Question

A wire of length $4\text{m}$ and cross-sectional area $1{\text{mm}}^2$ is carrying a current of $2\text{A}$. If each cubic metre of the material contains ${10}^{2}9$ free electrons. The average time taken by an electron to cross the length of the wire is ____ $\times {10}^3\text{s}$. (Give integer value)

Answer 1

Drift velocity , $V_d=\frac{i}{nAe}$

From the data given in the question,

$V_d=\frac{2}{{10}^{29}\times 1\times {10}^{-6}\times 1.6\times {10}^{-19}}$

$V_d=\frac{2}{1.6}\times {10}^{-4}{\text{ms}}^{-1}$

Average time ,$t=\frac{l}{V_d}$

Substituting the given data we get,

$t=\frac{4}{\left(\frac{2}{1.6}\right)\times {10}^{-4}}$

$=2\times 1.6\times {10}^4\text{s}$

$=32\times {10}^3\text{s}$

Accepted answer : $32$