A wire made of aluminium having resistivity ρ = 2.8 × 10 - 8 Ω - m with a circular cross-section and has a radius of 2 × 10 - 3 m . A current of 5 A flows through the wire. If the voltage difference between the ends is 1 V , the length of the wire in m is

Question

A wire made of aluminium having resistivity ρ = 2.8 × 10 - 8 Ω - m with a circular cross-section and has a radius of 2 × 10 - 3 m . A current of 5 A flows through the wire. If the voltage difference between the ends is 1 V , the length of the wire in m is, 50, 60, 90, 120

MARKS App · Accepted Answer

Given, resistivity ρ = 2.8 × 10 - 8 Ω - m , Radius r = 2 × 10 - 3 m , Current I = 5 A Voltage difference V = 1 V ∵ Resistivity ρ = R A l ∴ 2.8 × 10 - 8 = R π 2 × 10 - 3 2 l ⇒ l = R π × 4 × 10 - 6 2.8 × 10 - 8 ⇒ l = V I 4 π × 10 - 6 2.8 × 10 - 8 (from ohm's law , V = I R ) l = 1 5 × 4 π × 10 - 6 2.8 × 10 - 8 = 0.897 × 10 2 = 89.7 m ≈ 90 m

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