Question

A $9\Omega$ resistance is cut into three equal parts and connected in parallel. Find the equivalent resistance of the combination.

Answer 1

When the wire is cut into three equal parts the length of each part will be $\frac{1}{3}$

And resistance is directly proportional to the length.

$\therefore$ the resistance of each parts will be

$R=\frac{9}{3}=3\Omega$

Now we have three resistor each of $3\Omega$ connected parallel,

$\frac{1}{R_{eq}}=\frac{1}{3}+\frac{1}{3}+\frac{1}{3}$

$\frac{1}{R_{eq}}=\frac{1+1+1}{3}=\frac{3}{3}=1$

$\Rightarrow R_{eq}=1\Omega$

Hence the equivalent resistance of the combination is $1\Omega$