Question

A conducting wire of cross-sectional area $1c{m}^2$ has $3\times {10}^{23}$ number of charge carriers per unit volume. If wire carries a current of $24mA$, the drift speed of the carrier is ___________.

• A. $5\times {10}^{-6}m{s}^{-1}$
• B. $5\times {10}^{-3}m{s}^{-1}$
• C. $0.5m{s}^{-1}$
• D. $5\times {10}^{-2}m{s}^{-1}$

Answer 1

The correct option is B $5\times {10}^{-3}m{s}^{-1}$

Drift velocity of an electron is given by $v_d=\frac{i}{neA}$
Given:
No. of electrons per $m^3$, $n=3\times {10}^{23}$,
current $i=24mA$ and cross-sectional area, $A=1c{m}^2$ and electron charge $e=1.6\times {10}^{-19}C$.
On substituting the values, we get $v_d=\frac{24\times {10}^{-3}}{3\times {10}^{23}\times 1.6\times {10}^{-19}\times 1\times {10}^{-4}}$ = $5\times {10}^{-3}m{s}^{-1}$.