A current of 5 A passes through a copper conductor

Question:

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

1. (1) $1.8 \mathrm{~m}^{2} / \mathrm{V} \mathrm{s}$

2. (2) $1.5 \mathrm{~m}^{2} / \mathrm{V}_{\mathrm{S}}$

3. (3) $1.3 \mathrm{~m}^{2} / \mathrm{Vs}$

4. (4) $1.0 \mathrm{~m}^{2} / \mathrm{Vs}$

Correct Option: , 4

Solution:

(4) Charge mobility

$(\mu)=\frac{V_{d}}{E}\left[\right.$ Where $V_{d}=$ drift velocity $]$

and resistivity $(\rho)=\frac{E}{j}=\frac{E A}{I} \Rightarrow E=\frac{I(\rho)}{A}$

$\Rightarrow \mu=\frac{V_{\mathrm{d}}}{E}=\frac{V_{\mathrm{d}} \mathrm{A}}{\mathrm{I}_{\rho}}$

$=\frac{1.1 \times 10^{-3} \times \pi \times\left(5 \times 10^{-3}\right)^{2}}{5 \times 1.7 \times 10^{-8}}$

$\mu=1.0 \frac{\mathrm{m}^{2}}{\mathrm{~V}_{\mathrm{s}}}$