Question

A conducting wire of cross-sectional area 1 $c{{m}^{2}}$ has $3\times {{10}^{23}}$ charge carriers per $metr{{e}^{3}}$ . If wire carries a current $24 \,mA$, then rift velocity of carriers is

• A. $5\times {{10}^{-2}}m/s$
• B. $0.5\text{ }m/s$
• C. $5\times {{10}^{-3}}\text{ }m/s$
• D. $5\times {{10}^{-6}}\text{ }m/s$

Answer 1

Answer: (C)

$5\times {{10}^{-3}}\text{ }m/s$

Answer 2

The current $i$ crossing area of cross-section $A$ can be expressed in terms of drift velocity $v_{d}$ and the moving charges as $i=n e v_{d} A$ where, $n$ is number of charge carriers per unit volume and $e$ the charge on the carrier. $\therefore v_{d} =\frac{i}{n e A}=\frac{24 \times 10^{-3}}{\left(3 \times 10^{23}\right)\left(1.6 \times 10^{-19}\right)\left(10^{-4}\right)}$ $=5 \times 10^{-3} \,m / s$