Question

In how many equal parts a wire having resistance of $100\Omega$ be cut, so that we may obtain resistance of $1\Omega$ by connecting them in parallel?

• A. 10
• B. 15
• C. 20
• D. 100

Answer 1

The correct option is A 10

Let us suppose we divide the resistance of $R_o=100\Omega$ into n equal resistance.

Resistance of each section is $R=\frac{R_o}{n}$ since $R\propto L$

Now when these resistors are connected in parallel, equivalent resistance is

$R_{eq}=\frac{R}{n}$

$⟹R_{eq}=\frac{R_o}{n^2}$

$⟹1=\frac{100}{n^2}$

$⟹n^2=100$

$⟹n=10$

Answer-(A)