Question

A uniform wire of resistance 50 Ω is cut into 5 equal parts. These parts are now connected in parallel. The equivalent resistance of the combination is
(a) 2 Ω
(b) 10 Ω
(c) 250 Ω
(d) 6250 Ω

Answer 1

(a) 2 Ω

Resistance of a wire is directly proportional to its length.
So, when we cut the wire into 5 equal parts, the resistance of each part will be 10 Ω.
On connecting these wires in parallel, the net resistance will be
$$\begin{gathered} \frac{1}{R}=\frac{1}{10}+\frac{1}{10}+\frac{1}{10}+\frac{1}{10}+\frac{1}{10} \\ \Rightarrow R=2\mathrm{\Omega } \end{gathered}$$