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

JEE Main · 2023 · 25 Jan 2023 · Shift 1 · Current Electricity

A uniform metallic wire carries a current 2 A. when 3.4 V battery is connected across it. The mass of uniform metallic wire is

8.92 \times 1 0^{- 3} kg

. density is

8.92 \times 1 0^{3} kg / m^{3}

and resistivity is

1.7 \times 1 0^{- 8} Ω

-m. The length of wire is :

Answer: (B)

The resistance is

R = \frac{V}{I} = \frac{3.4}{2} = 1.7 Ω

. The wire's volume is

V = \frac{m}{ρ _{mass}} = \frac{8.92 \times 1 0 ^{- 3}}{8.92 \times 1 0 ^{3}} = 1 0^{- 6} m^{3}

, and since

V = A L

the cross-section is

A = \frac{1 0 ^{- 6}}{L}

. Putting this in

R = \frac{ρ L}{A} = \frac{ρ L ^{2}}{V}

gives

L^{2} = \frac{R V}{ρ} = \frac{1.7 \times 1 0 ^{- 6}}{1.7 \times 1 0 ^{- 8}} = 100

. The length of the wire is

L = 10 m

JEE Main · 2023 · 25 Jan 2023 · Shift 1 · Single correct option