Complete Question
A 10 gauge copper wire carries a current of 20 A. Assuming one free electron per copper atom, calculate the drift velocity of the electrons. (The cross-sectional area of a 10-gauge wire is 5.261 mm2.) mm/s
Answer:
The drift velocity is [tex]v = 0.0002808 \ m/s[/tex]
Explanation:
From the question we are told that
The current on the copper is [tex]I = 20 \ A[/tex]
The cross-sectional area is [tex]A = 5.261 \ mm^2 = 5.261 *10^{-6} \ m^2[/tex]
The number of copper atom in the wire is mathematically evaluated
[tex]n = \frac{\rho * N_a}Z}[/tex]
Where [tex]\rho[/tex] is the density of copper with a value [tex]\rho = 8.93 \ g/m^3[/tex]
[tex]N_a[/tex] is the Avogadro's number with a value [tex]N_a = 6.02 *10^{23}\ atom/mol[/tex]
Z is the molar mass of copper with a value [tex]Z = 63.55 \ g/mol[/tex]
So
[tex]n = \frac{8.93 * 6.02 *10^{23}}{63.55}[/tex]
[tex]n = 8.46 * 10^{28} \ atoms /m^3[/tex]
Given the 1 atom is equivalent to 1 free electron then the number of free electron is
[tex]N = 8.46 * 10^{28} \ electrons[/tex]
The current through the wire is mathematically represented as
[tex]I = N * e * v * A[/tex]
substituting values
[tex]20 = 8.46 *10^{28} * (1.60*10^{-19}) * v * 5.261 *10^{-6}[/tex]
=> [tex]v = 0.0002808 \ m/s[/tex]
