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15 October, 18:53

An aluminum wire having a cross-sectional area equal to 3.90 10-6 m2 carries a current of 6.00 A. The density of aluminum is 2.70 g/cm3. Assume each aluminum atom supplies one conduction electron per atom. Find the drift speed of the electrons in the wire.

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  1. 15 October, 19:20
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    Vd = 1.597 * 10⁻⁴ m/s

    Explanation:

    Given: A = 3.90*10⁻⁶ m², I = 6.00 A, ρ = 2.70 g/cm³

    To find:

    Drift Velocity Vd=?

    Solution:

    the formula is Vd = I/nqA (n is the number of charge per unit volume)

    n = No. of electron in a mole (Avogadro's No.) / Volume

    Volume = Molar mass / density (molar mass of Al = 27 g)

    V = 27 g / 2.70 g/cm³ = 10 cm³ = 1 * 10 ⁻⁵ m³

    n = (6.02 * 10 ²³) / (1 * 10 ⁻⁵ m³)

    n = 6.02 * 10 ²⁸

    Now

    Vd = (6A) / (6.02 * 10 ²⁸ * 1.6 * 10⁻¹⁹ C * 3.9*10⁻⁶ m²)

    Vd = 1.597 * 10⁻⁴ m/s
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