A current

Question:

A current of $10 \mathrm{~A}$ exists in a wire of crosssectional area of $5 \mathrm{~mm}^{2}$ with a drift velocity of $2 \times 10^{-3} \mathrm{~ms}^{-1}$. The number of free electrons in each cubic meter of the wire is

1. (1) $2 \times 10^{6}$

2. (2) $625 \times 10^{25}$

3. (3) $2 \times 10^{25}$

4. (4) $1 \times 10^{23}$

Correct Option: , 2

Solution:

(2)

$\mathrm{i}=10 \mathrm{~A}, \mathrm{~A}=5 \mathrm{~mm}^{2}=5 \times 10^{-6} \mathrm{~m}^{2}$

and $v_{\mathrm{d}}=2 \times 10^{-3} \mathrm{~m} / \mathrm{s}$

We know, $i=$ neAvd

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

$\Rightarrow \mathrm{n}=0.625 \times 10^{28}=625 \times 10^{25}$