# Equivalent Resistance between 2 points

Actually , I'm having trouble in solving for the net resistance of the below network of resistors.

Can anyone help me finding the equivalent resistance between points a & b.

My answer is $2/3r$ .

I've done it by first solving for the two resistances in the middle , Then coverting the circuit into a Wheatstone Bridge.

PS- SORRY for the bad diagram

My answer is r. 2 resistances on the vertical line are redundant as no current flows via that route due to the symmetry of the problem.

Consider this circuit joined to the source with A joined to the positive terminal, then current will equally split along two possible routes from A. Due to symmetry of the problem, the electric potential energy above the vertical line is same as the point below it. So no current flows via that part of the circuit. So that section of wire can be removed, yet giving same equivalent resistance. In our simplified circuit, 2 resistors of resistance 2r are in parallel giving equivalent resistance r.

• can you give a better explanation – Amritanshu Jul 6 '16 at 20:44

This is a case of wheatstone bridge. The points M and N are at same potential so no current will pass through MN and it can be removed.