A piece of wire of resistance 4 $\mathrm{\Omega }$ is bent through 180° at its midpoint and the two halves are twisted together. The new resistance will be :

When the wire is bent from its mid point  Resistance will be half and these resistances will be connected in parallel

$R\to \frac{R}{2}$

$R_{eq}=\frac{{\left({\displaystyle \frac{R}{2}}\right)}^2}{{\displaystyle \frac{R}{2}}+{\displaystyle \frac{R}{2}}}=\frac{R}{4}=\frac{4\Omega }{4}=1\Omega$