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 $1.5A$ ? (given, density of copper $=9\times 10^{3}kg{m}^{-3}$; atomic mass of copper $=63.5$; Avogadro's number $=6.023\times 10^{23}$ per gram atom)

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

Answer 1

Answer: (B)

Here, density of copper $(\rho )=9\times 10^{3}kg{m}^{-3}$,
Avogadro's number $(N)=6.023\times 10^{23}$.
Atomic mass of copper $(m)=63.5g=63.5\times 10^{-3}kg$
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.,
$v_d=\frac{i}{nAe}=\frac{1.5\times 63.5\times 10^{-3}}{6.023\times 10^{23}\times 9\times 10^3\times 10^{-7}\times 1.6\times 10^{-19}}$
$=1.1\times 10^{-3}m{s}^{-1}$