Q111 / 160 · JIPMER 2006 · Physics

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 :

  • A
    $R$
  • B
    $R / n$
  • Correct answer
    C
    $R / n^2$
  • D
    $n^2 R$

Solution

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

Hence, the correct answer is option: 'C'.

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