Question

Assume that a gold wire 0.32 mm in diameter carries one mobile electron per atom. The mass density and the molecular weight of gold are 1.89×10⁴ kg/m³ and 197.0 g/mol, respectively. Calculate the drift speed of the electrons in this wire when it carries a current of 2.44 A.
(ans. 3.28×10^-3 m/s)

Answer 1

given,

current, I = 2.44 A

diameter, d = 0.32mm = 0.32*10^-3 m

radius, r = d/2 = 0.16*10^-3 m

area of the wire, A = (pi)*r²​ = 3.14*( 0.16*10^-3 )²​ = 0.080384*10^-6 m²

mass density, m= 1.89*10⁴ kg/m³

molecular weight = 197.0 g/mol = 197 * 10^-3 kg/mol

Avogodro's number, Av = 6.023*10²³​ atoms/mol

no of electrons, n = mass density​ * Avogodro's number​ / molecular weight

n = 1.89*10⁴ ​*6.023*10²³​ ​/197 * 10^-3 ​ = 5.7784*10²⁸ electrons/m³

drift velocity, Vd = I / neA = 2.44 / (5.7784*10²⁸ ​*1.6*10^-19​ * 0.080384*10^-6 ​= 3.283*10^-3 m/sec