analysis and symmetry considerations. However, there is no explicit consensus on the correct equivalent resistance value, and multiple calculations are being presented.

Contextual Notes

Participants note constraints such as imposed homework rules that discourage the use of certain methods like Y-Δ transformations. There is also mention of the need to clarify the connections and potential differences in the circuit to better understand the flow of current.

  • #31
gneill said:
The correct one :smile:
I'm not sure it's the right time yet to give away the answer.

I did the same you did ...

So your answer is 33R/28 ?
 
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  • #32
cupid.callin said:
I did the same you did ...

So your answer is 33R/28 ?

Nope. A bit smaller.
 
  • #33
smaller than 1.7R ?

Here's how i solved ... Bold black lines are the resistances

attachment.php?attachmentid=33586&stc=1&d=1301182953.jpg
 

Attachments

  • HEX2.jpg
    HEX2.jpg
    12.1 KB · Views: 519
  • #34
What happened to the resistances ab, cd, a'b', c'd' ?
 
  • #35
there won't be any current through them right? so we can just remove them. Is that wrong ?:confused:
 
  • #36
cupid.callin said:
there won't be any current through them right? so we can just remove them. Is that wrong ?:confused:

I don't think that you can assume that there will be no current through them.
 
  • #37
gneill said:
Sure. I've only labeled some of the resistances, the rest should be obvious by color code and symmetry.

Did you get 17R/16?
 
  • #38
Abdul Quadeer said:
Did you get 17R/16?

Nope. A bit too small.
 
  • #39
Here's the next step in the simplification. The diagram is still symmetrical, so the Delta-Y transformations at either end will be the same...
 

Attachments

  • HEX3.jpg
    HEX3.jpg
    9.4 KB · Views: 416
  • #40
Yup. That's what I had & did.
 
  • #41
I got it - 23R/20
Thanks!
 
  • #42
Abdul Quadeer said:
I got it - 23R/20
Thanks!

Yes, that's it. Attached is the summary of the simplifications used.
 

Attachments

  • HEX1.jpg
    HEX1.jpg
    23.3 KB · Views: 469

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