Question

A conducting wire of cross-sectional area $1 \,cm ^{2}$ has $3 \times10^{23}$ charge carriers per $m ^{3}$. If wire carries a current of $24 \,mA$, then drift velocity of carriers is

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

Answer 1

Answer: (C)

Given, cross-sectional area,
$A=1\, cm ^{2}=10^{-4}\, m ^{2}$
Charge density, $n=3 \times 10^{23} \,m ^{-3}$
Current through wire, $I=24 \times 10^{-3} A$
We know that, for conductors,
$I=n A e v_{d} $
$\Rightarrow v_{d}=\frac{I}{n A e}=\frac{24 \times 10^{-3}}{3 \times 10^{23} \times 10^{-4} \times 1.6 \times 10^{-19}}$
$=\frac{8}{1.6} \times 10^{-3}=5 \times 10^{-3} \,m / s$