A uniform metallic wire carries a current 2A, when 3.4 V battery is connected across it. The mass of uniform metallic wire is ${8.92×10}^{- 3} kg$ , density is ${8.92×10}^{3} kg / m^{3}$ and resistivity is $1.7 \times 10^{- 8} Ω - m$ . The length of wire is :

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$l = 10 m$

$l = 5 m$

$l = 6.8 m$

$l = 100 m$

answer is A.

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Detailed Solution

$mass = 8.92 \times 10^{- 3} kg$

$\begin{array}{l} density d = 8.92 \times 10^{3} kg / m^{3} \\ ρ = 1.7 \times 10^{- 8} Ω - m \\ R = \frac{V}{i} = \frac{3.4}{2} = 1.7 Ω \\ R = \frac{ρl}{A} = \frac{{ρl}^{2}}{vol} = \frac{{ρl}^{2} d}{mass} (∵ d = \frac{mass}{vol}) \\ l = \sqrt{\frac{R \times mass}{ρd}} = \sqrt{\frac{1.7 \times 8.92 \times 10^{- 3}}{1.7 \times 10^{- 8} \times 8.92 \times 10^{3}}} = 10 m \end{array}$