Question

A wire of resistance $R$ is divided in $10$ equal parts. These parts are connected in parallel, the equivalent resistance of such connection will be

• A. $0.01R$
• B. $0.1R$
• C. $10R$
• D. $100R$

Answer 1

The correct option is A $0.01R$

When the wire is divided in $10$ equal parts, then each part will have a resistance

$R^{\prime }=\frac{R}{10}=r$

Let equivalent resistance of given parallel combination be $r_R$, then

$\frac{1}{r_R}=\frac{1}{r}+\frac{1}{r}+\frac{1}{r}+.......10\text{times}$

$\Rightarrow \frac{1}{r_R}=\frac{10}{r}=\frac{10}{\left(\frac{R}{10}\right)}=\frac{100}{R}$

$\therefore r_R=\frac{R}{100}=0.01R$

Hence, option $\left(a\right)$ is right.

Key concept: For $n$ resistors of equal resistance in parallel, equivalent resistance, $R_{eq}=R/n$