If wire is bent in the middle then

\(l'=\frac{1}{2}, A^{\prime}=2\, A\)

\(\therefore \) \(\text { New resistance, } \mathrm{R}^{\prime} =\rho \frac{l^{\prime}}{\mathrm{A}^{\prime}} \)

\(=\frac{\rho \frac{l}{2}}{2\, A}=\frac{\rho l}{4\, A}=\frac{R}{4}\)