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Resistance of a wire is $2 Ω$ . It is drawn in such a way that it experiences a longitudinal strain of 200%. Its new resistance is

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$18 Ω$

$14 Ω$

$8 Ω$

$4 Ω$

answer is A.

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Detailed Solution

$\frac{∆ l}{l} \times 100 = 200 ∆ l = 2 l$

$∴ l_{2} - l_{1} = 2 l \Rightarrow l_{2} = 3 l$

$l \propto R^{2}, for sreached wire$

$\frac{R_{1}}{R_{2}} = \frac{l_{1}^{2}}{l_{2}^{2}} \frac{l^{2}}{{(3 l)}^{2}}$

$\frac{2}{R_{2}} = \frac{l^{2}}{9 l^{2}} \Rightarrow R_{2} = 18 o h m$

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