Question

What is the drift velocity of electons, if the current flowing through a copper wire of $1\,mm$ diameter is $1.1\, A$ ? Assume that each atom of copper contributes on electron
(Given, density of $Cu= 9 g \, cm^{-3}$ and atomic weight of $Cu = 63$)

• A. $0.3\, mm\, s^{-1}$
• B. $0.5\, mm\, s^{-1}$
• C. $0.1\, mm\, s^{-1}$
• D. $0.2\, mm\, s^{-1}$

Answer 1

Answer: (C)

$i=n e A v_{d}$
$n=\frac{\text { Avogadros number }}{\text { Volume of 63 gof copper }}$
$\frac{6.02 \times 10^{23}}{\frac{63 \times 10^{-3}}{9 \times 10^{3}}}=\frac{6.02 \times 10^{23}}{7} cm ^{3}$
$n=\frac{6.02 \times 10^{29}}{7} m ^{3}$
$i=n e A v_{d}$ or $v_{d}=\frac{i}{n e A}$
$=\frac{1.1 \times 7}{6.02 \times 10^{29} \times 1.6 \times 10^{-19} \times \pi \times\left(0.5 \times 10^{-3}\right)^{2}}$
$0.1 \times 10^{-3} ms ^{-1}$
$=0.1\, mm\, s ^{-1}$