Question

A copper wire of 1-m length and 1-mm radius has a resistance of 5.5 × 10 − 3 [Ω] and carries a current of 4 [A]. The number of free electrons per unit volume in copper is 8.43 × 10 28 [m − 3 ]. Find (a) the current density, (b) the conductivity of the copper, (c) the power dissipated in the wire, (d) the (average) drift velocity of free electrons, and (e) the mobility of free electrons.

Answer 1

Answer: a)1.27 *10^6 A/m^2; b) 57.9*10^6 Ω*m; c) 94.16*10^-6 m/s;

d) 4.29*10^-3 m^2/V*s

Explanation: In order to explain this problem we have to take into account the following expressions:

The current density is equal:

J=I/A  where A is the area of the wire.

J=4A/(π*1*10^-6m^2)=1.27 *10^6 A/m^2

The resistence of the wire is given by:

R=L/(σ*A) where σ and L are the conductivity and the length of the wire, respectively.

Then we have:

σ= L/(R*A)=1/(5.5*10^-3*π*1*10^-6)=57.9 *10^6 Ω*m

The drift velocity of free electrons is given by:

Vd=i/(n*A*e) where n is the numer of electrons per volume. e is the electron charge.

then we have:

Vd=J/(n*e)= 1.27 *10^6/(8.43*10^28*1.6*10^-19)=94.16 *10^-6 m/s

Finally, the mobility of free electrons is equal to:

μ=Vd/E  ;  E=J/σ

μ=E*σ/J= 94.16*10^-6*57.9 *10^6/1.27 *10^6=4.29*10^-3 m^2/V*s