Question

A current of $10A$ exists in a wire of cross-sectional area of $5m{m}^2$ with a drift velocity of $2\times {10}^{-3}m{s}^{-1}$. The number of free electrons in each cubic meter of the wire is ________

• 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

$625\times {10}^{25}$

Step 1: Given data:

Current, $I=10A$
Area of cross section, $A=5m{m}^2$

$=5\times {10}^{-6}{m}^2$

Drift Velocity, $V_d=2\times {10}^{-3}m{s}^{-1}$

Step 2: Formula used:

$I=neA{V}_d$

Where, $I=$ Current

$n=$ Number of free electrons

$e=$ Electronic charge

$=1.6\times {10}^{-19}coloumb$

$A=$ Area of cross-section

$V_d=$ Drift velocity

Step 3: Calculating the Number of free electron:

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

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

$=\frac{10}{16\times {10}^{-28}}$

$=0.625\times {10}^{-28}$

$=625\times {10}^{25}$

Hence, option D is the correct answer.