Finding Effective Resistance Across A Hexagon: A Homework Solution

[Asphyx820]

Homework Statement

The diagram represents a regular hexagon. The resistances are r each
Find the effective resistance across points A & B

http://tinypic.com/r/153n39d/7

Homework Equations

The Attempt at a Solution

A resistance less wire passes through one of the diagonals. so can we remove the wire and then solve.
i tried but i didnt get the answer.
do none of the points have same potential

 

[gneill]

What exactly do you mean by "remove the wire"? You can't just erase it because that would create more nodes than the original circuit has (all points connected by unbroken wire conductor belong to same node).

 

[Doc Al]

A resistance less wire passes through one of the diagonals. so can we remove the wire and then solve.
i tried but i didnt get the answer.

Show what you did.

I assume that when you "remove the wire" you mean that points connected by the wire can be joined. Do that and look for combinations of resistors in series or parallel that can be replaced by their equivalent. Step by step you can simplify this arrangement.

 

[lewando]

Try redrawing the circuit after you collapse the horizontal line into a point. [edit: what Doc said ]

 

[Asphyx820]

Ok ! so what do I do?
I can't find any points having same potential. how will i simplify the circuit?

 

[Doc Al]

Ok ! so what do I do?
I can't find any points having same potential. how will i simplify the circuit?

Points connected by a wire have the same potential.

 

[Asphyx820]

Potential is same across the wire. so i get 4 pairs of parallel connections
http://tinypic.com/r/2s9briu/7
How will I solve this?