Question

A piece of wire of resistance $R$ is cut into n equal parts. These parts are then connected in parallel. If the equivalent resistance of the parallel combination is $R^{\prime }$ , then $\left(\frac{R}{R^{\prime }}\right)$ is

• A. $\frac{1}{1}$
• B. $\frac{n}{1}$
• C. $\frac{n^2}{1}$
• D. $\frac{1}{n}$

Answer 1

Answer: (C)

Resistance, $R=\frac{\rho l}{A}$
If $r$ be the resistance of one cut part, then
$r=\frac{\rho (l/n)}{A}=\frac{R}{n}$
The resistance $R^{{}^{\prime }}$ of the parallel combination is given by
$\frac{1}{R^{{}^{\prime }}}=\frac{1}{r}+\frac{1}{r}+\dots =\frac{n}{r}$
So, $R^{{}^{\prime }}=\frac{r}{n}=\frac{R/n}{n}=\frac{R}{n^2}$
Hence, $\frac{R}{R^{{}^{\prime }}}=\frac{n^2}{1}$