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 × 10 -3 kg, density is 8.92 × 10 3 kg/m 3 and resistivity is 1.7 × 10 ⁻⁸ Ω · m. The length of wire is: (a) l = 100 m (b) l = 6.8 m (c) l = 5 m (d) l = 10 m

Answer: (d). R = V/I = 3.4/2 = 1.7 Ω. Volume = m/d = 8.92×10⁻³/8.92×10³ = 10⁻⁶ m³. R = ρ l/A = ρ l²/Vol ⇒ l² = 1.7×10⁻⁶1.7×10⁻⁸ = 100 l = 10 m. The answer is (d).

A uniform metallic wire carries a current 2 A, when 3.4 V battery is… | JEE Main 2023 (25 Jan, Shift 1)

Q18JEE Main 2023 · 25 JAN · SHIFT 1Medium

Ohm's Law, Resistivity & Temperature

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 $-3$ kg, density is 8.92 $\times$ 10 $3$ kg/m $3$ and resistivity is 1.7 $\times$ 10 $^{-8}\ \Omega \cdot \text{m}$ . The length of wire is:

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Answer: (d)

$R = V/I = 3.4/2 = 1.7\ \Omega$ .
Volume $= m/d = 8.92\times10^{-3}/8.92\times10^{3} = 10^{-6}\ \text{m}^3$ .
$R = \rho l/A = \rho l^2/\text{Vol} \Rightarrow l^2 = \dfrac{1.7\times10^{-6}}{1.7\times10^{-8}} = 100$
$l = 10$ m. The answer is (d).

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