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If a wire is stretched to make it 0.1% longer, its resistance will

Option 1)
$increase\: by \: 0.05$

Option 2)
$increase\: by \: 0.2$

Option 3)
$decrease\: by \: 0.2$

Option 4)
$decrease\: by \: 0.05$

Answers (2)

best_answer

As we have learned

Ratio of resistances -

If length is given

$R$ $\alpha$ $l^{2}$

- wherein

$\frac{R_{1}}{R_{2}}=\left (\frac{l_{1}}{l_{2}} \right )^{2}$

$lA = constant \\A = \frac{K}{l}$

$R = \frac{\rho l}{A } = \rho \frac{l }{K/l }= \frac{\rho }{K }l^2$

$l= l_0 + (0.001 l)\\R' = \frac{\rho }{K}l_0^2 [ 1+0.001]^2 = R_0 [1+0.002]$

R increases by 0.2 %

Option 1)

$increase\: by \: 0.05$

Option 2)

$increase\: by \: 0.2$

Option 3)

$decrease\: by \: 0.2$

Option 4)

$decrease\: by \: 0.05$

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