Verified Solution • 2025–26 Session moderate

QJEEM23Ph0265: JEE Main 2023 Physics - Class 12 JEEM23Ph0265 Solution: A uniform metallic wire carries a current 2 A, when 3.4 V…

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^{-3} kg, density is 8.92 ×\times 10 3^{3} kg/m 3^3 and resistivity is 1.7 ×\times 10 −8 Ω^{-8}~\Omega - m\mathrm{m} . The length of wire is :

Multiple Choice Options

  • A l=100l=100 m
  • B l=6.8l=6.8 m
  • C l=5l=5 m
  • D l=10l=10 m

Step-by-Step Verified Solution

m=8.92×10−3 kgm=8.92 \times 10^{-3} \mathrm{~kg}

Density =8.92×103 kg/m3=8.92 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}

Volume =8.92×10−38.92×103=(10−6)m3=\frac{8.92 \times 10^{-3}}{8.92 \times 10^{3}}=\left(10^{-6}\right) \mathrm{m}^{3}

Resistance =3.42=1.7Ω=(ρlA)=\frac{3.4}{2}=1.7 \Omega=\left(\frac{\rho l}{A}\right)

1.7=ρl2(Al)1.7=\frac{\rho l^{2}}{(A l)}

⇒1.7=1.7×10−8×l210−6\Rightarrow 1.7=\frac{1.7 \times 10^{-8} \times l^{2}}{10^{-6}}

l2=100l^2=100

l=10 ml=10 \mathrm{~m}

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