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Q.

The resistance of a wire of radius 2 mm is $2 Ω$ . The resistance of the same wire when its radius becomes 1 mm is

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a

64 Ω

b

16 Ω

c

32 Ω

d

48 Ω

answer is B.

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Detailed Solution

R \propto \frac{1}{r^{4}}

$\frac{R_{2}}{R_{1}} = {(\frac{r_{1}}{r_{2}})}^{4} = {(\frac{2}{1})}^{4} = 16$

$R_{2} = 32 Ω$

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The resistance of a wire of radius 2 mm is 2 Ω . The resistance of the same wire when its radius becomes 1 mm is