Electronics > Beginners
Resistance across a 1k resistor cube.
<< < (8/9) > >>
rs20:

--- Quote from: Kirr on April 23, 2018, 11:32:20 am ---
--- Quote from: The Electrician on April 23, 2018, 10:45:26 am ---For extra credit, using these designators and values for the cube resistors, calculate the exact resistance between nodes A and G, showing the result as an improper fraction.  >:D
--- End quote ---
When ready, click to verify your answer, or to give up :)

--- End quote ---

Very nice! If I understand correctly, your solver is public domain, but closed source, right? I'd be curious to try adapting it to give closed-form formulae (i.e., the calls you currently make to GMP, make them to a symbolic algebra library instead, using variables instead of fixed rational numbers.) Would be interesting to see if it landed on the same solution as Maple after expansion.
gamalot:
 :)

Zero999:

--- Quote from: IanB on April 22, 2018, 12:59:04 am ---I would say 833.3 Ω ?

Edit: I could even say 833⅓ Ω now that the forum has been upgraded  :)

--- End quote ---
I prefer to use superscript and subscript for fractions, because I find it easier to read. 8331/3Ω.
Kirr:

--- Quote from: rs20 on April 23, 2018, 11:46:21 am ---
--- Quote from: Kirr on April 23, 2018, 11:32:20 am ---
--- Quote from: The Electrician on April 23, 2018, 10:45:26 am ---For extra credit, using these designators and values for the cube resistors, calculate the exact resistance between nodes A and G, showing the result as an improper fraction.  >:D
--- End quote ---
When ready, click to verify your answer, or to give up :)

--- End quote ---
Very nice! If I understand correctly, your solver is public domain, but closed source, right? I'd be curious to try adapting it to give closed-form formulae (i.e., the calls you currently make to GMP, make them to a symbolic algebra library instead, using variables instead of fixed rational numbers.) Would be interesting to see if it landed on the same solution as Maple after expansion.

--- End quote ---
Also nice work on the formula!

Correct about public domain and closed source. I'll probably clean it up enough for opening some day. However I'm also curious about adding symbolic solution to the solver. My only worry is that it can quickly grow out of control and turn out enormous in the end. Would be interesting to see memory requirement and speed on larger networks. Perhaps we could collaborate on this.

I guess the final expanded formula is unique for each network, so should be identical (other than order of terms in each sum).
The Electrician:

--- Quote from: rs20 on April 23, 2018, 11:38:12 am ---
--- Quote from: The Electrician on April 23, 2018, 10:45:26 am ---For extra credit, using these designators and values for the cube resistors, calculate the exact resistance between nodes A and G, showing the result as an improper fraction.  >:D

--- End quote ---

I already provided the arbitrary resistance closed-form formula back in message #18. Subbing in the values you wrote, the answer is: 6195184/1328873 Ohms.



--- End quote ---

In reply #18 you seemed not absolutely certain that your formula was perfectly correct:

"total resistance = (A*U*G*F*C*V + K*B*A*E*C*F + ...) / (U*A*B*E*V + K*C*G*V*F + ...)

Which is at least dimensionally consistent!"

and:

"Finally, setting all the resistances to 1000 gives an answer of 833.33..., which is reassuring :)"

I thought I'd give you another dataset to test.  :)
Navigation
Message Index
Next page
Previous page
There was an error while thanking
Thanking...

Go to full version
Powered by SMFPacks Advanced Attachments Uploader Mod