The density of mobile electrons in copper metal is 8.4*10^28 m-3. Suppose that i
ID: 2059600 • Letter: T
Question
The density of mobile electrons in copper metal is 8.4*10^28 m-3. Suppose that i = 7.5*10^18 electrons/s are drifting through a copper wire. (This is a typical value for a simple circuit.) The diameter of the wire is 2.6 mm. In this case, about how many minutes would it take for a single electron in the electron sea to drift from one end to the other end of a wire 33 cm long?a) _____ minutes
(A puzzle: if the drift speed is so slow, how can a lamp light up as soon as you turn it on? We'll come back to this in the next chapter.)
Explanation / Answer
density d = 8.4 x 10^28/m^3 i = 7.5 x 10^18 electrons/s diameter D = 2.6 mm = 2.6 x 10^-3 m length L = 33 cm = 0.33 m Then the volume of wire V = pi x (D/2)^2 x L = 3.14 x (2.6 x 10^-3/2)^2 x 0.33 = 1.75 x 10^-6 m^3 the number of electrons to drift is V x d = 1.75x 10^-6 m^3 x 8.4 x 10^28/m^3 = 14.70 x 10^22 every second number of electrons to drift is i = 7.5 x 10^18 electrons/s so the time is 14.70 x 10^22/ 7.5 x 10^18 s = 1.96 x 10^4 s