An aluminum wire having a cross-sectional area equal to 3.00 10-6 m2 carries a current of 7.00 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.

Vd = 2.42 * 10⁻⁴ m/s

Explanation:

Given: A = 3.00*10⁻⁶ m², I = 7.00 A, ρ = 2.70 g/cm³

To find Drift Velocity Vd=?

Sol

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 = (7A) / (6.02 * 10 ²⁸ * 1.6 * 10⁻¹⁹ C * 3.00*10⁻⁶ m²)

Vd = 2.42 * 10⁻⁴ m/s