The resistance of a wire is $$R.$$ It is bent at the middle by $${180^ \circ }$$ and both the ends are twisted together to make a shorter wire. The resistance of the new wire is

Solution :
Resistance of wire $$\left( R \right) = \rho \frac{l}{A}$$
If wire is bent in the middle then
$$l' = \frac{l}{2},A' = 2A$$
$$\therefore $$ New resistance, $$R' = \rho \frac{{l'}}{{A'}} = \frac{{\rho \frac{l}{A}}}{{2A}}$$
$$ = \frac{{\rho l}}{{4A}} = \frac{R}{4}.$$