Calculating Equivalent Resistance in a Hexagonal Prism Circuit

Click For Summary
SUMMARY

The discussion centers on calculating the equivalent resistance between points P and Q in a hexagonal prism circuit, where resistances on the front and back hexagonal faces are R, and those along the edges connecting the hexagons are 2R. Participants explore various methods, including symmetry and nodal analysis, to derive the equivalent resistance, with some suggesting values like 3R/2 and 73/36 R. The consensus indicates that the circuit does not behave like a balanced Wheatstone bridge due to the presence of 2R resistances, which significantly affects current flow and resistance calculations.

PREREQUISITES
  • Understanding of circuit analysis techniques, specifically nodal analysis
  • Familiarity with Wheatstone bridge principles and their applications
  • Knowledge of Y-Δ transformation methods for circuit simplification
  • Basic concepts of symmetry in electrical circuits
NEXT STEPS
  • Study the application of Y-Δ transformations in complex circuits
  • Learn advanced nodal analysis techniques for multi-loop circuits
  • Explore the implications of symmetry in circuit design and analysis
  • Investigate the conditions under which a Wheatstone bridge is considered balanced
USEFUL FOR

Electrical engineering students, circuit designers, and anyone involved in analyzing complex resistive networks will benefit from this discussion.

  • #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 ?
 
Physics news on Phys.org
  • #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: 514
  • #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: 410
  • #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: 464

Similar threads

Current through an inductor as a function of time
  • · Replies 10 ·
Replies
10
Views
969
Find the equivalent resistance of this circuit
  • · Replies 31 ·
2
Replies
31
Views
4K
How can I calculate the equivalent resistance of this circuit?
  • · Replies 9 ·
Replies
9
Views
2K
Calculate equivalent resistance
  • · Replies 5 ·
Replies
5
Views
2K
Equivalent resistance of a circuit
  • · Replies 3 ·
Replies
3
Views
2K
I need to calculate the equivalent resistance
  • · Replies 4 ·
Replies
4
Views
2K
Determining the equivalent resistence of a circuit
  • · Replies 4 ·
Replies
4
Views
2K
Find the equivalent resistance between AB
  • · Replies 15 ·
Replies
15
Views
4K
Measurement technology textbook problems
  • · Replies 1 ·
Replies
1
Views
749
Measurement technology textbook problems
  • · Replies 2 ·
Replies
2
Views
662