A thick wire is stretched so that its length becomes two times. Assuming that there is no change in its density then what is the ratio of change in resistance of wire to the initial resistance of wire?

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3 : 1

1 : 4

2 : 1

4 : 1

answer is C.

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Detailed Solution

In stretching $R \propto l^{2} \Rightarrow \frac{R_{2}}{R_{1}} = \frac{l_{2}^{2}}{l_{1}^{2}} \Rightarrow \frac{R_{2}}{R_{1}} = {(\frac{2}{1})}^{2}$

$\begin{array}{l} \Rightarrow R_{2} = 4 R_{1} . Change in resistance = R_{2} - R_{1} = 3 R_{1} \\ Now, \frac{Change in resistance}{Original resistance} = \frac{3 R_{1}}{R_{1}} = \frac{3}{1} \end{array}$

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