Question

Find the current in a copper wire having cross-sectional area $2{\text{mm}}^2$. Given that Electric field $E=8.5\times {10}^{-3}\text{V}{\text{m}}^{-1}$ and resistivity $\rho =1.7\times {10}^{-8}\Omega \text{m}$

​​​​​​​$[$1 Mark$]$

• A. $1\text{A}$
• B. $3\text{A}$
• C. $2\text{A}$
• D. $4\text{A}$

Answer 1

The correct option is A $1\text{A}$

Cross-sectional area, $A=2{\text{mm}}^2$
$A=2\times {10}^{-6}{\text{m}}^2$
Electric field, $E=8.5\times {10}^{-3}\text{V}{\text{m}}^{-1}$
Resistivity, $S=1.7\times {10}^{-8}\Omega \text{m}$
Now, resistance $R=\frac{\rho l}{A}$
let $l$ be the length of wire
also potential difference, $V=El$
Using ohm's law
$V=IR$
$El=I\frac{\rho l}{A}$
$\Rightarrow I=\frac{EA}{\rho }=\frac{8.5\times {10}^{-3}\times 2\times {10}^{-6}}{1.7\times {10}^{-8}}$
$\Rightarrow I=1\text{A}$
$\therefore$ $\left(a\right)$ is the correct option