Question

Assume that each atom of copper contributes one free electron. What is the average drift velocity of conduction electrons in a copper wire of cross-sectional area $10^{-7} m ^{2}$, carrying a current of $1.5 A$ ? (given, density of copper $=9 \times 10^{3} kgm ^{-3}$; atomic mass of copper $=63.5$; Avogadro's number $=6.023 \times 10^{23}$ per gram atom)

• A. $1.1 \times 10^{-2} ms ^{-1}$
• B. $1.1 \times 10^{-3} ms ^{-1}$
• C. $2.2 \times 10^{-2} ms ^{-1}$
• D. $2.2 \times 10^{-3} ms ^{-1}$

Answer 1

Answer: (B)

Here, density of copper $(\rho)=9 \times 10^{3} kgm ^{-3}$,
Avogadro's number $(N)=6.023 \times 10^{23}$.
Atomic mass of copper $(m)=63.5 g =63.5 \times 10^{-3} kg$
Number of free electrons per unit volume,
$n=\frac{N}{m} \rho=\frac{6.023 \times 10^{23}}{63.5 \times 10^{-3}} \times 9 \times 10^{3}$
Drift velocity i.e.,
$v_{d} =\frac{i}{n A e}=\frac{1.5 \times 63.5 \times 10^{-3}}{6.023 \times 10^{23} \times 9 \times 10^{3} \times 10^{-7} \times 1.6 \times 10^{-19}}$
$=1.1 \times 10^{-3} ms ^{-1}$