The length of a given cylindrical wire is increased to double of its original length. The percentage increase in the resistance of the wire will be _____ %

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TestHub · Accepted Answer

As volume is constant, so, length doubled and area reduces to half.

Resistance of a wire is given by $R = \frac{ρl}{A}$ , where, $ρ$ is resistivity of a material.

Here, $R_{1} = \frac{ρl}{A}$ and $R_{2} = \frac{ρ ( 2 l )}{\frac{A}{2}} = 4 R$

So percentage increase in the resistance will be $= \frac{4 R - R}{R} \times 100% = 300%$

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