A uniform wire of resistance $100\Omega$  is cut into three equal parts. These parts are now connected in parallel. Then the equivalent resistance of the combination is _______.

We know that resistance is directly proportional to the length of the resistor. Therefore, if the wire is cut into 3 equal parts, then the resistance of the wire will also get divided equally:

$\begin{array}{r}{\mathrm{R}}_1={\mathrm{R}}_2={\mathrm{R}}_3\end{array}= \frac{100}{3}\mathrm{\Omega }$

When these resistances are connected in parallel, the equivalent resistance can be given by:

$\begin{array}{r}\frac{1}{{\mathrm{R}}_{\mathrm{eq}}}=\frac{1}{{\mathrm{R}}_1}+\frac{1}{{\mathrm{R}}_2}+\frac{1}{{\mathrm{R}}_3}\\ \end{array}$
$\begin{array}{r}\frac{1}{{\mathrm{R}}_{\mathrm{eq}}}=\frac{1}{\frac{100}{3}}+\frac{1}{\frac{100}{3}}+\frac{1}{\frac{100}{3}}\end{array}$
$\frac{1}{{\mathrm{R}}_{\mathrm{eq}}}=\frac{3(1+1+1)}{100}=\frac{9}{100}$
${\mathrm{R}}_{\mathrm{eq}}=\frac{100}{9}\mathrm{\Omega }$