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1 kg piece of copper is drawn into a wire of 1 mm thick, and another piece into a wire 2 mm thick. Compare the resistance of these wires.

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2 : 1

4 : 1

8 : 1

16 : 1

answer is D.

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Detailed Solution

d_{1} = 1 mm = {1×10}^{- 3} m

$d_{2} = 2 mm = {2×10}^{3} m$

$R = ρ . \frac{l}{A}$

$R = \frac{ρ l A}{A^{2}}$

$R = ρ \frac{v}{A^{2}}$

$\Rightarrow R \propto \frac{1}{A^{2}}$

$\Rightarrow \frac{R_{1}}{R_{2}} = \frac{A_{2}^{2}}{A_{1}^{2}} = \frac{r_{2}^{4}}{r_{1}^{4}} = {(\frac{2}{1})}^{4}$

$\Rightarrow \frac{R_{1}}{R_{2}} = \frac{16}{1}$

$\Rightarrow R_{1} : R_{2} = 16 : 1$

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