Symmetry in a Triangular Circuit

[bananabandana]

Homework Statement

Find the resistance across AB. Use symmetry to determine currents.

Homework Equations

Please see diagram.

The Attempt at a Solution

I really don't seem to understand symmetry in circuits. What is the link between the geometrical symmetry of the situation and the way in which the current divides at a junction? Is it the case that if a current can follow two possible paths, and the paths have the same resistances in the same order, that the current along each path is equal??

In the diagram below for example, why is I6 supposed to be zero? How do I know that points D and A are at the same potential? I've tried expanding everything using Kirchoff's laws, but it just becomes very messy...

Thanks!

 

[Kishlay]

do you know a term something called as "weigh stone bridge" ??

 

[bananabandana]

Um, I think you mean 'Wheatstone bridge'. Yes, I do know that the example I've got is a balanced Wheatstone bridge, but I'd still like to better understand how symmetry works in circuits in general.

 

[Kishlay]

Um, I think you mean 'Wheatstone bridge'. Yes, I do know that the example I've got is a balanced Wheatstone bridge, but I'd still like to better understand how symmetry works in circuits in general.

at here if
R₁/R₂=R₃/R₄
then there will be no current through the R₆ i.e I₆=0

 

[bananabandana]

Yes, but why? How does the symmetry of the problem relate to this understanding? :P

 

[Kishlay]

all the subs scripts represents the resistance of your question i.e
R₁ is the resistance from where I_{1 current will flow and so on...}

 

[bananabandana]

Yes, I understand that! What I don't understand is why it is necessary, that, in this example, a balanced Wheatstone bridge must have no current flowing through the middle wire.. if that's not a stupid question :P

 

[berkeman]

If a bridge is balanced, then the 2 outside voltage dividers give equal voltages at each end of the middle resistor.