Find the effective resistance between point `A and B` of a hexagonal circuit

Answer

`0.5 r`

Explanation

By symmetry `C and D` are at the same potential hence no current flow in arm `CD` similarly no current flow in arm `DE` may be ignored.The equivalent circuit is

The equivalent resistance of Arm `GH = r + r = 2r`. The equivalent resistance of arm `I J = (1)/(2) + (r )/(2) = r`
The equivalent resistance of arm`FK`
`= r + r = 2r`
These there arm `GH,IJ and PK` are in parallel.
Therefore, `(1)/(R_(p)) = (1)/(2r) + (1)/(r ) + (1)/(2r) = (2)/(r)`
or `R_(p) = r//2 = 0.5 r`