Finding the Effective resistance of a tree of resistors

[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)

Homework Equations

Ohm's Law

The Attempt at a Solution

I have no idea how to start this. There was no other info given either.

 

[phinds]

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

 

[Ajonsight]

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

is it just resistors in series ?

 

[NascentOxygen]

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! !

 

[Ajonsight]

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! !

So there's 7 T ohms + R ohms
im just having a hard time seeing if they are in series or parallel

 

[NascentOxygen]

So there's 7 T ohms + R ohms
im just having a hard time seeing if they are in series or parallel

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.

 

[Ajonsight]

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.

is the answer 15R/8 ohms?

 

[Ajonsight]

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

 

[NascentOxygen]

is the answer 15R/8 ohms?

For (a), yes.

 

[NascentOxygen]

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

You're guessing. ✗[/size][/color]

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

 

[phinds]

is the answer 15R/8 ohms?

Good job !

 

[Ajonsight]

You're guessing. ✗

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

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

 

[phinds]

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

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.

 

[Ajonsight]

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.

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

 

[phinds]

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

Again, good job !