Find the equivalent resistance of the circuit between A and B

Answer

`1 Omega`

Explanation

If a cell is connected between point A and B then by symmetry same current will flow through `AC and AD` . So the potential drop across `AC` is equl to potential drop across `AD` so resistance in arm `CD` is ineffective. Therefore, the given circuit will be reduced in the equivalent circuit. If a `R` is the equivalent resistance `A and B` then

`(1)/(R ) = (1)/((2+ 2)) + (1)/((2 + 2)) + (1)/(2) = 1`
or `R =(1)/(1) = 1 Omega`