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  4. A uniform wire of length l and having resistance R is cut into n equal parts and all parts are connected in parallel, then the equivalent resistance will be :

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Q. A uniform wire of length $l$ and having resistance $R$ is cut into $n$ equal parts and all parts are connected in parallel, then the equivalent resistance will be :

JIPMERJIPMER 2006

Solution:

Resistance of each part $R'=\frac{R}{n}$
When, these parts are connected in parallel.
Then, $\frac{1}{R''}=\frac{1}{R'}+\frac{1}{R'} \ldots n$ time
$=\frac{n}{R'}$
$\therefore R''=\frac{R'}{n}=\frac{R}{n^{2}}$