Question

A current of $5\text{A}$ passes through a copper conductor (resistivity = $1.7\times {10}^{-8}\Omega \text{m})$ of radius of cross-section $5\text{mm}$. Find the mobility of the charges, if their drift velocity is $1.1\times {10}^{-3}\text{m/s}.$

• A. $1.0{\text{m}}^2/\text{Vs}$
• B. $1.5{\text{m}}^2/\text{Vs}$
• C. $1.3{\text{m}}^2/\text{Vs}$
• D. $1.8{\text{m}}^2/\text{Vs}$

Answer 1

The correct option is A $1.0{\text{m}}^2/\text{Vs}$

Given:
Current $=5\text{A}$
Resistivity of copper = $1.7\times {10}^{-8}\Omega \text{m}$
Radius of cross-section $=5\text{mm}$
Drift velocity is $=1.1\times {10}^{-3}\text{m/s}.$

We know that, Charge mobility
$\left(\mu \right)=\frac{V_d}{E}\text{[Where}{V}_d\text{=drift velocity]}$

Resistvity of conductor
$\left(\rho \right)=\frac{E}{j}=\frac{EA}{I}$ $(\because j=I/A)$

$\Rightarrow E=\frac{I\left(\rho \right)}{A}$

$\therefore \mu =\frac{V_d}{E}=\frac{V_{d}A}{I\left(\rho \right)}=\frac{1.1\times {10}^{-3}\times \pi \times (5\times {10}^{-3}{)}^2}{5\times 1.7\times {10}^{-8}}$

$\Rightarrow \mu =1.0\frac{{\text{m}}^2}{\text{V}\text{s}}$

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