Question

A uniform wire of resistance $50\Omega$ is cut into 5 equal parts. These parts are now connected in parallel. The equivalent resistance of the combination is

• A. $2\Omega$
• B. $10\Omega$
• C. $250\Omega$
• D. $6250\Omega$

Answer 1

The correct option is A $2\Omega$

Here, a uniform wire of resistance $50\Omega$ is cut into $5$ equal parts. Hence, resistance of each part is
$r=\frac{R}{n}$

$\Rightarrow r=\frac{50}{5}$

$\Rightarrow r=10\Omega$
Now, the parts are connected in parallel, the equivalent resistance of the combination is
$\frac{1}{R_{eq}}=\frac{1}{10}+\frac{1}{10}+\frac{1}{10}+\frac{1}{10}+\frac{1}{10}$
$\frac{1}{R_{eq}}=\frac{5}{10}=\frac{1}{2}$
$R_{eq}=2\Omega$