Question

Current is flowing with a current density $j = 480 Acm ^{-2}$ in a copper wire.
Assuming that each copper atom contributes one free electron and given that Avogadro number $= 6.0 \times 10^{23} \, atom \, mol^{-1}$
Density of copper $ = 9.0 \, g \, cm^{-2} \, $
Electronic charge $ = 1.6 \times 10^{-19} C $
Atomic weight of copper $= 64 \, g \, mol^{-1}$
The drift velocity of electrons is

• A. $1 mm \, s^{-1}$
• B. $2 mm \, s^{-1}$
• C. $0.5 mm \, s^{-1}$
• D. $0.36 mm \, s^{-1}$

Answer 1

Answer: (D)

Drift velocity is given by
$ \, \, \, \, \, \, \, \, v_d = \frac {I}{nqA}$
where I is current, n the number of electrons, A the area, q the charge.
Given $ \frac {I}{A} = \frac {480A}{cm^2} \, and \, q = 1.6 \times 10^{-19}C$
$ \, \, \, \, \, n = \frac {6 \times 10^{23}\times 9} {64}$
$\therefore \, \, \, \, \, v_d = 480 \times \frac {64}{6 \times 10^{23}\times 9 \times 1.6 \times 10^{-19}}$
$\Rightarrow \, \, \, \, v_d = \frac {480 \times 64}{6 \times 9 \times 1.6 \times 10000}cms^{-19}$
$\Rightarrow \, \, \, \, v_d = \frac {32}{900}cms^{-1}$
$\, \, \, \, \, = \frac {32 \times 10}{900}cms^{-1}$
$ \, \, \, \, \, \, \, \, = 0.36 mms^-1$
$\Rightarrow \, \, \, \, \, \, \, \, v_d = 0.36 \, mms^-1$