Question

Current is flowing with a current density $J=480amp/c{m}^2$ in a copper wire. Assuming that each copper atom contribution one free electron and gives that Avogadro number$=6.0\times {10}^{23}atoms/mole$ Density of copper $=9.0g/c{m}^3$ .Atomic weight of copper $=64g/mole$ Electronic charge $=1.6\times {10}^{-19}$ coulomb. The drift velocity of electrons is:

• A. $1mm/s$
• B. $2mm/s$
• C. $0.5mm/s$
• D. $0.36mm/s$

Answer 1

The correct option is D $0.36mm/s$

Given that,

Current density $J=480amp/c{m}^2$

Avogadro number $N=6.0\times {10}^{23}atoms/mole$

Density of copper $\rho =9.0g/c{m}^3$
Atomic weight of copper $m=64g/mole$

Electronic charge $e=1.6\times {10}^{-19}coulomb$

We know that

Current density $J=\frac{I}{A}$

Now, the drift velocity is

$v_d=\frac{J}{ne}....\left(I\right)$

We know that,

$n=N_A\times \frac{1}{m}\times \rho$

Now, put the value of n in equation (I)

$v_d=\frac{Jm}{N_{A}e\rho }$

$v_d=\frac{480\times 64}{6.0\times {10}^{23}\times 1.6\times {10}^{-19}\times 9}$

$v_d=\frac{30720}{86.4\times {10}^4}$

$v_d=355.5\times {10}^{-4}cm/s$

$v_d=0.36mm/s$

Hence, the drift velocity is $0.36mm/s$