Question

A cylindrical wire of radius 1 mm is made of copper metal. Assume that each copper atom in metallic copper has one mobile electron free to move and carry current. If one amp of current is flowing through this wire, a. What is the average drift speed of the electrons? (units m/s). b. How long would it take for an electron to drift through 100 meters of such wire?

Answer 1

(a). The drift velocity is
`2.34*10^(-5)\ m/s`.

(b). The time is
`4.27*10^(6)\ sec`

Step-by-step explanation:

Given that,

Radius = 1 mm

Current = 1 A

Distance = 100 m

(a). We need to calculate the drift speed

Using formula of drift velocity

`v_(d)=(i)/(neA)`

Where, i = Current

n = number density

e = charge on electron

A = area cross section

We know that,

The molar mass of copper is 63.55 g/mol.

The mass density is 8.96 g/cm³.

We need to calculate the number of density

`n=(\rho)/(M)`

Put the value into the formula

`n=(8.96)/(63.55)`

`n=0.141\ mol/cm^3`

`n=(0.141*6.022*10^(23))/(10^(-6))`

`n=8.49*10^(28)\ electron/cm^3`

Put the value into the formula of drift velocity

`v_(d)=(1)/(8.49*10^(28)*1.6*10^(-19)*\pi*(0.001)^2)`

`v_(d)=0.00002343\ m/s`

`v_(d)=2.34*10^(-5)\ m/s`

(b). We need to calculate the time

Using formula of distance

`t=(d)/(v)`

Put the value into the formula

`t=(100)/(2.34*10^(-5))`

`t=4.27*10^(6)\ sec`

Hence, (a). The drift velocity is
`2.34*10^(-5)\ m/s`.

(b). The time is
`4.27*10^(6)\ sec`