Question

A conductor wire having ${10}^{29}$ free electrons per unit volume carries a current of $20\text{A}$. If the cross-section of the wire is $1{\text{mm}}^2$, then the drift velocity of electrons will be -

Take $e=1.6\times {10}^{-19}\text{C}$

​​​​​​​$[$0.77 Mark$]$

• A. $1.25\times {10}^{-4}\text{m/s}$
• B. $1.25\times {10}^{-3}\text{m/s}$
• C. $1.25\times {10}^{-5}\text{m/s}$
• D. $1.25\times {10}^{-6}\text{m/s}$

Answer 1

The correct option is B $1.25\times {10}^{-3}\text{m/s}$

Given:

Current, $I=20\text{A}$
Free electron density, $n={10}^{29}$
Cross-sectional area of wire, $A=1{\text{mm}}^2={10}^{-6}{\text{m}}^2$
Magnitude of charge on an electron, $e=1.6\times {10}^{-19}\text{C}$

We know that, current,

$I=neA{v}_d$

$\Rightarrow v_d=\frac{I}{neA}=\frac{20}{{10}^{29}\times 1.6\times {10}^{-19}\times {10}^{-6}}$

$\Rightarrow v_d=1.25\times {10}^{-3}\text{m/s}$