Question

A current of $10\text{A}$ exists in a wire of cross-sectional area $5{\text{mm}}^2$. The drift velocity of the electrons is $2\times {10}^{-3}\text{m/s}$. The number of free electrons in each cubic meter of the wire are :

• A. $1\times {10}^{23}$
• B. $2\times {10}^6$
• C. $2\times {10}^{25}$
• D. $625\times {10}^{25}$

Answer 1

The correct option is D $625\times {10}^{25}$

Current through a wire is given by,

$I=neA{v}_d$

$\Rightarrow n=\frac{I}{eA{v}_d}$

From the given data,

$n=\frac{10}{1.6\times {10}^{-19}\times 5\times {10}^{-6}\times 2\times {10}^{-3}}$

$\Rightarrow n=6.25\times {10}^{27}=625\times {10}^{25}$

Hence, option $\left(D\right)$ is the correct answer.