A cylindrical wire is twisted with an angle $\mathrm{\theta }$, what is torsion produced in it?

Analogical to a spring that is elongated, the couple of a rod that is twisted is proportional to the angle by which it is twisted.

$\mathrm{\tau }\propto \mathrm{\theta }\Rightarrow \mathrm{\tau }=\mathrm{C\theta }$