A current of $10\, amp$ is passing through a metallic wire of cross sectional area $4 \times 10^{-6}\, m ^{2}$. If the density of the aluminum conductor is $2.7\, gm / cc$ considering aluminum gives $1$ electrons per atom for conduction find the drift speed of the electrons is ......... $\times 10^{-4} \,m / s$ if molecular weight of aluminum is $27 \,gm$.
AIIMS 2019, Diffcult
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The expression to calculate the drift speed is given by,
$i = neAv _{ d }$
Calculate the value of $n$ as follows.
$n =\frac{ N _{ A }}{ V } \times \frac{ M }{ m _{ W }}$
$=\frac{ N _{ A } \rho}{ m _{ w }}$
$=\frac{6 \times 10^{23} \times 2.7 \times 10^{3}}{27 \times 10^{-3}}$
$=6 \times 10^{28}$
Substitute the values in the above expression.
$i = neAV _{ d }$
$v _{ d }=\frac{ i }{ neA }$
$=\frac{10 \times 10^{19}}{6 \times 10^{28} \times 4 \times 10^{-6} \times 1.6}$
$=2.6 \times 10^{-4} m / s$
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