A uniform metallic wire carries a current of 2 A, when a 3.4 V battery is connected across it. The mass of the uniform metallic wire is , density is and resistivity is . The length of the wire is [2023]

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Solution

Q.
A uniform metallic wire carries a current of 2 A, when a 3.4 V battery is connected across it. The mass of the uniform metallic wire is $8.92 \times 10^{- 3} kg$ , density is $8.92 \times 10^{3} {kg/m}^{3}$ and resistivity is $1.7 \times 10^{- 8} Ω -m$ . The length of the wire is [2023]

1 $l = 10 m$

2 $l = 100 m$

3 $l = 5 m$

4 $l = 6.8 m$

Ans.
(1)

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

$Density, d = 8.92 \times 10^{3} {kg/m}^{3}$

$ρ = 1.7 \times 10^{- 8} Ω - m$

$R = \frac{V}{i} = \frac{3.4}{2} = 1.7 Ω$

$R = \frac{ρ l}{A} = \frac{ρ l^{2}}{vol} = \frac{ρ l^{2} d}{mass} (∵ d = \frac{mass}{vol})$

$l = \sqrt{\frac{R m}{ρ d}} = \sqrt{\frac{1.7 \times 8.92 \times 10^{- 3}}{1.7 \times 10^{- 8} \times 8.92 \times 10^{3}}} = 10 m$

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