# Homework Help: 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 !