Answer to Question #188367 in Electric Circuits for FREDERICK

Question

You have a wire with a cross-sectional area of 0.10 mm2. If there are 4.0 × 1028 atoms per cubic meter in this wire, and if each atom contributes 2 free electrons, what is the drift velocity of the electrons when the current in the wire is 6.0 A?

Answer 1

to find the drift velocity(due to which electric current is produced in the conductor) of electron

$I$ $=$ $neAV$_d

where $I=$ electric current $=6A$

$n=$ no. of free electrons per $m$³= charge density = $2 \times 4 \times 10$²⁸  electrons per unit volume

Because each atom contribute 2 free electrons and there are $4 \times 10$²⁸  no. of atoms )

$e=$ charge of electron $= 1.6 \times 10$^-19

$A=$ area of cross section $=0.1 mm$²$= 0.1 \times 10$^-6 m²

$V$_d $=$ drift velocity of electrons

Now put all values in the given above formula

$V$_d = $I/neA = 6/$ $(8 \times 10$²⁸$\times 1.6 \times 10$ ^-19$\times0.1 \times 10$^-6$)$

$V$_d$= 4.7 \times 10$^-3 $m/sec$

so so drift velocity of electron in given conductor is

$= 4.7 \times 10$^-3 $m/sec$