Question

A 10 gauge copper wire carries a current of 20 A. Assuming one free electron per copper atom, calculate the magnitude of the drift velocity of the electrons.

Answer 1

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 $v = 0.0002808 \ m/s$

Explanation:

From the question we are told that

    The current on the copper is  $I = 20 \ A$

     The cross-sectional area is  $A = 5.261 \ mm^2 = 5.261 *10^{-6} \ m^2$

The number of copper atom in the wire is  mathematically evaluated

      $n = \frac{\rho * N_a}Z}$

Where $\rho$ is the density of copper with a value $\rho = 8.93 \ g/m^3$

          $N_a$ is the Avogadro's number with a value $N_a = 6.02 *10^{23}\ atom/mol$

         Z  is the molar mass of copper with a value  $Z = 63.55 \ g/mol$

So

     $n = \frac{8.93 * 6.02 *10^{23}}{63.55}$

     $n = 8.46 * 10^{28} \ atoms /m^3$

Given the 1 atom is equivalent to 1 free electron then the number of free electron is  

         $N = 8.46 * 10^{28} \ electrons$

The current through the wire is mathematically represented as

         $I = N * e * v * A$

substituting values

        $20 = 8.46 *10^{28} * (1.60*10^{-19}) * v * 5.261 *10^{-6}$

=>     $v = 0.0002808 \ m/s$