A uniform metallic wire carries a current 2 A when a 3.4 V battery is connected across it. The mass of the wire is 8.92 × 10⁻³ kg, density is 8.92 × 10³ kg m⁻³ and resistivity is 1.7 × 10⁻⁸ Ω m. The length of wire is:
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Question

A uniform metallic wire carries a current 2 A when a 3.4 V battery is connected across it. The mass of the wire is 8.92 × 10⁻³ kg, density is 8.92 × 10³ kg m⁻³ and resistivity is 1.7 × 10⁻⁸ Ω m. The length of wire is:

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G1 Physics · Accepted Answer

R = V/I = 3.4/2 = 1.7 Ω. Volume = mass/density = 10⁻⁶ m³ = AL. Also R = ρL/A = ρL²/(AL) = ρL²/Volume. Hence L² = R×Volume/ρ = 1.7×10⁻⁶/(1.7×10⁻⁸) = 100, so L = 10 m.