Finding the Effective resistance of a tree of resistors

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1. Sep 30, 2014

Ajonsight

1. A) Find the Effective resistance of a tree of resistors that bifurcates 3 times.
B) Find the effective resistance of a tree of infinite resistors. (if the tree below went on to infinity)

2. Relevant equations
Ohm's Law

3. The attempt at a solution
I have no idea how to start this. There was no other info given either.

Last edited by a moderator: Apr 17, 2017
2. Sep 30, 2014

phinds

Surely you can draw the 3-bifurcation one to completion and solve it? At least give it a try.

3. Sep 30, 2014

Ajonsight

is it just resistors in series ?

4. Sep 30, 2014

Staff: Mentor

Let's denote the resistance of that whole tree as T ohms. We don't know what it will be, yet, but at least we have given it a symbol.

Wherever you look, you find sub-trees that are all identical to that parent. So in place of each of those sub-trees going off to infinity you can substitute a single resistor of value T ohms. This simplifies the figure considerably!! !!

5. Sep 30, 2014

Ajonsight

So theres 7 T ohms + R ohms
im just having a hard time seeing if they are in series or parallel

6. Sep 30, 2014

Staff: Mentor

I think you mean 8? These will all be going to ground at their farther end.

See whether you can do it using fewer than 8.

7. Sep 30, 2014

Ajonsight

8. Sep 30, 2014

Ajonsight

and for part b would it just be 1 since theres a infinite number of resistors and bifurcations?

9. Oct 1, 2014

Staff: Mentor

For (a), yes.

10. Oct 1, 2014

Staff: Mentor

You're guessing.

The resistance is going to have to be at least R.

11. Oct 1, 2014

phinds

Good job !

12. Oct 1, 2014

Ajonsight

so the answer to part b is R ohms because it would be infinity over infinity?

13. Oct 1, 2014

phinds

If you want to really get a sense of what's going on, do it for 1 branch, 2 branches, 3 branches (already done), and maybe 4 branches and see if there is a pattern that you could extrapolate to a limit.

14. Oct 1, 2014

Ajonsight

oh ok. so its 2R ohms since is approaching 2R ohms. The next branch added would be 31R/16

15. Oct 1, 2014

phinds

Again, good job !