When a wire of resistance 4R is bent in the form of circle, then the resistance of each segment across the diameter becomes 2R as shown in the figure.
Equivalent resistance between A and B: \(\frac 1 {R_{AB}} = \frac 1{R_A} + \frac 1{R_B}\) (in parallel combination)
\(\therefore \frac 1 {R_{AB}} = \frac 1{2R} + \frac 1{2R}\)
\(\frac 1{R_{AB}} = \frac 2 {2R}\)
\(\Rightarrow R_{AB} = R\)
