Five resistors are connected in the configuration as shown in the figure. Calculate the equivalent resistance between the points a and b.

Explanation

To find the equivalent resistance between the points a and b, we assume that current is entering the junction a, Since all the resistances in the outside loop are the same `(1Omega)`, the current in the branches ac and ad must be equal. So the electric potential at the point c and d is the same hence no current flows into `5Omega` resistance. It implies that the `5Omega` has no role in determining the equivalent resistance and it can be removed. So the circuit is simplified as shown in the figure.

The equivalent resistance of the circuit between a and b is `R_(eq)=1Omega`.