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`

Step-by-step 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 = (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`