Question

A piece of wire of resistance R is cut into five equal parts. When these parts are connected in parallel. Then the equivalent resistance of this combination is R' .The ratio $\frac{R}{R^{\prime }}$ is

Answer 1

Resistance of piece of wire is proportional to its length. A piece of wire has a resistnce $R$. The wire is cut into five equal parts

Resistance of each part is $\frac{R}{5}$

$\frac{1}{R^{\prime }}=\frac{5}{R}+\frac{5}{R}+\frac{5}{R}+\frac{5}{R}+\frac{5}{R}$

$=\frac{5+5+5+5+5}{R}$

$\Rightarrow$ $\frac{1}{R^{\prime }}=\frac{25}{R}$

$\frac{R}{R^{\prime }}=25$