The number density of free electrons in a copper conductor estimated is `8.5 xx 10^(28) m^(-3)`. How long does an electron take to drift from one end of a wire 3.0 m long to its other end ? The area of cross-section of the wire is 2.0` xx 10^(-6) m^(2)` and it is carrying current of 3.0 A.

Explanation

If free electrons drift through length l of a given wire in time t then their drift speed is,
`v_(d) = (l)/(l)`
Now, current passing through given wire is,
`I = Av_(d) ` ne
`therefore I = A ((l)/(l)) ` ne
`therefore t = ("Alen")/(I)`
`therefore t = (2 xx 10^(-6) xx 3 xx 8.5 xx 10^(28) xx 1.6 xx 10^(-19))/(3)`
`therefore t = 27200 s `
Note : If above time is asked in h, min and s then :
`therefore t = (27200)/(3600) ` h
`therefore t = 7.556 `h
` therefore t = 7 h + (0.556 xx 60) ` min
` = 7 h 33.36 ` min
7h 33 min + `(0.36 xx 60)` s
`therefore t = 7 h 33 ` min 22 s