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Which of the following is correct regarding resistance?
I. A wire of resistance $R$ is elongated $n$ -fold to make a new uniform wire. The new resistance of new wire is $n^{2} R$
II. The radius of a cylindrical wire is doubled by keeping the volume constant, the ratio of initial to final resistance is 16
III. If a wire is stretched to make it 2% longer, its resistance will increase by 4%.

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I, II, III

I, II

II, III

I, III

answer is D.

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Detailed Solution

While changing length/area of wire, its volume remains same.

I. $R = \frac{ρ l}{A}, R' = ρ \frac{n l}{A / n} = n^{2} R$

II. $R = \frac{ρ l}{π r^{2}}, R' = ρ \frac{l / 4}{π {(2 r)}^{2}} \Rightarrow \frac{R}{R'} = \frac{1}{16}$

III. $R = \frac{ρ l}{A}, R' = \frac{ρ l (1 + \frac{2}{100})}{A (1 + \frac{2}{100})}$

$(\frac{R'}{R} - 1) = \frac{4}{100} i . e 4 %$

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